Sample records for lagrangian eulerian code

  1. Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary Lagrangian-Eulerian Code

    NASA Astrophysics Data System (ADS)

    Cornille, Brian; White, Dan

    2017-10-01

    We will present methods formulated for the Eulerian advection stage of an arbitrary Lagrangian-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a Lagrangian formulation of the system. When this Lagrangian motion produces substantial distortion of the mesh, it can be difficult or impossible to progress the simulation forward. This is overcome by relaxation of the mesh while the physical fields are frozen. The code has already successfully been extended to include evolution of magnetic field diffusion during the Lagrangian motion stage. This magnetic field is discretized using an H(div) compatible finite element basis. The advantage of this basis is that the divergence-free constraint of magnetic fields is maintained exactly during the Lagrangian motion evolution. Our goal is to preserve this property during Eulerian advection as well. We will demonstrate this property and the importance of MHD effects in several numerical experiments. In pulsed-power experiments magnetic fields may be imposed or spontaneously generated. When these magnetic fields are present, the evolution of the experiment may differ from a comparable configuration without magnetic fields. Prepared by LLNL under Contract DE-AC52-07NA27344. Supported by DOE CSGF under Grant Number DE-FG02-97ER25308.

  2. ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Noble, Charles R.; Anderson, Andrew T.; Barton, Nathan R.

    ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.

  3. Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash

    NASA Technical Reports Server (NTRS)

    Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.

    2012-01-01

    In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.

  4. Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in FLASH

    NASA Astrophysics Data System (ADS)

    Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.

    2012-08-01

    In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.

  5. An Eulerian/Lagrangian coupling procedure for three-dimensional vortical flows

    NASA Technical Reports Server (NTRS)

    Felici, Helene M.; Drela, Mark

    1993-01-01

    A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of 3D vortical flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method, added to the Eulerian time-marching procedure, provides a correction of the Eulerian solution. In turn, the Eulerian solution is used to integrate the Lagrangian state-vector along the particles trajectories. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers describe accurately the convection properties and enhance the vorticity and entropy capturing capabilities of the Eulerian solver. The Eulerian/Lagrangian coupling strategies are discussed and the combined scheme is tested on a constant stagnation pressure flow in a 90 deg bend and on a swirling pipe flow. As the numerical diffusion is reduced when using the Lagrangian correction, a vorticity gradient augmentation is identified as a basic problem of this inviscid calculation.

  6. Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data

    DTIC Science & Technology

    2015-09-30

    Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation

  7. Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence

    NASA Technical Reports Server (NTRS)

    Squires, Kyle D.; Eaton, John K.

    1991-01-01

    Direct numerical simulation is used to study dispersion in decaying isotropic turbulence and homogeneous shear flow. Both Lagrangian and Eulerian data are presented allowing direct comparison, but at fairly low Reynolds number. The quantities presented include properties of the dispersion tensor, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The Lagrangian time microscale is found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame.

  8. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

    NASA Technical Reports Server (NTRS)

    Felici, Helene Marie

    1992-01-01

    A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

  9. Adjoint of the global Eulerian-Lagrangian coupled atmospheric transport model (A-GELCA v1.0): development and validation

    NASA Astrophysics Data System (ADS)

    Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander

    2016-02-01

    We present the development of the Adjoint of the Global Eulerian-Lagrangian Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an Eulerian three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the Lagrangian Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the Eulerian model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The Lagrangian component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed Eulerian adjoint was coupled with the Lagrangian component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the Eulerian model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an Eulerian discrete adjoint formulation with the flexibility, accuracy, and high resolution of a Lagrangian backward trajectory formulation. A-GELCA will be incorporated

  10. Eulerian and Lagrangian Plasma Jet Modeling for the Plasma Liner Experiment

    NASA Astrophysics Data System (ADS)

    Hatcher, Richard; Cassibry, Jason; Stanic, Milos; Loverich, John; Hakim, Ammar

    2011-10-01

    The Plasma Liner Experiment (PLX) aims to demonstrate the feasibility of using spherically-convergent plasma jets to from an imploding plasma liner. Our group has modified two hydrodynamic simulation codes to include radiative loss, tabular equations of state (EOS), and thermal transport. Nautilus, created by TechX Corporation, is a finite-difference Eulerian code which solves the MHD equations formulated as systems of hyperbolic conservation laws. The other is SPHC, a smoothed particle hydrodynamics code produced by Stellingwerf Consulting. Use of the Lagrangian fluid particle approach of SPH is motivated by the ability to accurately track jet interfaces, the plasma vacuum boundary, and mixing of various layers, but Eulerian codes have been in development for much longer and have better shock capturing. We validate these codes against experimental measurements of jet propagation, expansion, and merging of two jets. Precursor jets are observed to form at the jet interface. Conditions that govern evolution of two and more merging jets are explored.

  11. Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Zhou, Ye

    1998-01-01

    Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.

  12. Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

    NASA Technical Reports Server (NTRS)

    Felici, Helene M.; Drela, Mark

    1993-01-01

    A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

  13. Assimilating Eulerian and Lagrangian data in traffic-flow models

    NASA Astrophysics Data System (ADS)

    Xia, Chao; Cochrane, Courtney; DeGuire, Joseph; Fan, Gaoyang; Holmes, Emma; McGuirl, Melissa; Murphy, Patrick; Palmer, Jenna; Carter, Paul; Slivinski, Laura; Sandstede, Björn

    2017-05-01

    Data assimilation of traffic flow remains a challenging problem. One difficulty is that data come from different sources ranging from stationary sensors and camera data to GPS and cell phone data from moving cars. Sensors and cameras give information about traffic density, while GPS data provide information about the positions and velocities of individual cars. Previous methods for assimilating Lagrangian data collected from individual cars relied on specific properties of the underlying computational model or its reformulation in Lagrangian coordinates. These approaches make it hard to assimilate both Eulerian density and Lagrangian positional data simultaneously. In this paper, we propose an alternative approach that allows us to assimilate both Eulerian and Lagrangian data. We show that the proposed algorithm is accurate and works well in different traffic scenarios and regardless of whether ensemble Kalman or particle filters are used. We also show that the algorithm is capable of estimating parameters and assimilating real traffic observations and synthetic observations obtained from microscopic models.

  14. A Combined Eulerian-Lagrangian Data Representation for Large-Scale Applications.

    PubMed

    Sauer, Franz; Xie, Jinrong; Ma, Kwan-Liu

    2017-10-01

    The Eulerian and Lagrangian reference frames each provide a unique perspective when studying and visualizing results from scientific systems. As a result, many large-scale simulations produce data in both formats, and analysis tasks that simultaneously utilize information from both representations are becoming increasingly popular. However, due to their fundamentally different nature, drawing correlations between these data formats is a computationally difficult task, especially in a large-scale setting. In this work, we present a new data representation which combines both reference frames into a joint Eulerian-Lagrangian format. By reorganizing Lagrangian information according to the Eulerian simulation grid into a "unit cell" based approach, we can provide an efficient out-of-core means of sampling, querying, and operating with both representations simultaneously. We also extend this design to generate multi-resolution subsets of the full data to suit the viewer's needs and provide a fast flow-aware trajectory construction scheme. We demonstrate the effectiveness of our method using three large-scale real world scientific datasets and provide insight into the types of performance gains that can be achieved.

  15. Examination of Eulerian and Lagrangian Coordinate Systems.

    ERIC Educational Resources Information Center

    Remillard, Wilfred J.

    1978-01-01

    Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. Gives examples which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems. (Author/GA)

  16. Eulerian-Lagrangian Simulations of Transonic Flutter Instabilities

    NASA Technical Reports Server (NTRS)

    Bendiksen, Oddvar O.

    1994-01-01

    This paper presents an overview of recent applications of Eulerian-Lagrangian computational schemes in simulating transonic flutter instabilities. This approach, the fluid-structure system is treated as a single continuum dynamics problem, by switching from an Eulerian to a Lagrangian formulation at the fluid-structure boundary. This computational approach effectively eliminates the phase integration errors associated with previous methods, where the fluid and structure are integrated sequentially using different schemes. The formulation is based on Hamilton's Principle in mixed coordinates, and both finite volume and finite element discretization schemes are considered. Results from numerical simulations of transonic flutter instabilities are presented for isolated wings, thin panels, and turbomachinery blades. The results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with significantly less error than existing methods. Localized flutter modes and panel flutter modes involving traveling waves can also be simulated effectively with no a priori knowledge of the type of instability involved.

  17. Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and Eulerian accelerations and passive scalar dynamics.

    PubMed

    Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie

    2016-01-01

    The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the Eulerian acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and Eulerian accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.

  18. Modeling and Numerical Challenges in Eulerian-Lagrangian Computations of Shock-driven Multiphase Flows

    NASA Astrophysics Data System (ADS)

    Diggs, Angela; Balachandar, Sivaramakrishnan

    2015-06-01

    The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Eulerian Projection (EP) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Lagrangian Projection (LP) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, EP methods are used in multiphase flow, but sub-grid resolution can be obtained through use of LP methods. By evaluating the total error and its components we compare the performance of EP and LP methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities. Most importantly, we will show that such careful attention to numerical methodologies is needed in order to capture complex shock interaction with a bed of particles. Supported by U.S. Department of Defense SMART Program and the U.S. Department of Energy PSAAP-II program under Contract No. DE-NA0002378.

  19. Eulerian and Lagrangian approaches to multidimensional condensation and collection

    NASA Astrophysics Data System (ADS)

    Li, Xiang-Yu; Brandenburg, A.; Haugen, N. E. L.; Svensson, G.

    2017-06-01

    Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence.Plain Language SummaryThe bottleneck problem of cloud droplet growth is one of the most challenging problems in cloud physics. Cloud droplet growth is neither dominated by condensation nor gravitational collision in the size range of 15 μm ˜ 40 μm [1]. Turbulence-generated collection has been thought to be the mechanism to bridge the size gap, i.e., the bottleneck problem. This study compares the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> schemes in detail to tackle with the turbulence-generated collection.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70013978','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70013978"><span><span class="hlt">Eulerian-Lagrangian</span> solution of the convection-dispersion equation in natural coordinates</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cheng, Ralph T.; Casulli, Vincenzo; Milford, S. Nevil</p> <p>1984-01-01</p> <p>The vast majority of numerical investigations of transport phenomena use an <span class="hlt">Eulerian</span> formulation for the convenience that the computational grids are fixed in space. An <span class="hlt">Eulerian-Lagrangian</span> method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the <span class="hlt">Lagrangian</span> concept in an <span class="hlt">Eulerian</span> computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order <span class="hlt">Lagrangian</span> polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li class="active"><span>1</span></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_1 --> <div id="page_2" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li class="active"><span>2</span></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="21"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDQ34007F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDQ34007F"><span>Uncertainty quantification in <span class="hlt">Eulerian-Lagrangian</span> models for particle-laden flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fountoulakis, Vasileios; Jacobs, Gustaaf; Udaykumar, Hs</p> <p>2017-11-01</p> <p>A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based <span class="hlt">Eulerian-Lagrangian</span> model, which traces individual particles in their <span class="hlt">Lagrangian</span> frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear <span class="hlt">Eulerian-Lagrangian</span> systems. This research is supported by AFOSR under Grant FA9550-16-1-0008.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016OcMod..97...27F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016OcMod..97...27F"><span>A LES-based <span class="hlt">Eulerian-Lagrangian</span> approach to predict the dynamics of bubble plumes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.</p> <p>2016-01-01</p> <p>An approach for <span class="hlt">Eulerian-Lagrangian</span> large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main numerical novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> frameworks through the use of delta functions. The model's performance is thoroughly validated for a bubble plume in a cubic tank in initially quiescent water using experimental data obtained from high-resolution ADV and PIV measurements. The predicted time-averaged velocities and second-order statistics show good agreement with the measurements, including the reproduction of the anisotropic nature of the plume's turbulence. Further, the predicted <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> velocity fields, second-order turbulence statistics and interfacial gas-liquid forces are quantified and discussed as well as the visualization of the time-averaged primary and secondary flow structure in the tank.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1247151','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1247151"><span>Adaptive reconnection-based arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Bo, Wurigen; Shashkov, Mikhail</p> <p></p> <p>We present a new adaptive Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit <span class="hlt">Lagrangian</span> phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the <span class="hlt">Lagrangian</span> solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1247151-adaptive-reconnection-based-arbitrary-lagrangian-eulerian-method','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1247151-adaptive-reconnection-based-arbitrary-lagrangian-eulerian-method"><span>Adaptive reconnection-based arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Bo, Wurigen; Shashkov, Mikhail</p> <p>2015-07-21</p> <p>We present a new adaptive Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit <span class="hlt">Lagrangian</span> phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the <span class="hlt">Lagrangian</span> solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=Herrera&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=Herrera&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>AN <span class="hlt">EULERIAN-LAGRANGIAN</span> LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include <span class="hlt">Eulerian-Lagrangian</span> methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19940033879&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19940033879&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3DLagrangian"><span>The piecewise-linear predictor-corrector <span class="hlt">code</span> - A <span class="hlt">Lagrangian</span>-remap method for astrophysical flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lufkin, Eric A.; Hawley, John F.</p> <p>1993-01-01</p> <p>We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing <span class="hlt">Eulerian</span> schemes in its use of operator-splitting and artificial viscosity, except that we solve the <span class="hlt">Lagrangian</span> equations of motion with a predictor-corrector and then remap onto a fixed <span class="hlt">Eulerian</span> grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the <span class="hlt">code</span> has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector <span class="hlt">Lagrangian</span>-remap <span class="hlt">code</span> has great flexibility for application to a variety of astrophysical problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29051631','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29051631"><span>Acoustic streaming: an arbitrary <span class="hlt">Lagrangian-Eulerian</span> perspective.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco</p> <p>2017-08-25</p> <p>We analyse acoustic streaming flows using an arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the <span class="hlt">Lagrangian</span> flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the <span class="hlt">Lagrangian</span> velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017WRR....53.9040S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017WRR....53.9040S"><span>A <span class="hlt">Lagrangian</span> Transport <span class="hlt">Eulerian</span> Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sund, Nicole; Porta, Giovanni; Bolster, Diogo; Parashar, Rishi</p> <p>2017-11-01</p> <p>Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a <span class="hlt">Lagrangian</span> framework, while in others an <span class="hlt">Eulerian</span> might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a <span class="hlt">Lagrangian</span> closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a <span class="hlt">LAgrangian</span> Transport <span class="hlt">Eulerian</span> Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the <span class="hlt">Lagrangian</span> Spatial Markov model and maps concentrations to an <span class="hlt">Eulerian</span> grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the <span class="hlt">Eulerian</span> reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016IJMPS..4260159F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016IJMPS..4260159F"><span>a Marker-Based <span class="hlt">Eulerian-Lagrangian</span> Method for Multiphase Flow with Supersonic Combustion Applications</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fan, Xiaofeng; Wang, Jiangfeng</p> <p>2016-06-01</p> <p>The atomization of liquid fuel is a kind of intricate dynamic process from continuous phase to discrete phase. Procedures of fuel spray in supersonic flow are modeled with an <span class="hlt">Eulerian-Lagrangian</span> computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated numerical simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (<span class="hlt">Eulerian</span>) Cartesian grid is used to resolve the flow field, and multi-component Navier-Stokes equations are adopted in present work, with accounting for the mass exchange and heat transfer occupied by vaporization process. The marker-based moving (<span class="hlt">Lagrangian</span>) grid is utilized to depict the behavior of atomized liquid sprays injected into a gaseous environment, and discrete droplet model 13 is adopted. To verify the current approach, the proposed method is applied to simulate processes of liquid atomization in supersonic cross flow. Three classic breakup models, TAB model, wave model and K-H/R-T hybrid model, are discussed. The numerical results are compared with multiple perspectives quantitatively, including spray penetration height and droplet size distribution. In addition, the complex flow field structures induced by the presence of liquid spray are illustrated and discussed. It is validated that the maker-based <span class="hlt">Eulerian-Lagrangian</span> method is effective and reliable.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040031690','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040031690"><span>A <span class="hlt">Eulerian-Lagrangian</span> Model to Simulate Two-Phase/Particulate Flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Apte, S. V.; Mahesh, K.; Lundgren, T.</p> <p>2003-01-01</p> <p>Figure 1 shows a snapshot of liquid fuel spray coming out of an injector nozzle in a realistic gas-turbine combustor. Here the spray atomization was simulated using a stochastic secondary breakup model (Apte et al. 2003a) with point-particle approximation for the droplets. Very close to the injector, it is observed that the spray density is large and the droplets cannot be treated as point-particles. The volume displaced by the liquid in this region is significant and can alter the gas-phase ow and spray evolution. In order to address this issue, one can compute the dense spray regime by an <span class="hlt">Eulerian-Lagrangian</span> technique using advanced interface tracking/level-set methods (Sussman et al. 1994; Tryggvason et al. 2001; Herrmann 2003). This, however, is computationally intensive and may not be viable in realistic complex configurations. We therefore plan to develop a methodology based on <span class="hlt">Eulerian-Lagrangian</span> technique which will allow us to capture the essential features of primary atomization using models to capture interactions between the fluid and droplets and which can be directly applied to the standard atomization models used in practice. The numerical scheme for unstructured grids developed by Mahesh et al. (2003) for incompressible flows is modified to take into account the droplet volume fraction. The numerical framework is directly applicable to realistic combustor geometries. Our main objectives in this work are: Develop a numerical formulation based on <span class="hlt">Eulerian-Lagrangian</span> techniques with models for interaction terms between the fluid and particles to capture the Kelvin- Helmholtz type instabilities observed during primary atomization. Validate this technique for various two-phase and particulate flows. Assess its applicability to capture primary atomization of liquid jets in conjunction with secondary atomization models.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFD.L2012Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFD.L2012Z"><span>Scalable Methods for <span class="hlt">Eulerian-Lagrangian</span> Simulation Applied to Compressible Multiphase Flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zwick, David; Hackl, Jason; Balachandar, S.</p> <p>2017-11-01</p> <p>Multiphase flows can be found in countless areas of physics and engineering. Many of these flows can be classified as dispersed two-phase flows, meaning that there are solid particles dispersed in a continuous fluid phase. A common technique for simulating such flow is the <span class="hlt">Eulerian-Lagrangian</span> method. While useful, this method can suffer from scaling issues on larger problem sizes that are typical of many realistic geometries. Here we present scalable techniques for <span class="hlt">Eulerian-Lagrangian</span> simulations and apply it to the simulation of a particle bed subjected to expansion waves in a shock tube. The results show that the methods presented here are viable for simulation of larger problems on modern supercomputers. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138. This work was supported in part by the U.S. Department of Energy under Contract No. DE-NA0002378.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AIPC.1896n0006K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AIPC.1896n0006K"><span>Comparison of updated <span class="hlt">Lagrangian</span> FEM with arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> method for 3D thermo-mechanical extrusion of a tube profile</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kronsteiner, J.; Horwatitsch, D.; Zeman, K.</p> <p>2017-10-01</p> <p>Thermo-mechanical numerical modelling and simulation of extrusion processes faces several serious challenges. Large plastic deformations in combination with a strong coupling of thermal with mechanical effects leads to a high numerical demand for the solution as well as for the handling of mesh distortions. The two numerical methods presented in this paper also reflect two different ways to deal with mesh distortions. <span class="hlt">Lagrangian</span> Finite Element Methods (FEM) tackle distorted elements by building a new mesh (called re-meshing) whereas Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) methods use an "advection" step to remap the solution from the distorted to the undistorted mesh. Another difference between conventional <span class="hlt">Lagrangian</span> and ALE methods is the separate treatment of material and mesh in ALE, allowing the definition of individual velocity fields. In theory, an ALE formulation contains the <span class="hlt">Eulerian</span> formulation as a subset to the <span class="hlt">Lagrangian</span> description of the material. The investigations presented in this paper were dealing with the direct extrusion of a tube profile using EN-AW 6082 aluminum alloy and a comparison of experimental with <span class="hlt">Lagrangian</span> and ALE results. The numerical simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and numerical results could be found, however, major differences between <span class="hlt">Lagrangian</span> and ALE methods concerning thermo-mechanical coupling lead to deviations in the thermal results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CTM....16..435J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CTM....16..435J"><span>Comparisons of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jaishree, J.; Haworth, D. C.</p> <p>2012-06-01</p> <p>Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, <span class="hlt">Lagrangian</span> particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, <span class="hlt">Lagrangian</span> particle PDF methods are computationally intensive and are not readily integrated into conventional <span class="hlt">Eulerian</span> computational fluid dynamics (CFD) <span class="hlt">codes</span>. <span class="hlt">Eulerian</span> field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid <span class="hlt">Lagrangian</span> particle/<span class="hlt">Eulerian</span> mesh (LPEM) method, a stochastic <span class="hlt">Eulerian</span> field (SEF) method and a deterministic <span class="hlt">Eulerian</span> field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane-air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 <span class="hlt">Eulerian</span> fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..1817332C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..1817332C"><span>Coupled <span class="hlt">Eulerian-Lagrangian</span> transport of large debris by tsunamis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos</p> <p>2016-04-01</p> <p>Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> paradigms will be used to assess the relevance of <span class="hlt">Lagrangian-Eulerian</span> coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed <span class="hlt">Eulerian-Lagrangian</span> formulation and the resolution of the mesh used in the <span class="hlt">Eulerian</span> solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930062646&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930062646&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian"><span>Extension of rezoned <span class="hlt">Eulerian-Lagrangian</span> method to astrophysical plasma applications</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Song, M. T.; Wu, S. T.; Dryer, Murray</p> <p>1993-01-01</p> <p>The rezoned <span class="hlt">Eulerian-Lagrangian</span> procedure developed by Brackbill and Pracht (1973), which is limited to simple configurations of the magnetic fields, is modified in order to make it applicable to astrophysical plasma. For this purpose, two specific methods are introduced, which make it possible to determine the initial field topology for which no analytical expressions are available. Numerical examples illustrating these methods are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900048341&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900048341&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian"><span>Modeling of confined turbulent fluid-particle flows using <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> schemes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Adeniji-Fashola, A.; Chen, C. P.</p> <p>1990-01-01</p> <p>Two important aspects of fluid-particulate interaction in dilute gas-particle turbulent flows (the turbulent particle dispersion and the turbulence modulation effects) are addressed, using the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> modeling approaches to describe the particulate phase. Gradient-diffusion approximations are employed in the <span class="hlt">Eulerian</span> formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangina formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. Models proposed for both schemes are used to predict turbulent fully-developed gas-solid vertical pipe flow with reasonable accuracy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA542504','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA542504"><span>Hybrid <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Simulation of Steep and Breaking Waves and Surface Fluxes in High Winds</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2010-09-30</p> <p>simulating violent free - surface flows , and show the importance of wave breaking in energy transport...using <span class="hlt">Eulerian</span> simulation . 3 IMPACT/APPLICATION This project aims at developing an advanced simulation tool for multi-fluids free - surface flows that...several <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> methods for free - surface turbulence and wave simulation . The WIND–SNOW is used to simulate 1 Report</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890001792','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890001792"><span>Modeling of combustion processes of stick propellants via combined <span class="hlt">Eulerian-Lagrangian</span> approach</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kuo, K. K.; Hsieh, K. C.; Athavale, M. M.</p> <p>1988-01-01</p> <p>This research is motivated by the improved ballistic performance of large-caliber guns using stick propellant charges. A comprehensive theoretical model for predicting the flame spreading, combustion, and grain deformation phenomena of long, unslotted stick propellants is presented. The formulation is based upon a combined <span class="hlt">Eulerian-Lagrangian</span> approach to simulate special characteristics of the two phase combustion process in a cartridge loaded with a bundle of sticks. The model considers five separate regions consisting of the internal perforation, the solid phase, the external interstitial gas phase, and two lumped parameter regions at either end of the stick bundle. For the external gas phase region, a set of transient one-dimensional fluid-dynamic equations using the <span class="hlt">Eulerian</span> approach is obtained; governing equations for the stick propellants are formulated using the <span class="hlt">Lagrangian</span> approach. The motion of a representative stick is derived by considering the forces acting on the entire propellant stick. The instantaneous temperature and stress fields in the stick propellant are modeled by considering the transient axisymmetric heat conduction equation and dynamic structural analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920064328&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920064328&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian"><span>An <span class="hlt">Eulerian/Lagrangian</span> method for computing blade/vortex impingement</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Steinhoff, John; Senge, Heinrich; Yonghu, Wenren</p> <p>1991-01-01</p> <p>A combined <span class="hlt">Eulerian/Lagrangian</span> approach to calculating helicopter rotor flows with concentrated vortices is described. The method computes a general evolving vorticity distribution without any significant numerical diffusion. Concentrated vortices can be accurately propagated over long distances on relatively coarse grids with cores only several grid cells wide. The method is demonstrated for a blade/vortex impingement case in 2D and 3D where a vortex is cut by a rotor blade, and the results are compared to previous 2D calculations involving a fifth-order Navier-Stokes solver on a finer grid.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70016242','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70016242"><span>Stability analysis of <span class="hlt">Eulerian-Lagrangian</span> methods for the one-dimensional shallow-water equations</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Casulli, V.; Cheng, R.T.</p> <p>1990-01-01</p> <p>In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined <span class="hlt">Eulerian-Lagrangian</span> approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit <span class="hlt">Eulerian-Lagrangian</span> method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the <span class="hlt">Eulerian-Lagrangian</span> approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li class="active"><span>2</span></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_2 --> <div id="page_3" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li class="active"><span>3</span></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="41"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29060488','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29060488"><span>Serial fusion of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> approaches for accurate heart-rate estimation using face videos.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Gupta, Puneet; Bhowmick, Brojeshwar; Pal, Arpan</p> <p>2017-07-01</p> <p>Camera-equipped devices are ubiquitous and proliferating in the day-to-day life. Accurate heart rate (HR) estimation from the face videos acquired from the low cost cameras in a non-contact manner, can be used in many real-world scenarios and hence, require rigorous exploration. This paper has presented an accurate and near real-time HR estimation system using these face videos. It is based on the phenomenon that the color and motion variations in the face video are closely related to the heart beat. The variations also contain the noise due to facial expressions, respiration, eye blinking and environmental factors which are handled by the proposed system. Neither <span class="hlt">Eulerian</span> nor <span class="hlt">Lagrangian</span> temporal signals can provide accurate HR in all the cases. The cases where <span class="hlt">Eulerian</span> temporal signals perform spuriously are determined using a novel poorness measure and then both the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> temporal signals are employed for better HR estimation. Such a fusion is referred as serial fusion. Experimental results reveal that the error introduced in the proposed algorithm is 1.8±3.6 which is significantly lower than the existing well known systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70033100','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70033100"><span><span class="hlt">Eulerian-Lagrangian</span> numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cox, T.J.; Runkel, R.L.</p> <p>2008-01-01</p> <p>Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, <span class="hlt">Eulerian</span> numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking <span class="hlt">Lagrangian</span> control volumes across a fixed (<span class="hlt">Eulerian</span>) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative <span class="hlt">Eulerian</span> numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the <span class="hlt">Lagrangian</span> scheme performs better than the <span class="hlt">Eulerian</span> scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative <span class="hlt">Eulerian</span> scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative <span class="hlt">Eulerian</span> scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1419712','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1419712"><span><span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Parameterization of the Oceanic Mixed Layer using Large Eddy Simulation and MPAS-Ocean</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Van Roekel, Luke</p> <p></p> <p>We have conducted a suite of Large Eddy Simulation (LES) to form the basis of a multi-model comparison (left). The results have led to proposed model improvements. We have verified that <span class="hlt">Eulerian-Lagrangian</span> effective diffusivity estimates of mesoscale mixing are consistent with traditional particle statistics metrics (right). LES and <span class="hlt">Lagrangian</span> particles will be utilized to better represent the movement of water into and out of the mixed layer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014EGUGA..1613316G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..1613316G"><span><span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gotovac, Hrvoje; Srzic, Veljko</p> <p>2014-05-01</p> <p>Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different <span class="hlt">Eulerian</span>, <span class="hlt">Lagrangian</span> and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ACP....12.8979P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ACP....12.8979P"><span>Comparing <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> models for CO2 transport - a step towards Bayesian inverse modeling using WRF/STILT-VPRM</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pillai, D.; Gerbig, C.; Kretschmer, R.; Beck, V.; Karstens, U.; Neininger, B.; Heimann, M.</p> <p>2012-10-01</p> <p>We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the <span class="hlt">Eulerian</span>-based Weather Research Forecasting (WRF) model and the <span class="hlt">Lagrangian</span>-based Stochastic Time-Inverted <span class="hlt">Lagrangian</span> Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (<span class="hlt">Eulerian</span> vs. <span class="hlt">Lagrangian</span>) on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and <span class="hlt">Lagrangian</span> time-scale in STILT is needed to achieve a better match between the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19029589','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19029589"><span>Simulation of atmospheric dispersion of radionuclides using an <span class="hlt">Eulerian-Lagrangian</span> modelling system.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Basit, Abdul; Espinosa, Francisco; Avila, Ruben; Raza, S; Irfan, N</p> <p>2008-12-01</p> <p>In this paper we present an atmospheric dispersion scenario for a proposed nuclear power plant in Pakistan involving the hypothetical accidental release of radionuclides. For this, a concept involving a <span class="hlt">Lagrangian</span> stochastic particle model (LSPM) coupled with an <span class="hlt">Eulerian</span> regional atmospheric modelling system (RAMS) is used. The atmospheric turbulent dispersion of radionuclides (represented by non-buoyant particles/neutral traces) in the LSPM is modelled by applying non-homogeneous turbulence conditions. The mean wind velocities governed by the topography of the region and the surface fluxes of momentum and heat are calculated by the RAMS <span class="hlt">code</span>. A moving least squares (MLS) technique is introduced to calculate the concentration of radionuclides at ground level. The numerically calculated vertical profiles of wind velocity and temperature are compared with observed data. The results obtained demonstrate that in regions of complex terrain it is not sufficient to model the atmospheric dispersion of particles using a straight-line Gaussian plume model, and that by utilising a <span class="hlt">Lagrangian</span> stochastic particle model and regional atmospheric modelling system a much more realistic estimation of the dispersion in such a hypothetical scenario was ascertained. The particle dispersion results for a 12 h ground release show that a triangular area of about 400 km(2) situated in the north-west quadrant of release is under radiological threat. The particle distribution shows that the use of a Gaussian plume model (GPM) in such situations will yield quite misleading results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/15013474','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/15013474"><span>Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Anderson, R W; Pember, R B; Elliott, N S</p> <p>2001-10-22</p> <p>A new method that combines staggered grid Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid <span class="hlt">Lagrangian</span> integration method. The novel components of the method are mainly driven by the need to reconcile traditionalmore » AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by <span class="hlt">Lagrangian</span> methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhPl...24d2702V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhPl...24d2702V"><span>Plasma transport in an <span class="hlt">Eulerian</span> AMR <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.; Molvig, K.; Simakov, A. N.; Haines, B. M.</p> <p>2017-04-01</p> <p>A plasma transport model has been implemented in an <span class="hlt">Eulerian</span> AMR radiation-hydrodynamics <span class="hlt">code</span>, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions to flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 μm and smaller for viscous effects to appear and 10 μm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more <span class="hlt">Lagrangian</span>-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an <span class="hlt">Eulerian</span> computation of complex and dynamically evolving mix regions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ACPD...12.1267P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ACPD...12.1267P"><span>Comparing <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> models for CO2 transport - a step towards Bayesian inverse modeling using WRF/STILT-VPRM</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pillai, D.; Gerbig, C.; Kretschmer, R.; Beck, V.; Karstens, U.; Neininger, B.; Heimann, M.</p> <p>2012-01-01</p> <p>We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the <span class="hlt">Eulerian</span>-based Weather Research Forecasting (WRF) model and the <span class="hlt">Lagrangian</span>-based Stochastic Time-Inverted <span class="hlt">Lagrangian</span> Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (<span class="hlt">Eulerian</span> vs. <span class="hlt">Lagrangian</span>) on models' spatial resolution is further investigated. A case study using airborne measurements during which both models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and <span class="hlt">Lagrangian</span> time-scale in STILT is needed to achieve a better match between the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data. Thus suggests that it is reasonable to use STILT as an adjoint model of WRF atmospheric transport.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015OcDyn..65..679R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015OcDyn..65..679R"><span>Comparison of HF radar measurements with <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> surface currents</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Röhrs, Johannes; Sperrevik, Ann Kristin; Christensen, Kai Håkon; Broström, Göran; Breivik, Øyvind</p> <p>2015-05-01</p> <p>High-frequency (HF) radar-derived ocean currents are compared with in situ measurements to conclude if the radar observations include effects of surface waves that are of second order in the wave amplitude. <span class="hlt">Eulerian</span> current measurements from a high-resolution acoustic Doppler current profiler and <span class="hlt">Lagrangian</span> measurements from surface drifters are used as references. Directional wave spectra are obtained from a combination of pressure sensor data and a wave model. Our analysis shows that the wave-induced Stokes drift is not included in the HF radar-derived currents, that is, HF radars measure the <span class="hlt">Eulerian</span> current. A disputed nonlinear correction to the phase velocity of surface gravity waves, which may affect HF radar signals, has a magnitude of about half the Stokes drift at the surface. In our case, this contribution by nonlinear dispersion would be smaller than the accuracy of the HF radar currents, hence no conclusion can be made. Finally, the analysis confirms that the HF radar data represent an exponentially weighted vertical average where the decay scale is proportional to the wavelength of the transmitted signal.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26456304','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26456304"><span>The Trapping Index: How to integrate the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> approach for the computation of the transport time scales of semi-enclosed basins.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cucco, Andrea; Umgiesser, Georg</p> <p>2015-09-15</p> <p>In this work, we investigated if the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> approaches for the computation of the Transport Time Scales (TTS) of semi-enclosed water bodies can be used univocally to define the spatial variability of basin flushing features. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> TTS were computed for both simplified test cases and a realistic domain: the Venice Lagoon. The results confirmed the two approaches cannot be adopted univocally and that the spatial variability of the water renewal capacity can be investigated only through the computation of both the TTS. A specific analysis, based on the computation of a so-called Trapping Index, was then suggested to integrate the information provided by the two different approaches. The obtained results proved the Trapping Index to be useful to avoid any misleading interpretation due to the evaluation of the basin renewal features just from an <span class="hlt">Eulerian</span> only or from a <span class="hlt">Lagrangian</span> only perspective. Copyright © 2015 Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950017213','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950017213"><span>A Generalized <span class="hlt">Eulerian-Lagrangian</span> Analysis, with Application to Liquid Flows with Vapor Bubbles</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dejong, Frederik J.; Meyyappan, Meyya</p> <p>1993-01-01</p> <p>Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined <span class="hlt">Eulerian-Lagrangian</span> technique, in which <span class="hlt">Eulerian</span> conservation equations are solved for the liquid phase, while <span class="hlt">Lagrangian</span> equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the <span class="hlt">Lagrangian</span> analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1361797-plasma-transport-eulerian-amr-code','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1361797-plasma-transport-eulerian-amr-code"><span>Plasma transport in an <span class="hlt">Eulerian</span> AMR <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.; ...</p> <p>2017-04-04</p> <p>A plasma transport model has been implemented in an <span class="hlt">Eulerian</span> AMR radiation-hydrodynamics <span class="hlt">code</span>, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions tomore » flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 μm and smaller for viscous effects to appear and 10 μm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more <span class="hlt">Lagrangian</span>-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an <span class="hlt">Eulerian</span> computation of complex and dynamically evolving mix regions.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.A31C2183S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A31C2183S"><span>Insights into the physico-chemical evolution of pyrogenic organic carbon emissions from biomass burning using coupled <span class="hlt">Lagrangian-Eulerian</span> simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Suciu, L. G.; Griffin, R. J.; Masiello, C. A.</p> <p>2017-12-01</p> <p>Wildfires and prescribed burning are important sources of particulate and gaseous pyrogenic organic carbon (PyOC) emissions to the atmosphere. These emissions impact atmospheric chemistry, air quality and climate, but the spatial and temporal variabilities of these impacts are poorly understood, primarily because small and fresh fire plumes are not well predicted by three-dimensional <span class="hlt">Eulerian</span> chemical transport models due to their coarser grid size. Generally, this results in underestimation of downwind deposition of PyOC, hydroxyl radical reactivity, secondary organic aerosol formation and ozone (O3) production. However, such models are very good for simulation of multiple atmospheric processes that could affect the lifetimes of PyOC emissions over large spatiotemporal scales. Finer resolution models, such as <span class="hlt">Lagrangian</span> reactive plumes models (or plume-in-grid), could be used to trace fresh emissions at the sub-grid level of the <span class="hlt">Eulerian</span> model. Moreover, <span class="hlt">Lagrangian</span> plume models need background chemistry predicted by the <span class="hlt">Eulerian</span> models to accurately simulate the interactions of the plume material with the background air during plume aging. Therefore, by coupling the two models, the physico-chemical evolution of the biomass burning plumes can be tracked from local to regional scales. In this study, we focus on the physico-chemical changes of PyOC emissions from sub-grid to grid levels using an existing chemical mechanism. We hypothesize that finer scale <span class="hlt">Lagrangian-Eulerian</span> simulations of several prescribed burns in the U.S. will allow more accurate downwind predictions (validated by airborne observations from smoke plumes) of PyOC emissions (i.e., submicron particulate matter, organic aerosols, refractory black carbon) as well as O3 and other trace gases. Simulation results could be used to optimize the implementation of additional PyOC speciation in the existing chemical mechanism.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/934850','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/934850"><span><span class="hlt">Lagrangian</span> continuum dynamics in ALEGRA.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Wong, Michael K. W.; Love, Edward</p> <p></p> <p>Alegra is an ALE (Arbitrary <span class="hlt">Lagrangian-Eulerian</span>) multi-material finite element <span class="hlt">code</span> that emphasizes large deformations and strong shock physics. The <span class="hlt">Lagrangian</span> continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013MS%26E...52a2003M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013MS%26E...52a2003M"><span>A cavitation model based on <span class="hlt">Eulerian</span> stochastic fields</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Magagnato, F.; Dumond, J.</p> <p>2013-12-01</p> <p>Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo <span class="hlt">codes</span> based on <span class="hlt">Lagrangian</span> "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on <span class="hlt">Eulerian</span> fields has been proposed which eliminates the necessity to mix <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1013698','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1013698"><span>Near-Surface Monsoonal Circulation of the Vietnam East Sea from <span class="hlt">Lagrangian</span> Drifters</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2015-09-30</p> <p>Sea from <span class="hlt">Lagrangian</span> Drifters Luca Centurioni Scripps Institution of Oceanography 9500 Gilman Drive Mail <span class="hlt">Code</span> 0213 La Jolla, California 92103...Contribute to the study of coastal and open ocean current systems in sparsely sampled regions such us the South China Sea (SCS), using a <span class="hlt">Lagrangian</span> ...We intend to make new <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> observations to measure the seasonal circulation 1) in the coastal waters of Vietnam and 2) in the SCS</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AtmEn.184..304D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AtmEn.184..304D"><span><span class="hlt">Eulerian-Lagrangian</span> CFD modelling of pesticide dust emissions from maize planters</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Devarrewaere, Wouter; Foqué, Dieter; Nicolai, Bart; Nuyttens, David; Verboven, Pieter</p> <p>2018-07-01</p> <p>An <span class="hlt">Eulerian-Lagrangian</span> 3D computational fluid dynamics (CFD) model of pesticide dust drift from precision vacuum planters in field conditions was developed. Tractor and planter models were positioned in an atmospheric computational domain, representing the field and its edges. Physicochemical properties of dust abraded from maize seeds (particle size, shape, porosity, density, a.i. content), dust emission rates and exhaust air velocity values at the planter fan outlets were measured experimentally and implemented in the model. The wind profile, the airflow pattern around the machines and the dust dispersion were computed. Various maize sowing scenarios with different wind conditions, dust properties, planter designs and vacuum pressures were simulated. Dust particle trajectories were calculated by means of <span class="hlt">Lagrangian</span> particle tracking, considering nonspherical particle drag, gravity and turbulent dispersion. The dust dispersion model was previously validated with wind tunnel data. In this study, simulated pesticide concentrations in the air and on the soil in the different sowing scenarios were compared and discussed. The model predictions were similar to experimental literature data in terms of concentrations and drift distance. Pesticide exposure levels to bees during flight and foraging were estimated from the simulated concentrations. The proposed CFD model can be used in risk assessment studies and in the evaluation of dust drift mitigation measures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790021661','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790021661"><span>CELFE: Coupled <span class="hlt">Eulerian-Lagrangian</span> Finite Element program for high velocity impact. Part 1: Theory and formulation. [hydroelasto-viscoplastic model</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lee, C. H.</p> <p>1978-01-01</p> <p>A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by <span class="hlt">Eulerian</span> formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the <span class="hlt">Eulerian</span> mode to the <span class="hlt">Lagrangian</span> mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the <span class="hlt">Lagrangian</span> formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..1818317B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..1818317B"><span><span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> description of bed-load particle kinematics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ballio, Francesco; Sadabadi, Seyed Abbas Hosseini; Pokrajac, Dubravka; Radice, Alessio</p> <p>2016-04-01</p> <p>The motion of bed-load sediment particles transported by a flow can be analyzed within a <span class="hlt">Lagrangian</span> or an <span class="hlt">Eulerian</span> framework. In the former case, we consider the particles as individual objects in motion and we study their kinematic properties. The latter approach is instead referred to suitably chosen control volumes. Quantities describing sediment motion in the two frameworks are different, and the relationships among the two approaches are not straightforward. In this work, we intend to discuss the kinematic properties of sediment transport: first, a set of quantities is univocally defined; then, relationships among different representations are explored. Proof-of-concept results presented in the study are from a recent experiment involving weak bed-load sediment transport, where the moving particles were released over a fixed rough bed. The bulk flow velocity was 1.4 times the critical value for incipient particle motion, and particles were mostly moving by rolling and sliding, with limited saltation. The particle motion was filmed from the top and the measurements were conducted by image-based methods, obtaining extensive samples of virtually-instantaneous quantities.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li class="active"><span>3</span></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_3 --> <div id="page_4" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li class="active"><span>4</span></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="61"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA062335','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA062335"><span>Incorporation of the NAG-FRAG Model for Ductile and Brittle Fracture into Help, a 2D Multimaterial <span class="hlt">Eulerian</span> Program</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1978-09-01</p> <p>Models HELP Ductile Material HEMP Brittle Material PUFF Iron Aluminum <span class="hlt">Eulerian</span> Codea Tap«.r«»H Flyor Pl^«-» rmp«^» tO. ABITRACT (Conllmjm M r«v... HEMP ) <span class="hlt">code</span> with those obtained by the <span class="hlt">Eulerian</span> (HELP) <span class="hlt">code</span> 5.3 Relative void volume of damage regions at three times after impact in the 1145...plate calculation 5.5 Relative void volume of material in the 1145 aluminum target at 1.46 us after impact as computed by the <span class="hlt">Lagrangian</span> ( HEMP</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19770023699','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19770023699"><span>Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an <span class="hlt">Eulerian-Lagrangian</span> marker particle technique</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Pavish, D. L.; Spaulding, M. L.</p> <p>1977-01-01</p> <p>A computer <span class="hlt">coded</span> <span class="hlt">Lagrangian</span> marker particle in <span class="hlt">Eulerian</span> finite difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/12779582','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/12779582"><span><span class="hlt">Lagrangian</span> averages, averaged <span class="hlt">Lagrangians</span>, and the mean effects of fluctuations in fluid dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Holm, Darryl D.</p> <p>2002-06-01</p> <p>We begin by placing the generalized <span class="hlt">Lagrangian</span> mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged <span class="hlt">Lagrangian</span>. This is the <span class="hlt">Lagrangian</span> averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a <span class="hlt">Lagrangian</span> trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the <span class="hlt">Eulerian</span> mean fluid quantities by the fluctuating displacements of the <span class="hlt">Lagrangian</span> trajectories in terms of their <span class="hlt">Eulerian</span> second moments. The derivation of the glm equations uses the linearized relations between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> fluctuations, in the tradition of <span class="hlt">Lagrangian</span> stability analysis for fluids. The glm derivation also uses the method of averaged <span class="hlt">Lagrangians</span>, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the <span class="hlt">Lagrangian</span> statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for <span class="hlt">Lagrangian</span> averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EGUGA..1511185C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..1511185C"><span>A <span class="hlt">lagrangian-eulerian</span> description of debris transport by a tsunami in the Lisbon waterfront</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Conde, Daniel; Canelas, Ricardo; Baptista, Maria Ana; João Telhado, Maria; Ferreira, Rui M. L.</p> <p>2013-04-01</p> <p>Several major tsunamis are known to have struck the Portuguese coast over the past millennia (Baptista and Miranda, 2009). The Tagus estuary has great exposure to tsunami occurrences and, being bordered by the largest metropolitan area in the country, is a particularly worrisome location in what concerns safety of populations and economic losses due to disruption of built infrastructures. The last major earthquake and tsunami combination known to have critically affected the Tagus estuary dates back to November 1st 1755. This catastrophe critically damaged Lisbon's infrastructures, led to numerous casualties and priceless heritage losses. The urban tissue of the present city still bears visible the effects of the catastrophe and of the ensuing protection measures. The objective of this work is to simulate the propagation of debris carried by a 1755-like tsunami along the present-day bathimetric and altimetric conditions of Lisbon waterfront. Particular emphasis was directed to the modeling of vehicles since the tsunami is likely to affect areas that are major traffic nodes such as Alcântara, with more than 1500 vehicles in road network of about 3 km. The simulation tool employed is based on a 2DH spatial (<span class="hlt">eulerian</span>) shallow-flow approach suited to complex and dynamic bottom boundaries. The discretization technique relies on a finite-volume scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver (Canelas et al. 2013). Two formulations were employed to model the advection of debris: a fully coupled continuum approach, where solid bodies are described by the concentration only and an uncoupled material (<span class="hlt">lagrangian</span>) formulation where solid bodies are tracked between two time-steps once the flow field is determined by the <span class="hlt">eulerian</span> solver. In the latter case, concentrations are updated after tracking the solid bodies thus correcting the mass and momentum balance to be used for the next time-step. The urban tissue was</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70164425','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70164425"><span>On tide-induced <span class="hlt">Lagrangian</span> residual current and residual transport: 1. <span class="hlt">Lagrangian</span> residual current</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi</p> <p>1986-01-01</p> <p>Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a <span class="hlt">Lagrangian</span> mean velocity than an <span class="hlt">Eulerian</span> mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> residual currents. When k is small, the first-order <span class="hlt">Lagrangian</span> residual is shown to be the sum of the <span class="hlt">Eulerian</span> residual current and the Stokes drift. The <span class="hlt">Lagrangian</span> residual drift velocity or the second-order <span class="hlt">Lagrangian</span> residual current has been shown to be dependent on the phase of tidal current. The <span class="hlt">Lagrangian</span> drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the <span class="hlt">Lagrangian</span> residual current.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70164423','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70164423"><span>On <span class="hlt">Lagrangian</span> residual currents with applications in south San Francisco Bay, California</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cheng, Ralph T.; Casulli, Vincenzo</p> <p>1982-01-01</p> <p>The <span class="hlt">Lagrangian</span> residual circulation has often been introduced as the sum of the <span class="hlt">Eulerian</span> residual circulation and the Stokes' drift. Unfortunately, this definition of the <span class="hlt">Lagrangian</span> residual circulation is conceptually incorrect because both the <span class="hlt">Eulerian</span> residual circulation and the Stokes' drift are <span class="hlt">Eulerian</span> variables. In this paper a classification of various residual variables are reviewed and properly defined. The <span class="hlt">Lagrangian</span> residual circulation is then studied by means of a two-stage formulation of a computer model. The tidal circulation is first computed in a conventional <span class="hlt">Eulerian</span> way, and then the <span class="hlt">Lagrangian</span> residual circulation is determined by a method patterned after the method of markers and cells. To demonstrate properties of the <span class="hlt">Lagrangian</span> residual circulation, application of this approach in South San Francisco Bay, California, is considered. With the aid of the model results, properties of the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> residual circulation are examined. It can be concluded that estimation of the <span class="hlt">Lagrangian</span> residual circulation from <span class="hlt">Eulerian</span> data may lead to unacceptable error, particularly in a tidal estuary where the tidal excursion is of the same order of magnitude as the length scale of the basin. A direction calculation of the <span class="hlt">Lagrangian</span> residual circulation must be made and has been shown to be feasible.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016ascl.soft02021T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ascl.soft02021T"><span>COLAcode: COmoving <span class="hlt">Lagrangian</span> Acceleration <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tassev, Svetlin V.</p> <p>2016-02-01</p> <p>COLAcode is a serial particle mesh-based N-body <span class="hlt">code</span> illustrating the COLA (COmoving <span class="hlt">Lagrangian</span> Acceleration) method; it solves for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in <span class="hlt">Lagrangian</span> Perturbation Theory (LPT). It differs from standard N-body <span class="hlt">code</span> by trading accuracy at small-scales to gain computational speed without sacrificing accuracy at large scales. This is useful for generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing; such catalogs are needed to perform detailed error analysis for ongoing and future surveys of LSS.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDD37005K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDD37005K"><span>Investigation of erosion behavior in different pipe-fitting using <span class="hlt">Eulerian-Lagrangian</span> approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kulkarni, Harshwardhan; Khadamkar, Hrushikesh; Mathpati, Channamallikarjun</p> <p>2017-11-01</p> <p>Erosion is a wear mechanism of piping system in which wall thinning occurs because of turbulent flow along with along with impact of solid particle on the pipe wall, because of this pipe ruptures causes costly repair of plant and personal injuries. In this study two way coupled <span class="hlt">Eulerian-Lagrangian</span> approach is used to solve the liquid solid (water-ferrous suspension) flow in the different pipe fitting namely elbow, t-junction, reducer, orifice and 50% open gate valve. Simulations carried out using incomressible transient solver in OpenFOAM for different Reynolds's number (10k, 25k, 50k) and using WenYu drag model to find out possible higher erosion region in pipe fitting. Used transient solver is a hybrid in nature which is combination of <span class="hlt">Lagrangian</span> library and pimpleFoam. Result obtained from simulation shows that exit region of elbow specially downstream of straight, extradose of the bend section more affected by erosion. Centrifugal force on solid particle at bend affect the erosion behavior. In case of t-junction erosion occurs below the locus of the projection of branch pipe on the wall. For the case of reducer, orifice and a gate valve reduction area as well as downstream is getting more affected by erosion because of increase in velocities.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://files.eric.ed.gov/fulltext/ED119999.pdf','ERIC'); return false;" href="http://files.eric.ed.gov/fulltext/ED119999.pdf"><span>The Case for Including <span class="hlt">Eulerian</span> Kinematics in Undergraduate Dynamics.</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Uram, Earl M.</p> <p></p> <p>A <span class="hlt">Eulerian</span> framework is proposed as an alternative to the <span class="hlt">Lagrangian</span> framework usually used in undergraduate dynamics courses. An attempt to introduce <span class="hlt">Eulerian</span> kinematics into a dynamics course is discussed. (LMH)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70011338','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70011338"><span>Euler-<span class="hlt">Lagrangian</span> computation for estuarine hydrodynamics</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cheng, Ralph T.</p> <p>1983-01-01</p> <p>The transport of conservative and suspended matter in fluid flows is a phenomenon of <span class="hlt">Lagrangian</span> nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an <span class="hlt">Eulerian</span> formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an <span class="hlt">Eulerian</span> reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> computational techniques.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1399708-eulerian-formulation-interacting-particle-representation-model-homogeneous-turbulence','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1399708-eulerian-formulation-interacting-particle-representation-model-homogeneous-turbulence"><span><span class="hlt">Eulerian</span> formulation of the interacting particle representation model of homogeneous turbulence</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca</p> <p>2016-10-21</p> <p>The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the con nes of a one-point model. In the original formulation [Kassinos & Reynolds, Center for Turbulence Research: Annual Research Briefs, 31{51, (1996)], the IPRM was developed in a <span class="hlt">Lagrangian</span> setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is re-formulated in an <span class="hlt">Eulerian</span> framework and evolution equations are developed for the marginal PDFs. <span class="hlt">Eulerian</span> methods avoid the issues associated with statistical estimators used by <span class="hlt">Lagrangian</span> approaches, such as slow convergence. Amore » specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with <span class="hlt">Eulerian</span> simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new <span class="hlt">Eulerian</span> solution method are thoroughly analyzed. The sensitivity of the <span class="hlt">Eulerian</span> simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new <span class="hlt">Eulerian</span> solution method and the original <span class="hlt">Lagrangian</span> approach.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003STIN...0316602M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003STIN...0316602M"><span>Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Melis, Matthew E.</p> <p>2003-01-01</p> <p>Explicit finite element techniques employing an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methodology, within the transient dynamic <span class="hlt">code</span> LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20030016601','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20030016601"><span>Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary <span class="hlt">Lagrangian-eulerian</span> Approach</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Melis, Matthew E.</p> <p>2003-01-01</p> <p>Explicit finite element techniques employing an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methodology, within the transient dynamic <span class="hlt">code</span> LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MMTB...48.1248L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MMTB...48.1248L"><span>Modeling of Quasi-Four-Phase Flow in Continuous Casting Mold Using Hybrid <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Zhongqiu; Sun, Zhenbang; Li, Baokuan</p> <p>2017-04-01</p> <p><span class="hlt">Lagrangian</span> tracking model combined with <span class="hlt">Eulerian</span> multi-phase model is employed to predict the time-dependent argon-steel-slag-air quasi-four-phase flow inside a slab continuous casting mold. The <span class="hlt">Eulerian</span> approach is used for the description of three phases (molten steel, liquid slag, and air at the top of liquid slag layer). The dispersed argon bubble injected from the SEN is treated in the <span class="hlt">Lagrangian</span> way. The complex interfacial momentum transfers between various phases are considered. Validation is supported by the measurement data of cold model experiments and industrial practice. Close agreements were achieved for the gas volume fraction, liquid flow pattern, level fluctuation, and exposed slag eye phenomena. Many known phenomena and new predictions were successfully reproduced using this model. The vortex slag entrapment phenomenon at the slag-steel interface was obtained using this model, some small slag drops are sucked deep into the liquid pool of molten steel. Varying gas flow rates have a large effect on the steel flow pattern in the upper recirculation zone. Three typical flow patterns inside the mold with different argon gas flow rates have been obtained: double roll, three roll, and single roll. Effects of argon gas flow rate, casting speed, and slag layer thickness on the exposed slag eye and level fluctuation at the slag-steel interface were studied. A dimensionless value of H ave/ h was proposed to describe the time-averaged level fluctuation of slag-steel interface. The exposed slag eye near the SEN would be formed when the value of H ave/ h is larger than 0.4.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JGRC..122.5445S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JGRC..122.5445S"><span>Impact of data assimilation on <span class="hlt">Eulerian</span> versus <span class="hlt">Lagrangian</span> estimates of upper ocean transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sperrevik, Ann Kristin; Röhrs, Johannes; Christensen, Kai Hâkon</p> <p>2017-07-01</p> <p>Using four-dimensional variational analysis, we produce an estimate of the state of a coastal region in Northern Norway during the late winter and spring in 1984. We use satellite sea surface temperature and in situ observations from a series of intensive field campaigns, and obtain a more realistic distribution of water masses both in the horizontal and the vertical than a pure downscaling approach can achieve. Although the distribution of <span class="hlt">Eulerian</span> surface current speeds are similar, we find that they are more variable and less dependent on model bathymetry in our reanalysis compared to a hindcast produced using the same modeling system. <span class="hlt">Lagrangian</span> drift currents on the other hand are significantly changed, with overall higher kinetic energy levels in the reanalysis than in the hindcast, particularly in the superinertial frequency band.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19970001872','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19970001872"><span>An Extended <span class="hlt">Lagrangian</span> Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, Meng-Sing</p> <p>1995-01-01</p> <p>A unique formulation of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. The present method and the Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the <span class="hlt">Lagrangian</span> method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same <span class="hlt">code</span> an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDA37008R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDA37008R"><span>GPU acceleration of <span class="hlt">Eulerian-Lagrangian</span> particle-laden turbulent flow simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Richter, David; Sweet, James; Thain, Douglas</p> <p>2017-11-01</p> <p>The <span class="hlt">Lagrangian</span> point-particle approximation is a popular numerical technique for representing dispersed phases whose properties can substantially deviate from the local fluid. In many cases, particularly in the limit of one-way coupled systems, large numbers of particles are desired; this may be either because many physical particles are present (e.g. LES of an entire cloud), or because the use of many particles increases statistical convergence (e.g. high-order statistics). Solving the trajectories of very large numbers of particles can be problematic in traditional MPI implementations, however, and this study reports the benefits of using graphical processing units (GPUs) to integrate the particle equations of motion while preserving the original MPI version of the <span class="hlt">Eulerian</span> flow solver. It is found that GPU acceleration becomes cost effective around one million particles, and performance enhancements of up to 15x can be achieved when O(108) particles are computed on the GPU rather than the CPU cluster. Optimizations and limitations will be discussed, as will prospects for expanding to two- and four-way coupled systems. ONR Grant No. N00014-16-1-2472.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20130010995','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20130010995"><span>Ice Accretion Modeling using an <span class="hlt">Eulerian</span> Approach for Droplet Impingement</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kim, Joe Woong; Garza, Dennis P.; Sankar, Lakshmi N.; Kreeger, Richard E.</p> <p>2012-01-01</p> <p>A three-dimensional <span class="hlt">Eulerian</span> analysis has been developed for modeling droplet impingement on lifting bodes. The <span class="hlt">Eulerian</span> model solves the conservation equations of mass and momentum to obtain the droplet flow field properties on the same mesh used in CFD simulations. For complex configurations such as a full rotorcraft, the <span class="hlt">Eulerian</span> approach is more efficient because the <span class="hlt">Lagrangian</span> approach would require a significant amount of seeding for accurate estimates of collection efficiency. Simulations are done for various benchmark cases such as NACA0012 airfoil, MS317 airfoil and oscillating SC2110 airfoil to illustrate its use. The present results are compared with results from the <span class="hlt">Lagrangian</span> approach used in an industry standard analysis called LEWICE.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.753h2031F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.753h2031F"><span>Wake modeling in complex terrain using a hybrid <span class="hlt">Eulerian-Lagrangian</span> Split Solver</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fuchs, Franz G.; Rasheed, Adil; Tabib, Mandar; Fonn, Eivind</p> <p>2016-09-01</p> <p>Wake vortices (WVs) generated by aircraft are a source of risk to the following aircraft. The probability of WV related accidents increases in the vicinity of airport runways due to the shorter time of recovery after a WV encounter. Hence, solutions that can reduce the risk of WV encounters are needed to ensure increased flight safety. In this work we propose an interesting approach to model such wake vortices in real time using a hybrid <span class="hlt">Eulerian</span>- <span class="hlt">Lagrangian</span> approach. We derive an appropriate mathematical model, and show a comparison of the different types of solvers. We will conclude with a real life application of the methodology by simulating how wake vortices left behind by an aircraft at the Vffirnes airport in Norway get transported and decay under the influence of a background wind and turbulence field. Although the work demonstrates the application in an aviation context the same approach can be used in a wind energy context.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1360930-modeling-shockwaves-impact-phenomena-eulerian-peridynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1360930-modeling-shockwaves-impact-phenomena-eulerian-peridynamics"><span>Modeling shockwaves and impact phenomena with <span class="hlt">Eulerian</span> peridynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Silling, Stewart A.; Parks, Michael L.; Kamm, James R.; ...</p> <p>2017-05-09</p> <p>Most previous development of the peridynamic theory has assumed a <span class="hlt">Lagrangian</span> formulation, in which the material model refers to an undeformed reference configuration. Here, an <span class="hlt">Eulerian</span> form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The formulation is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the <span class="hlt">Lagrangian</span> form unsuitable. The <span class="hlt">Eulerian</span> capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li class="active"><span>4</span></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_4 --> <div id="page_5" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li class="active"><span>5</span></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="81"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1360930','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1360930"><span>Modeling shockwaves and impact phenomena with <span class="hlt">Eulerian</span> peridynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Silling, Stewart A.; Parks, Michael L.; Kamm, James R.</p> <p></p> <p>Most previous development of the peridynamic theory has assumed a <span class="hlt">Lagrangian</span> formulation, in which the material model refers to an undeformed reference configuration. Here, an <span class="hlt">Eulerian</span> form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The formulation is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the <span class="hlt">Lagrangian</span> form unsuitable. The <span class="hlt">Eulerian</span> capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1412853-computing-eddy-driven-effective-diffusivity-using-lagrangian-particles','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1412853-computing-eddy-driven-effective-diffusivity-using-lagrangian-particles"><span>Computing eddy-driven effective diffusivity using <span class="hlt">Lagrangian</span> particles</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Wolfram, Phillip J.; Ringler, Todd D.</p> <p>2017-08-14</p> <p>A novel method to derive effective diffusivity from <span class="hlt">Lagrangian</span> particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from <span class="hlt">Lagrangian</span> particles. We compute the effective diffusivity by first performing scalar transport on <span class="hlt">Lagrangian</span> control areas using stored trajectories computed from online <span class="hlt">Lagrangian</span> In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the <span class="hlt">Lagrangian</span> scalar transport scheme is comparedmore » against an <span class="hlt">Eulerian</span> scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1412853','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1412853"><span>Computing eddy-driven effective diffusivity using <span class="hlt">Lagrangian</span> particles</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Wolfram, Phillip J.; Ringler, Todd D.</p> <p></p> <p>A novel method to derive effective diffusivity from <span class="hlt">Lagrangian</span> particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from <span class="hlt">Lagrangian</span> particles. We compute the effective diffusivity by first performing scalar transport on <span class="hlt">Lagrangian</span> control areas using stored trajectories computed from online <span class="hlt">Lagrangian</span> In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the <span class="hlt">Lagrangian</span> scalar transport scheme is comparedmore » against an <span class="hlt">Eulerian</span> scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1194068-point-centered-arbitrary-lagrangian-eulerian-hydrodynamic-approach-tetrahedral-meshes','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1194068-point-centered-arbitrary-lagrangian-eulerian-hydrodynamic-approach-tetrahedral-meshes"><span>A point-centered arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> hydrodynamic approach for tetrahedral meshes</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...</p> <p>2015-02-24</p> <p>We present a three dimensional (3D) arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1996dmu..conf..543B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1996dmu..conf..543B"><span><span class="hlt">Lagrangian</span> Perturbation Approach to the Formation of Large-scale Structure</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Buchert, Thomas</p> <p></p> <p>The present lecture notes address three columns on which the <span class="hlt">Lagrangian</span> perturbation approach to cosmological dynamics is based: 1. the formulation of a <span class="hlt">Lagrangian</span> theory of self-gravitating flows in which the dynamics is described in terms of a single field variable; 2. the procedure, how to obtain the dynamics of <span class="hlt">Eulerian</span> fields from the <span class="hlt">Lagrangian</span> picture, and 3. a precise definition of a Newtonian cosmology framework in which <span class="hlt">Lagrangian</span> perturbation solutions can be studied. While the first is a discussion of the basic equations obtained by transforming the <span class="hlt">Eulerian</span> evolution and field equations to the <span class="hlt">Lagrangian</span> picture, the second exemplifies how the <span class="hlt">Lagrangian</span> theory determines the evolution of <span class="hlt">Eulerian</span> fields including kinematical variables like expansion, vorticity, as well as the shear and tidal tensors. The third column is based on a specification of initial and boundary conditions, and in particular on the identification of the average flow of an inhomogeneous cosmology with a `Hubble-flow'. Here, we also look at the limits of the <span class="hlt">Lagrangian</span> perturbation approach as inferred from comparisons with N-body simulations and illustrate some striking properties of the solutions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFMNG23A..04D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFMNG23A..04D"><span>Bayesian <span class="hlt">Lagrangian</span> Data Assimilation and Drifter Deployment Strategies</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dutt, A.; Lermusiaux, P. F. J.</p> <p>2017-12-01</p> <p>Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). <span class="hlt">Lagrangian</span> Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such <span class="hlt">Lagrangian</span> transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint <span class="hlt">Eulerian-Lagrangian</span> Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of <span class="hlt">Eulerian</span> variables (e.g. velocity, temperature, salinity, etc.) and <span class="hlt">Lagrangian</span> variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017BoLMe.165..251D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017BoLMe.165..251D"><span>Water-Channel Estimation of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Time Scales of the Turbulence in Idealized Two-Dimensional Urban Canopies</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Di Bernardino, Annalisa; Monti, Paolo; Leuzzi, Giovanni; Querzoli, Giorgio</p> <p>2017-11-01</p> <p><span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the <span class="hlt">Eulerian</span> (TE) and <span class="hlt">Lagrangian</span> (TL) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width ( W) to the height ( H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the <span class="hlt">Eulerian</span> time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the <span class="hlt">Lagrangian</span> time scale, T_u^L and T_w^L , follow Raupach's linear law within the constant-flux layer. The same holds true for T_w^L in both the canopies analyzed (AR= 1 and AR= 2) and also for T_u^L when AR = 1. In contrast, for AR = 2, T_u^L follows Raupach's law only above z=2H. Below that level, T_u^L is nearly constant with height, showing at z=H a value approximately one order of magnitude greater than that found for AR = 1. It is shown that the assumption usually adopted for flat terrain, that β =TL/TE is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, γ /i_u fits well β _u =T_u^L /T_u^E in both the configurations by choosing γ to be 0.35 (here, i_u =σ _u / \\bar{u} , where \\bar{u} and σ _u are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, β _w =T_w^L /T_w^E follows approximately γ /i_w =0.65/( {σ _w /\\bar{u} } ) for z > 2H, irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum (KT) and the Kolmogorov constant (C_0). It is</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JCoPh.268..154K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JCoPh.268..154K"><span>Compatible, total energy conserving and symmetry preserving arbitrary <span class="hlt">Lagrangian-Eulerian</span> hydrodynamics in 2D rz - Cylindrical coordinates</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail</p> <p>2014-07-01</p> <p>We present a new discretization for 2D arbitrary <span class="hlt">Lagrangian-Eulerian</span> hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic <span class="hlt">Lagrangian</span> hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the <span class="hlt">Lagrangian</span> equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for <span class="hlt">Lagrangian</span> equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary <span class="hlt">Lagrangian-Eulerian</span> algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.1476M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.1476M"><span>An <span class="hlt">Eulerian-Lagrangian</span> description for fluvial coarse sediment transport: theory and verification with low-cost inertial sensors.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Maniatis, Georgios</p> <p>2017-04-01</p> <p>Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. One reference frame descriptions (<span class="hlt">Eulerian</span> or <span class="hlt">Lagrangian</span>) yield useful results but restrict the theoretical understanding of the process as differences between the two phases (liquid and solid) are not explicitly accounted. Recently, affordable Inertial Measurement Units (IMUs) that can be embedded in coarse (100 mm diameter scale) natural or artificial particles became available. These sensors are subjected to technical limitations when deployed for natural sediment transport. However, they give us the ability to measure for the first time the inertial dynamics (acceleration and angular velocity) of moving sediment grains under fluvial transport. Theoretically, the assumption of an ideal (IMU), rigidly attached at the centre of the mass of a sediment particle can simplify greatly the derivation of a general <span class="hlt">Eulerian-Lagrangian</span> (E-L) model. This approach accounts for inertial characteristics of particles in a <span class="hlt">Lagrangian</span> (particle fixed) frame, and for the hydrodynamics in an independent <span class="hlt">Eulerian</span> frame. Simplified versions of the E-L model have been evaluated in laboratory experiments using real-IMUs [Maniatis et. al 2015]. Here, experimental results are presented relevant to the evaluation of the complete E-L model. Artificial particles were deployed in a series of laboratory and field experiments. The particles are equipped with an IMU capable of recording acceleration at ± 400 g and angular velocities at ± 1200 rads/sec ranges. The sampling frequency ranges from 50 to 200 Hz for the total IMU measurement. Two sets of laboratory experiments were conducted in a 0.9m wide laboratory flume. The first is a set of entrainment threshold experiments using two artificial particles: a spherical of D=90mm (A) and an ellipsoid with axes of 100, 70 and 30 mm (B). For the second set of experiments, a spherical artificial enclosure of D</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70018031','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70018031"><span>A finite-volume <span class="hlt">Eulerian-Lagrangian</span> Localized Adjoint Method for solution of the advection-dispersion equation</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Healy, R.W.; Russell, T.F.</p> <p>1993-01-01</p> <p>A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on <span class="hlt">Lagrangian</span> space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003APS..DPPQP1015B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003APS..DPPQP1015B"><span>Comparisons of 'Identical' Simulations by the <span class="hlt">Eulerian</span> Gyrokinetic <span class="hlt">Codes</span> GS2 and GYRO</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bravenec, R. V.; Ross, D. W.; Candy, J.; Dorland, W.; McKee, G. R.</p> <p>2003-10-01</p> <p>A major goal of the fusion program is to be able to predict tokamak transport from first-principles theory. To this end, the <span class="hlt">Eulerian</span> gyrokinetic <span class="hlt">code</span> GS2 was developed years ago and continues to be improved [1]. Recently, the <span class="hlt">Eulerian</span> <span class="hlt">code</span> GYRO was developed [2]. These <span class="hlt">codes</span> are not subject to the statistical noise inherent to particle-in-cell (PIC) <span class="hlt">codes</span>, and have been very successful in treating electromagnetic fluctuations. GS2 is fully spectral in the radial coordinate while GYRO uses finite-differences and ``banded" spectral schemes. To gain confidence in nonlinear simulations of experiment with these <span class="hlt">codes</span>, ``apples-to-apples" comparisons (identical profile inputs, flux-tube geometry, two species, etc.) are first performed. We report on a series of linear and nonlinear comparisons (with overall agreement) including kinetic electrons, collisions, and shaped flux surfaces. We also compare nonlinear simulations of a DIII-D discharge to measurements of not only the fluxes but also the turbulence parameters. [1] F. Jenko, et al., Phys. Plasmas 7, 1904 (2000) and refs. therein. [2] J. Candy, J. Comput. Phys. 186, 545 (2003).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDG18003H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDG18003H"><span><span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> methods for vortex tracking in 2D and 3D flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Huang, Yangzi; Green, Melissa</p> <p>2014-11-01</p> <p>Coherent structures are a key component of unsteady flows in shear layers. Improvement of experimental techniques has led to larger amounts of data and requires of automated procedures for vortex tracking. Many vortex criteria are <span class="hlt">Eulerian</span>, and identify the structures by an instantaneous local swirling motion in the field, which are indicated by closed or spiral streamlines or pathlines in a reference frame. Alternatively, a <span class="hlt">Lagrangian</span> Coherent Structures (LCS) analysis is a <span class="hlt">Lagrangian</span> method based on the quantities calculated along fluid particle trajectories. In the current work, vortex detection is demonstrated on data from the simulation of two cases: a 2D flow with a flat plate undergoing a 45 ° pitch-up maneuver and a 3D wall-bounded turbulence channel flow. Vortices are visualized and tracked by their centers and boundaries using Γ1, the Q criterion, and LCS saddle points. In the cases of 2D flow, saddle points trace showed a rapid acceleration of the structure which indicates the shedding from the plate. For channel flow, saddle points trace shows that average structure convection speed exhibits a similar trend as a function of wall-normal distance as the mean velocity profile, and leads to statistical quantities of vortex dynamics. Dr. Jeff Eldredge and his research group at UCLA are gratefully acknowledged for sharing the database of simulation for the current research. This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26754057','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26754057"><span>Modified Mixed <span class="hlt">Lagrangian-Eulerian</span> Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Suk, Heejun</p> <p>2016-07-01</p> <p>MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the <span class="hlt">Lagrangian</span> concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the <span class="hlt">Lagrangian</span> concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the <span class="hlt">Eulerian-Lagrangian</span> method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDM31008C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDM31008C"><span>Evaluation of particle-based flow characteristics using novel <span class="hlt">Eulerian</span> indices</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cho, Youngmoon; Kang, Seongwon</p> <p>2017-11-01</p> <p>The main objective of this study is to evaluate flow characteristics in complex particle-laden flows efficiently using novel <span class="hlt">Eulerian</span> indices. For flows with a large number of particles, a <span class="hlt">Lagrangian</span> approach leads to accurate yet inefficient prediction in many engineering problems. We propose a technique based on <span class="hlt">Eulerian</span> transport equation and ensemble-averaged particle properties, which enables efficient evaluation of various particle-based flow characteristics such as the residence time, accumulated travel distance, mean radial force, etc. As a verification study, we compare the developed <span class="hlt">Eulerian</span> indices with those using <span class="hlt">Lagrangian</span> approaches for laminar flows with and without a swirling motion and density ratio. The results show satisfactory agreement between two approaches. The accumulated travel distance is modified to analyze flow motions inside IC engines and, when applied to flow bench cases, it can predict swirling and tumbling motions successfully. For flows inside a cyclone separator, the mean radial force is applied to predict the separation of particles and is shown to have a high correlation to the separation efficiency for various working conditions. In conclusion, the proposed <span class="hlt">Eulerian</span> indices are shown to be useful tools to analyze complex particle-based flow characteristics. Corresponding author.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.351..422P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.351..422P"><span>An adaptive reconstruction for <span class="hlt">Lagrangian</span>, direct-forcing, immersed-boundary methods</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Posa, Antonio; Vanella, Marcos; Balaras, Elias</p> <p>2017-12-01</p> <p><span class="hlt">Lagrangian</span>, direct-forcing, immersed boundary (IB) methods have been receiving increased attention due to their robustness in complex fluid-structure interaction problems. They are very sensitive, however, on the selection of the <span class="hlt">Lagrangian</span> grid, which is typically used to define a solid or flexible body immersed in a fluid flow. In the present work we propose a cost-efficient solution to this problem without compromising accuracy. Central to our approach is the use of isoparametric mapping to bridge the relative resolution requirements of <span class="hlt">Lagrangian</span> IB, and <span class="hlt">Eulerian</span> grids. With this approach, the density of surface <span class="hlt">Lagrangian</span> markers, which is essential to properly enforce boundary conditions, is adapted dynamically based on the characteristics of the underlying <span class="hlt">Eulerian</span> grid. The markers are not stored and the <span class="hlt">Lagrangian</span> data-structure is not modified. The proposed scheme is implemented in the framework of a moving least squares reconstruction formulation, but it can be adapted to any <span class="hlt">Lagrangian</span>, direct-forcing formulation. The accuracy and robustness of the approach is demonstrated in a variety of test cases of increasing complexity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFD.Q6008A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFD.Q6008A"><span>Compressibility Effects on Particle-Fluid Interaction Force for <span class="hlt">Eulerian-Eulerian</span> Simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Akiki, Georges; Francois, Marianne; Zhang, Duan</p> <p>2017-11-01</p> <p>Particle-fluid interaction forces are essential in modeling multiphase flows. Several models can be found in the literature based on empirical, numerical, and experimental results from various simplified flow conditions. Some of these models also account for finite Mach number effects. Using these models is relatively straightforward with <span class="hlt">Eulerian-Lagrangian</span> calculations if the model for the total force on particles is used. In <span class="hlt">Eulerian-Eulerian</span> simulations, however, there is the pressure gradient terms in the momentum equation for particles. For low Mach number flows, the pressure gradient force is negligible if the particle density is much greater than that of the fluid. For supersonic flows where a standing shock is present, even for a steady and uniform flow, it is unclear whether the significant pressure-gradient force should to be separated out from the particle force model. To answer this conceptual question, we perform single-sphere fully-resolved DNS simulations for a wide range of Mach numbers. We then examine whether the total force obtained from the DNS can be categorized into well-established models, such as the quasi-steady, added-mass, pressure-gradient, and history forces. Work sponsored by Advanced Simulation and Computing (ASC) program of NNSA and LDRD-CNLS of LANL.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1423820-evaluation-eulerian-multi-material-mixture-formulation-based-single-inverse-deformation-gradient-tensor-field','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1423820-evaluation-eulerian-multi-material-mixture-formulation-based-single-inverse-deformation-gradient-tensor-field"><span>Evaluation of an <span class="hlt">Eulerian</span> multi-material mixture formulation based on a single inverse deformation gradient tensor field</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.; ...</p> <p>2017-12-31</p> <p>We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to <span class="hlt">Lagrangian</span> (Benson 1992) and arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methods (Donea et al. 2004), fully <span class="hlt">Eulerian</span> methods use grids that do not change in time. Consequently, <span class="hlt">Eulerian</span> methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1423820','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1423820"><span>Evaluation of an <span class="hlt">Eulerian</span> multi-material mixture formulation based on a single inverse deformation gradient tensor field</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.</p> <p></p> <p>We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to <span class="hlt">Lagrangian</span> (Benson 1992) and arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methods (Donea et al. 2004), fully <span class="hlt">Eulerian</span> methods use grids that do not change in time. Consequently, <span class="hlt">Eulerian</span> methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4851392','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4851392"><span>Fluid-Structure Interaction Simulation of Prosthetic Aortic Valves: Comparison between Immersed Boundary and Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Techniques for the Mesh Representation</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick</p> <p>2016-01-01</p> <p>In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary <span class="hlt">Lagrangian-Eulerian</span>) or an <span class="hlt">Eulerian</span> formulation. The majority of the reported 3D heart valve FSI simulations are performed with the <span class="hlt">Eulerian</span> formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an <span class="hlt">Eulerian</span>-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results. PMID:27128798</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows"><span>Verification of <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> simulations for turbulent fluid-particle flows</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Patel, Ravi G.; Desjardins, Olivier; Kong, Bo; ...</p> <p>2017-09-01</p> <p>Here, we present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posingmore » fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent <span class="hlt">Eulerian</span> statistics remains a challenge for all methods.« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li class="active"><span>5</span></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_5 --> <div id="page_6" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li class="active"><span>6</span></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="101"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows"><span>Verification of <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> simulations for turbulent fluid-particle flows</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Patel, Ravi G.; Desjardins, Olivier; Kong, Bo</p> <p></p> <p>Here, we present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posingmore » fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent <span class="hlt">Eulerian</span> statistics remains a challenge for all methods.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790007154','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790007154"><span>CELFE/NASTRAN <span class="hlt">Code</span> for the Analysis of Structures Subjected to High Velocity Impact</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chamis, C. C.</p> <p>1978-01-01</p> <p>CELFE (Coupled <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> Finite Element)/NASTRAN <span class="hlt">Code</span> three-dimensional finite element <span class="hlt">code</span> has the capability for analyzing of structures subjected to high velocity impact. The local response is predicted by CELFE and, for large problems, the far-field impact response is predicted by NASTRAN. The coupling of the CELFE <span class="hlt">code</span> with NASTRAN (CELFE/NASTRAN <span class="hlt">code</span>) and the application of the <span class="hlt">code</span> to selected three-dimensional high velocity impact problems are described.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910001565','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910001565"><span>A combined <span class="hlt">Eulerian-Lagrangian</span> two-phase analysis of the SSME HPOTP nozzle plug trajectories</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Garcia, Robert; Mcconnaughey, P. K.; Dejong, F. J.; Sabnis, J. S.; Pribik, D.</p> <p>1989-01-01</p> <p>As a result of high cycle fatigue, hydrogen embrittlement, and extended engine use, it was observed in testing that the trailing edge on the first stage nozzle plug in the High Pressure Oxygen Turbopump (HPOTP) could detach. The objective was to predict the trajectories followed by particles exiting the turbine. Experiments had shown that the heat exchanger soils, which lie downstream of the turbine, would be ruptured by particles traveling in the order of 360 ft/sec. An axisymmetric solution of the flow was obtained from the work of Lin et. al., who used INS3D to obtain the solution. The particle trajectories were obtained using the method of de Jong et. al., which employs <span class="hlt">Lagrangian</span> tracking of the particle through the <span class="hlt">Eulerian</span> flow field. The collision parameters were obtained from experiments conducted by Rocketdyne using problem specific alloys, speeds, and projectile geometries. A complete 3-D analysis using the most likely collision parameters shows maximum particle velocities of 200 ft/sec. in the heat exchanger region. Subsequent to this analysis, an engine level test was conducted in which seven particles passed through the turbine but no damage was observed on the heat exchanger coils.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1270630','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1270630"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro</p> <p></p> <p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> formulation, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. Furthermore, all the perturbative models fare better than linear theory.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22525478-lagrangian-effective-field-theory','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22525478-lagrangian-effective-field-theory"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro, E-mail: zvlah@stanford.edu, E-mail: mwhite@berkeley.edu, E-mail: aviles@berkeley.edu</p> <p></p> <p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> formulation, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. All the perturbative models fare better than linear theory.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1270630-lagrangian-effective-field-theory','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1270630-lagrangian-effective-field-theory"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro</p> <p>2015-09-02</p> <p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> formulation, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. Furthermore, all the perturbative models fare better than linear theory.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015WRR....51.1916W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015WRR....51.1916W"><span>Variational <span class="hlt">Lagrangian</span> data assimilation in open channel networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wu, Qingfang; Tinka, Andrew; Weekly, Kevin; Beard, Jonathan; Bayen, Alexandre M.</p> <p>2015-04-01</p> <p>This article presents a data assimilation method in a tidal system, where data from both <span class="hlt">Lagrangian</span> drifters and <span class="hlt">Eulerian</span> flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be formulated as the minimization of the difference between the observed variables and model outputs, and eventually provide the velocity and water stage of the hydrodynamic system. The governing equations are linearized and discretized using an implicit discretization scheme, resulting in linear equality constraints in the optimization program. Thus, the flow estimation can be formed as an optimization problem and efficiently solved. The effectiveness of the proposed method was substantiated by a large-scale field experiment in the Sacramento-San Joaquin River Delta in California. A fleet of 100 sensors developed at the University of California, Berkeley, were deployed in Walnut Grove, CA, to collect a set of <span class="hlt">Lagrangian</span> data, a time series of positions as the sensors moved through the water. Measurements were also taken from <span class="hlt">Eulerian</span> sensors in the region, provided by the United States Geological Survey. It is shown that the proposed method can effectively integrate <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> measurement data, resulting in a suited estimation of the flow variables within the hydraulic system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1122032','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1122032"><span>Development of <span class="hlt">Eulerian</span> <span class="hlt">Code</span> Modeling for ICF Experiments</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Bradley, Paul A.</p> <p>2014-02-27</p> <p>One of the most pressing unexplained phenomena standing in the way of ICF ignition is understanding mix and how it interacts with burn. Experiments were being designed and fielded as part of the Defect-Induced Mix Experiment (DIME) project to obtain data about the extent of material mix and how this mix influenced burn. Experiments on the Omega laser and National Ignition Facility (NIF) provided detailed data for comparison to the <span class="hlt">Eulerian</span> <span class="hlt">code</span> RAGE1. The Omega experiments were able to resolve the mix and provide “proof of principle” support for subsequent NIF experiments, which were fielded from July 2012 through Junemore » 2013. The Omega shots were fired at least once per year between 2009 and 2012. RAGE was not originally designed to model inertial confinement fusion (ICF) implosions. It still lacks lasers, so the <span class="hlt">code</span> has been validated using an energy source. To test RAGE, the simulation output is compared to data and by means of postprocessing tools that were developed. Here, the various postprocessing tools are described with illustrative examples.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010AGUFMOS42A..05T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AGUFMOS42A..05T"><span>Modeling possible spreadings of a buoyant surface plume with <span class="hlt">lagrangian</span> and <span class="hlt">eulerian</span> approaches at different resolutions using flow syntheses from 1992-2007 - a Gulf of Mexico study</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tulloch, R.; Hill, C. N.; Jahn, O.</p> <p>2010-12-01</p> <p>We present results from an ensemble of BP oil spill simulations. The oil spill slick is modeled as a buoyant surface plume that is transported by ocean currents modulated, in some experiments, by surface winds. Ocean currents are taken from ECCO2 project (see http://ecco2.org ) observationally constrained state estimates spanning 1992-2007. In this work we (i) explore the role of increased resolution of ocean eddies, (ii) compare inferences from particle based, <span class="hlt">lagrangian</span>, approaches with <span class="hlt">eulerian</span>, field based, approaches and (ii) examine the impact of differential response of oil particles and water to normal and extreme, hurricane derived, wind stress. We focus on three main questions. Is the simulated response to an oil spill markedly different for different years, depending on ocean circulation and wind forcing? Does the simulated response depend heavily on resolution and are <span class="hlt">lagrangian</span> and <span class="hlt">eulerian</span> estimates comparable? We start from two regional configurations of the MIT General Circulation Model (MITgcm - see http://mitgcm.org ) at 16km and 4km resolutions respectively, both covering the Gulf of Mexico and western North Atlantic regions. The simulations are driven at open boundaries with momentum and hydrographic fields from ECCO2 observationally constrained global circulation estimates. The time dependent surface flow fields from these simulations are used to transport a dye that can optionally decay over time (approximating biological breakdown) and to transport <span class="hlt">lagrangian</span> particles. Using these experiments we examine the robustness of conclusions regarding the fate of a buoyant slick, injected at a single point. In conclusion we discuss how future drilling operations could use similar approaches to better anticipate outcomes of accidents both in this region and elsewhere.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JGRC..123..759C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JGRC..123..759C"><span>Nitrate Sources, Supply, and Phytoplankton Growth in the Great Australian Bight: An <span class="hlt">Eulerian-Lagrangian</span> Modeling Approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cetina-Heredia, Paulina; van Sebille, Erik; Matear, Richard J.; Roughan, Moninya</p> <p>2018-02-01</p> <p>The Great Australian Bight (GAB), a coastal sea bordered by the Pacific, Southern, and Indian Oceans, sustains one of the largest fisheries in Australia but the geographical origin of nutrients that maintain its productivity is not fully known. We use 12 years of modeled data from a coupled hydrodynamic and biogeochemical model and an <span class="hlt">Eulerian-Lagrangian</span> approach to quantify nitrate supply to the GAB and the region between the GAB and the Subantarctic Australian Front (GAB-SAFn), identify phytoplankton growth within the GAB, and ascertain the source of nitrate that fuels it. We find that nitrate concentrations have a decorrelation timescale of ˜60 days; since most of the water from surrounding oceans takes longer than 60 days to reach the GAB, 23% and 75% of nitrate used by phytoplankton to grow are sourced within the GAB and from the GAB-SAFn, respectively. Thus, most of the nitrate is recycled locally. Although nitrate concentrations and fluxes into the GAB are greater below 100 m than above, 79% of the nitrate fueling phytoplankton growth is sourced from above 100 m. Our findings suggest that topographical uplift and stratification erosion are key mechanisms delivering nutrients from below the nutricline into the euphotic zone and triggering large phytoplankton growth. We find annual and semiannual periodicities in phytoplankton growth, peaking in the austral spring and autumn when the mixed layer deepens leading to a subsurface maximum of phytoplankton growth. This study highlights the importance of examining phytoplankton growth at depth and the utility of <span class="hlt">Lagrangian</span> approaches.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AtmEn..45..839O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AtmEn..45..839O"><span>Development and evaluation of GRAL-C dispersion model, a hybrid <span class="hlt">Eulerian-Lagrangian</span> approach capturing NO-NO 2-O 3 chemistry</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Oettl, Dietmar; Uhrner, Ulrich</p> <p>2011-02-01</p> <p>Based on two recent publications using <span class="hlt">Lagrangian</span> dispersion models to simulate NO-NO 2-O 3 chemistry for industrial plumes, a similar modified approach was implemented using GRAL-C ( Graz <span class="hlt">Lagrangian</span> Model with Chemistry) and tested on two urban applications. In the hybrid dispersion model GRAL-C, the transport and turbulent diffusion of primary species such as NO and NO 2 are treated in a <span class="hlt">Lagrangian</span> framework while those of O 3 are treated in an <span class="hlt">Eulerian</span> framework. GRAL-C was employed on a one year street canyon simulation in Berlin and on a four-day simulation during a winter season in Graz, the second biggest city in Austria. In contrast to Middleton D.R., Jones A.R., Redington A.L., Thomson D.J., Sokhi R.S., Luhana L., Fisher B.E.A. (2008. <span class="hlt">Lagrangian</span> modelling of plume chemistry for secondary pollutants in large industrial plumes. Atmospheric Environment 42, 415-427) and Alessandrini S., Ferrero E. (2008. A <span class="hlt">Lagrangian</span> model with chemical reactions: application in real atmosphere. Proceedings of the 12th Int. Conf. on Harmonization within atmospheric dispersion modelling for regulatory purposes. Croatian Meteorological Journal, 43, ISSN: 1330-0083, 235-239) the treatment of ozone was modified in order to facilitate urban scale simulations encompassing dense road networks. For the street canyon application, modelled daily mean NO x/NO 2 concentrations deviated by +0.4%/-15% from observations, while the correlations for NO x and NO 2 were 0.67 and 0.76 respectively. NO 2 concentrations were underestimated in summer, but were captured well for other seasons. In Graz a fair agreement for NO x and NO 2 was obtained between observed and modelled values for NO x and NO 2. Simulated diurnal cycles of NO 2 and O 3 matched observations reasonably well, although O 3 was underestimated during the day. A possible explanation here might lie in the non-consideration of volatile organic compounds (VOCs) chemistry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/332751','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/332751"><span>ALEGRA -- A massively parallel h-adaptive <span class="hlt">code</span> for solid dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Summers, R.M.; Wong, M.K.; Boucheron, E.A.</p> <p>1997-12-31</p> <p>ALEGRA is a multi-material, arbitrary-<span class="hlt">Lagrangian-Eulerian</span> (ALE) <span class="hlt">code</span> for solid dynamics designed to run on massively parallel (MP) computers. It combines the features of modern <span class="hlt">Eulerian</span> shock <span class="hlt">codes</span>, such as CTH, with modern <span class="hlt">Lagrangian</span> structural analysis <span class="hlt">codes</span> using an unstructured grid. ALEGRA is being developed for use on the teraflop supercomputers to conduct advanced three-dimensional (3D) simulations of shock phenomena important to a variety of systems. ALEGRA was designed with the Single Program Multiple Data (SPMD) paradigm, in which the mesh is decomposed into sub-meshes so that each processor gets a single sub-mesh with approximately the same number of elements. Usingmore » this approach the authors have been able to produce a single <span class="hlt">code</span> that can scale from one processor to thousands of processors. A current major effort is to develop efficient, high precision simulation capabilities for ALEGRA, without the computational cost of using a global highly resolved mesh, through flexible, robust h-adaptivity of finite elements. H-adaptivity is the dynamic refinement of the mesh by subdividing elements, thus changing the characteristic element size and reducing numerical error. The authors are working on several major technical challenges that must be met to make effective use of HAMMER on MP computers.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000021221','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000021221"><span>Unsteady Cascade Aerodynamic Response Using a Multiphysics Simulation <span class="hlt">Code</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lawrence, C.; Reddy, T. S. R.; Spyropoulos, E.</p> <p>2000-01-01</p> <p>The multiphysics <span class="hlt">code</span> Spectrum(TM) is applied to calculate the unsteady aerodynamic pressures of oscillating cascade of airfoils representing a blade row of a turbomachinery component. Multiphysics simulation is based on a single computational framework for the modeling of multiple interacting physical phenomena, in the present case being between fluids and structures. Interaction constraints are enforced in a fully coupled manner using the augmented-<span class="hlt">Lagrangian</span> method. The arbitrary <span class="hlt">Lagrangian-Eulerian</span> method is utilized to account for deformable fluid domains resulting from blade motions. Unsteady pressures are calculated for a cascade designated as the tenth standard, and undergoing plunging and pitching oscillations. The predicted unsteady pressures are compared with those obtained from an unsteady Euler <span class="hlt">co-de</span> refer-red in the literature. The Spectrum(TM) <span class="hlt">code</span> predictions showed good correlation for the cases considered.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22373526-lagrangian-eulerian-real-fourier-all-approaches-large-scale-structure-created-equal','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22373526-lagrangian-eulerian-real-fourier-all-approaches-large-scale-structure-created-equal"><span><span class="hlt">Lagrangian</span> or <span class="hlt">Eulerian</span>; real or Fourier? Not all approaches to large-scale structure are created equal</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Tassev, Svetlin, E-mail: tassev@astro.princeton.edu</p> <p></p> <p>We present a pedagogical systematic investigation of the accuracy of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> perturbation theories of large-scale structure. We show that significant differences exist between them especially when trying to model the Baryon Acoustic Oscillations (BAO). We find that the best available model of the BAO in real space is the Zel'dovich Approximation (ZA), giving an accuracy of ∼<3% at redshift of z = 0 in modelling the matter 2-pt function around the acoustic peak. All corrections to the ZA around the BAO scale are perfectly perturbative in real space. Any attempt to achieve better precision requires calibrating the theorymore » to simulations because of the need to renormalize those corrections. In contrast, theories which do not fully preserve the ZA as their solution, receive O(1) corrections around the acoustic peak in real space at z = 0, and are thus of suspicious convergence at low redshift around the BAO. As an example, we find that a similar accuracy of 3% for the acoustic peak is achieved by <span class="hlt">Eulerian</span> Standard Perturbation Theory (SPT) at linear order only at z ≈ 4. Thus even when SPT is perturbative, one needs to include loop corrections for z∼<4 in real space. In Fourier space, all models perform similarly, and are controlled by the overdensity amplitude, thus recovering standard results. However, that comes at a price. Real space cleanly separates the BAO signal from non-linear dynamics. In contrast, Fourier space mixes signal from short mildly non-linear scales with the linear signal from the BAO to the level that non-linear contributions from short scales dominate. Therefore, one has little hope in constructing a systematic theory for the BAO in Fourier space.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910015431','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910015431"><span>Parallel computing using a <span class="hlt">Lagrangian</span> formulation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, May-Fun; Loh, Ching Yuen</p> <p>1991-01-01</p> <p>A new <span class="hlt">Lagrangian</span> formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The <span class="hlt">Lagrangian</span> formulation represents the inherent parallelism of the flow field better than the common <span class="hlt">Eulerian</span> formulation and offers a competitive alternative on parallel computers. The implementation of the <span class="hlt">Lagrangian</span> formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950059889&hterms=fun&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfun','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950059889&hterms=fun&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfun"><span>Parallel computing using a <span class="hlt">Lagrangian</span> formulation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, May-Fun; Loh, Ching-Yuen</p> <p>1992-01-01</p> <p>This paper adopts a new <span class="hlt">Lagrangian</span> formulation of the Euler equation for the calculation of two dimensional supersonic steady flow. The <span class="hlt">Lagrangian</span> formulation represents the inherent parallelism of the flow field better than the common <span class="hlt">Eulerian</span> formulation and offers a competitive alternative on parallel computers. The implementation of the <span class="hlt">Lagrangian</span> formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, we have achieved better than six times speed-up on a 8192-processor CM-2 over a single processor of a CRAY-2.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1911392T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1911392T"><span>Mass and tracer transport within oceanic <span class="hlt">Lagrangian</span> coherent vortices as diagnosed in a global mesoscale eddying climate model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tarshish, Nathaniel; Abernathey, Ryan; Dufour, Carolina; Frenger, Ivy; Griffies, Stephen</p> <p>2017-04-01</p> <p>Transient ocean mesoscale fluctuations play a central role in the global climate system, transporting climate relevant tracers such as heat and carbon. In satellite observations and numerical simulations, mesoscale vortices feature prominently as collectively rotating regions that remain visibly coherent. Prior studies on transport from ocean vortices typically rely on <span class="hlt">Eulerian</span> identification methods, in which vortices are identified by selecting closed contours of <span class="hlt">Eulerian</span> fields (e.g. sea surface height, or the Okubo-Weiss parameter) that satisfy geometric criteria and anomaly thresholds. In contrast, recent studies employ <span class="hlt">Lagrangian</span> analysis of virtual particle trajectories initialized within the selected <span class="hlt">Eulerian</span> contours, revealing significant discrepancies between the advection of the contour's material interior and the evolution of the <span class="hlt">Eulerian</span> field contour. This work investigates the global mass and tracer transport associated with materially coherent surface ocean vortices. Further, it addresses differences between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> analyses for the detection of vortices. To do so, we use GFDL's CM2.6 coupled climate model with 5-10km horizontal grid spacing. We identify coherent vortices in CM2.6 by implementing the Rotationally Coherent <span class="hlt">Lagrangian</span> Vortex (RCLV) framework, which recently emerged from dynamical systems theory. This approach involves the numerical advection of millions of <span class="hlt">Lagrangian</span> particles and guarantees material coherence by construction. We compute the statistics, spatial distribution, and lifetimes of coherent vortices in addition to calculating the associated mass and tracer transports. We offer compelling evidence that <span class="hlt">Eulerian</span> vortex methods are poorly suited to answer questions of mass and tracer transport.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012EGUGA..1413605S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012EGUGA..1413605S"><span>An online-coupled NWP/ACT model with conserved <span class="hlt">Lagrangian</span> levels</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sørensen, B.; Kaas, E.; Lauritzen, P. H.</p> <p>2012-04-01</p> <p>Numerical weather and climate modelling is under constant development. Semi-implicit semi-<span class="hlt">Lagrangian</span> (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-<span class="hlt">Lagrangian</span> schemes with quasi-<span class="hlt">Lagrangian</span> vertical coordinates the <span class="hlt">Lagrangian</span> levels are remapped to <span class="hlt">Eulerian</span> model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-<span class="hlt">Lagrangian</span> advection method is introduced, it combines an inherently mass conserving 2D semi-<span class="hlt">Lagrangian</span> scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully <span class="hlt">Lagrangian</span> vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the <span class="hlt">Lagrangian</span> levels suffer from traditional <span class="hlt">Lagrangian</span> limitations caused by the convergence and divergence of the flow, remappings to the <span class="hlt">Eulerian</span> model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AtmEn.170....1P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AtmEn.170....1P"><span>Improved quantification of CO2 emission at Campi Flegrei by combined <span class="hlt">Lagrangian</span> Stochastic and <span class="hlt">Eulerian</span> dispersion modelling</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pedone, Maria; Granieri, Domenico; Moretti, Roberto; Fedele, Alessandro; Troise, Claudia; Somma, Renato; De Natale, Giuseppe</p> <p>2017-12-01</p> <p>This study investigates fumarolic CO2 emissions at Campi Flegrei (Southern Italy) and their dispersion in the lowest atmospheric boundary layer. We innovatively utilize a <span class="hlt">Lagrangian</span> Stochastic dispersion model (WindTrax) combined with an <span class="hlt">Eulerian</span> model (DISGAS) to diagnose the dispersion of diluted gas plumes over large and complex topographic domains. New measurements of CO2 concentrations acquired in February and October 2014 in the area of Pisciarelli and Solfatara, the two major fumarolic fields of Campi Flegrei caldera, and simultaneous measurements of meteorological parameters are used to: 1) test the ability of WindTrax to calculate the fumarolic CO2 flux from the investigated sources, and 2) perform predictive numerical simulations to resolve the mutual interference between the CO2 emissions of the two adjacent areas. This novel approach allows us to a) better quantify the CO2 emission of the fumarolic source, b) discriminate ;true; CO2 contributions for each source, and c) understand the potential impact of the composite CO2 plume (Pisciarelli ;plus; Solfatara) on the highly populated areas inside the Campi Flegrei caldera.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70016855','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70016855"><span>Solution of the advection-dispersion equation by a finite-volume <span class="hlt">eulerian-lagrangian</span> local adjoint method</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Healy, R.W.; Russell, T.F.</p> <p>1992-01-01</p> <p>A finite-volume <span class="hlt">Eulerian-Lagrangian</span> local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li class="active"><span>6</span></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_6 --> <div id="page_7" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li class="active"><span>7</span></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="121"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930017014','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930017014"><span>An extended <span class="hlt">Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, Meng-Sing</p> <p>1992-01-01</p> <p>A unique formulation of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous <span class="hlt">Lagrangian</span> methods. Unlike the <span class="hlt">Lagrangian</span> method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21279359','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21279359"><span>Differential geometry based solvation model II: <span class="hlt">Lagrangian</span> formulation.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Chen, Zhan; Baker, Nathan A; Wei, G W</p> <p>2011-12-01</p> <p>Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a <span class="hlt">Lagrangian</span> formulation of our differential geometry based solvation models. The <span class="hlt">Lagrangian</span> representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the <span class="hlt">Lagrangian</span> representation does not need to resort to artificially enlarged van der Waals radii as often required by the <span class="hlt">Eulerian</span> representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the <span class="hlt">Lagrangian</span> representation, the resulting potential-driven geometric flow equation is embedded into the <span class="hlt">Eulerian</span> representation for the purpose of</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3113640','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3113640"><span>Differential geometry based solvation model II: <span class="hlt">Lagrangian</span> formulation</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Chen, Zhan; Baker, Nathan A.; Wei, G. W.</p> <p>2010-01-01</p> <p>Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a <span class="hlt">Lagrangian</span> formulation of our differential geometry based solvation model. The <span class="hlt">Lagrangian</span> representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the <span class="hlt">Lagrangian</span> representation does not need to resort to artificially enlarged van der Waals radii as often required by the <span class="hlt">Eulerian</span> representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the <span class="hlt">Lagrangian</span> representation, the resulting potential-driven geometric flow equation is embedded into the <span class="hlt">Eulerian</span> representation for</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhFl...28f1901S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhFl...28f1901S"><span>An unstructured mesh arbitrary <span class="hlt">Lagrangian-Eulerian</span> unsteady incompressible flow solver and its application to insect flight aerodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Su, Xiaohui; Cao, Yuanwei; Zhao, Yong</p> <p>2016-06-01</p> <p>In this paper, an unstructured mesh Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CompM..50..805L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CompM..50..805L"><span>A coupled PFEM-<span class="hlt">Eulerian</span> approach for the solution of porous FSI problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Larese, A.; Rossi, R.; Oñate, E.; Idelsohn, S. R.</p> <p>2012-12-01</p> <p>This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well as in its vicinity. A combination of a <span class="hlt">Lagrangian</span> model for the structural behavior and an <span class="hlt">Eulerian</span> approach for the fluid is used. The particle finite element method is adopted for the evaluation of the structural response, whereas an <span class="hlt">Eulerian</span> fixed-mesh approach is employed for the fluid. The free surface is tracked by the use of a level set technique. The numerical results are validated with experiments on scale models rockfill dams.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035994&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035994&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary-layer separation. II - The spinning sphere</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Van Dommelen, Leon L.</p> <p>1990-01-01</p> <p>A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A <span class="hlt">Lagrangian</span> numerical scheme is developed which gives results in good agreement with <span class="hlt">Eulerian</span> computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the <span class="hlt">Eulerian</span> structure, including the presence of logarithmic terms. Further, while the <span class="hlt">Eulerian</span> computations broke down at the first occurrence of separation, it is found that the <span class="hlt">Lagrangian</span> computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5643019','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5643019"><span>Acoustic streaming: an arbitrary Lagrangian–<span class="hlt">Eulerian</span> perspective</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco</p> <p>2017-01-01</p> <p>We analyse acoustic streaming flows using an arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the <span class="hlt">Lagrangian</span> flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the <span class="hlt">Lagrangian</span> velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid–structure interaction problems in microacoustofluidic devices. After the formulation’s exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches. PMID:29051631</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26753780','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26753780"><span>Geometric effects in microfluidics on heterogeneous cell stress using an <span class="hlt">Eulerian-Lagrangian</span> approach.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Warren, K M; Mpagazehe, J N; LeDuc, P R; Higgs, C F</p> <p>2016-02-07</p> <p>The response of individual cells at the micro-scale in cell mechanics is important in understanding how they are affected by changing environments. To control cell stresses, microfluidics can be implemented since there is tremendous control over the geometry of the devices. Designing microfluidic devices to induce and manipulate stress levels on biological cells can be aided by computational modeling approaches. Such approaches serve as an efficient precursor to fabricating various microfluidic geometries that induce predictable levels of stress on biological cells, based on their mechanical properties. Here, a three-dimensional, multiphase computational fluid dynamics (CFD) modeling approach was implemented for soft biological materials. The computational model incorporates the physics of the particle dynamics, fluid dynamics and solid mechanics, which allows us to study how stresses affect the cells. By using an <span class="hlt">Eulerian-Lagrangian</span> approach to treat the fluid domain as a continuum in the microfluidics, we are conducting studies of the cells' movement and the stresses applied to the cell. As a result of our studies, we were able to determine that a channel with periodically alternating columns of obstacles was capable of stressing cells at the highest rate, and that microfluidic systems can be engineered to impose heterogenous cell stresses through geometric configuring. We found that when using controlled geometries of the microfluidics channels with staggered obstructions, we could increase the maximum cell stress by nearly 200 times over cells flowing through microfluidic channels with no obstructions. Incorporating computational modeling in the design of microfluidic configurations for controllable cell stressing could help in the design of microfludic devices for stressing cells such as cell homogenizers.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUOSEC14C1023C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUOSEC14C1023C"><span>On modeling heterogeneous coastal sediment transport - A numerical study using multiphase <span class="hlt">Eulerian</span> and Euler-<span class="hlt">Lagrangian</span> approaches</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cheng, Z.; Yu, X.; Hsu, T. J.; Calantoni, J.; Chauchat, J.</p> <p>2016-02-01</p> <p>Regional scale coastal evolution models do not explicitly resolve wave-driven sediment transport and must rely on bedload/suspended modules that utilize empirical assumptions. Under extreme wave events or in regions of high sediment heterogeneity, these empirical bedload/suspended load modules may need to be reevaluated with detailed observation and more sophisticated small-scale models. In the past decade, significant research efforts have been devoted to modeling sediment transport using multiphase <span class="hlt">Eulerian</span> or Euler-<span class="hlt">Lagrangian</span> approaches. Recently, an open-source multi-dimensional Reynolds-averaged two-phase sediment transport model, SedFOAM is developed by the authors and it has been adopted by many researchers to study momentary bed failure, granular rheology in sheet flow and scour around structures. In this abstract, we further report our recent progress made in extending the model with 3D turbulence-resolving capability and to model the sediment phase with the Discrete Element method (DEM). Adopting the large-eddy simulation methodology, we validate the 3D model with measured fine sediment transport is oscillatory sheet flow and demonstrate that the model is able to resolve sediment burst events during flow reversals. To better resolve the intergranular interactions and to model heterogeneous properties of sediment (e.g., mixed grain sizes and grain shape), we use an Euler-<span class="hlt">Lagrangian</span> solver called CFDEM, which couples OpenFOAM for the fluid phase and LIGGGHTS for the particle phase. We improve the model by better enforcing conservation of mass in the pressure solver. The modified CFDEM solver is validated with measured oscillatory sheet flow data for coarse sand and we demonstrated that the model can reproduce the well-known armoring effects. We show that under Stokes second-order wave forcing, the armoring effect is more significant during the energetic positive peak, and hence the net onshore transport is reduced. Preliminary results modeling the shape</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950063861&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950063861&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing"><span>An extended <span class="hlt">Lagrangian</span> method for subsonic flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, Meng-Sing; Loh, Ching Y.</p> <p>1992-01-01</p> <p>It is well known that fluid motion can be specified by either the <span class="hlt">Eulerian</span> of <span class="hlt">Lagrangian</span> description. Most of Computational Fluid Dynamics (CFD) developments over the last three decades have been based on the <span class="hlt">Eulerian</span> description and considerable progress has been made. In particular, the upwind methods, inspired and guided by the work of Gudonov, have met with many successes in dealing with complex flows, especially where discontinuities exist. However, this shock capturing property has proven to be accurate only when the discontinuity is aligned with one of the grid lines since most upwind methods are strictly formulated in 1-D framework and only formally extended to multi-dimensions. Consequently, the attractive property of crisp resolution of these discontinuities is lost and research on genuine multi-dimensional approach has just been undertaken by several leading researchers. Nevertheless they are still based on the <span class="hlt">Eulerian</span> description.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25127407','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25127407"><span>Dynamic analysis of a needle insertion for soft materials: Arbitrary <span class="hlt">Lagrangian-Eulerian</span>-based three-dimensional finite element analysis.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Yamaguchi, Satoshi; Tsutsui, Kihei; Satake, Koji; Morikawa, Shigehiro; Shirai, Yoshiaki; Tanaka, Hiromi T</p> <p>2014-10-01</p> <p>Our goal was to develop a three-dimensional finite element model that enables dynamic analysis of needle insertion for soft materials. To demonstrate large deformation and fracture, we used the arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) method for fluid analysis. We performed ALE-based finite element analysis for 3% agar gel and three types of copper needle with bevel tips. To evaluate simulation results, we compared the needle deflection and insertion force with corresponding experimental results acquired with a uniaxial manipulator. We studied the shear stress distribution of agar gel on various time scales. For 30°, 45°, and 60°, differences in deflections of each needle between both sets of results were 2.424, 2.981, and 3.737mm, respectively. For the insertion force, there was no significant difference for mismatching area error (p<0.05) between simulation and experimental results. Our results have the potential to be a stepping stone to develop pre-operative surgical planning to estimate an optimal needle insertion path for MR image-guided microwave coagulation therapy and for analyzing large deformation and fracture in biological tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://water.usgs.gov/nrp/gwsoftware/moc3d/doc/moc3dv3.5.pdf','USGSPUBS'); return false;" href="http://water.usgs.gov/nrp/gwsoftware/moc3d/doc/moc3dv3.5.pdf"><span>A three-dimensional finite-volume <span class="hlt">Eulerian-Lagrangian</span> Localized Adjoint Method (ELLAM) for solute-transport modeling</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Heberton, C.I.; Russell, T.F.; Konikow, Leonard F.; Hornberger, G.Z.</p> <p>2000-01-01</p> <p>This report documents the U.S. Geological Survey <span class="hlt">Eulerian-Lagrangian</span> Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20030052220','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20030052220"><span>A Vertically <span class="hlt">Lagrangian</span> Finite-Volume Dynamical Core for Global Models</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lin, Shian-Jiann</p> <p>2003-01-01</p> <p>A finite-volume dynamical core with a terrain-following <span class="hlt">Lagrangian</span> control-volume discretization is described. The vertically <span class="hlt">Lagrangian</span> discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-<span class="hlt">Lagrangian</span>-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-<span class="hlt">Lagrangian</span> algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the <span class="hlt">Lagrangian</span> dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating <span class="hlt">Lagrangian</span> control-volume to an <span class="hlt">Eulerian</span> terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the <span class="hlt">Lagrangian</span> surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930061006&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930061006&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing"><span>An extended <span class="hlt">Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, Meng-Sing</p> <p>1993-01-01</p> <p>A unique formulation of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous <span class="hlt">Lagrangian</span> methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70020645','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70020645"><span>Solution of the advection-dispersion equation in two dimensions by a finite-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Healy, R.W.; Russell, T.F.</p> <p>1998-01-01</p> <p>We extend the finite-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009EGUGA..1110202W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009EGUGA..1110202W"><span>ATLAS - A new <span class="hlt">Lagrangian</span> transport and mixing model with detailed stratospheric chemistry</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wohltmann, I.; Rex, M.; Lehmann, R.</p> <p>2009-04-01</p> <p>We present a new global Chemical Transport Model (CTM) with full stratospheric chemistry and <span class="hlt">Lagrangian</span> transport and mixing called ATLAS. <span class="hlt">Lagrangian</span> models have some crucial advantages over <span class="hlt">Eulerian</span> grid-box based models, like no numerical diffusion, no limitation of the time step of the model by the CFL criterion, conservation of mixing ratios by design and easy parallelization of <span class="hlt">code</span>. The transport module is based on a trajectory <span class="hlt">code</span> developed at the Alfred Wegener Institute. The horizontal and vertical resolution, the vertical coordinate system (pressure, potential temperature, hybrid coordinate) and the time step of the model are flexible, so that the model can be used both for process studies and long-time runs over several decades. Mixing of the <span class="hlt">Lagrangian</span> air parcels is parameterized based on the local shear and strain of the flow with a method similar to that used in the CLaMS model, but with some modifications like a triangulation that introduces no vertical layers. The stratospheric chemistry module was developed at the Institute and includes 49 species and 170 reactions and a detailed treatment of heterogenous chemistry on polar stratospheric clouds. We present an overview over the model architecture, the transport and mixing concept and some validation results. Comparison of model results with tracer data from flights of the ER2 aircraft in the stratospheric polar vortex in 1999/2000 which are able to resolve fine tracer filaments show that excellent agreement with observed tracer structures can be achieved with a suitable mixing parameterization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AdWR..113..141E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AdWR..113..141E"><span>Shear and shearless <span class="hlt">Lagrangian</span> structures in compound channels</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Enrile, F.; Besio, G.; Stocchino, A.</p> <p>2018-03-01</p> <p>Transport processes in a physical model of a natural stream with a composite cross-section (compound channel) are investigated by means of a <span class="hlt">Lagrangian</span> analysis based on nonlinear dynamical system theory. Two-dimensional free surface <span class="hlt">Eulerian</span> experimental velocity fields of a uniform flow in a compound channel form the basis for the identification of the so-called <span class="hlt">Lagrangian</span> Coherent Structures. <span class="hlt">Lagrangian</span> structures are recognized as the key features that govern particle trajectories. We seek for two particular class of <span class="hlt">Lagrangian</span> structures: Shear and shearless structures. The former are generated whenever the shear dominates the flow whereas the latter behave as jet-cores. These two type of structures are detected as ridges and trenches of the Finite-Time Lyapunov Exponents fields, respectively. Besides, shearlines computed applying the geodesic theory of transport barriers mark Shear <span class="hlt">Lagrangian</span> Coherent Structures. So far, the detection of these structures in real experimental flows has not been deeply investigated. Indeed, the present results obtained in a wide range of the controlling parameters clearly show a different behaviour depending on the shallowness of the flow. Shear and Shearless <span class="hlt">Lagrangian</span> Structures detected from laboratory experiments clearly appear as the flow develops in shallow conditions. The presence of these <span class="hlt">Lagrangian</span> Structures tends to fade in deep flow conditions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011APS..DFD.G6009Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..DFD.G6009Y"><span><span class="hlt">Lagrangian</span> statistics in compressible isotropic homogeneous turbulence</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yang, Yantao; Wang, Jianchun; Shi, Yipeng; Chen, Shiyi</p> <p>2011-11-01</p> <p>In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the <span class="hlt">Lagrangian</span> point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the <span class="hlt">Eulerian</span> field solver which was developed by Wang et al. (2010, J. Comp. Phys., 229, 5257-5279), and a <span class="hlt">Lagrangian</span> module for tracking the tracers and recording the data. The <span class="hlt">Lagrangian</span> probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The <span class="hlt">Lagrangian</span> structure functions and cross-correlation between various quantities will also be discussed. This work was supported in part by the China's Turbulence Program under Grant No.2009CB724101.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018GMD....11..103G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018GMD....11..103G"><span><span class="hlt">Lagrangian</span> condensation microphysics with Twomey CCN activation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Grabowski, Wojciech W.; Dziekan, Piotr; Pawlowska, Hanna</p> <p>2018-01-01</p> <p>We report the development of a novel <span class="hlt">Lagrangian</span> microphysics methodology for simulations of warm ice-free clouds. The approach applies the traditional <span class="hlt">Eulerian</span> method for the momentum and continuous thermodynamic fields such as the temperature and water vapor mixing ratio, and uses <span class="hlt">Lagrangian</span> <q>super-droplets</q> to represent condensed phase such as cloud droplets and drizzle or rain drops. In other applications of the <span class="hlt">Lagrangian</span> warm-rain microphysics, the super-droplets outside clouds represent unactivated cloud condensation nuclei (CCN) that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows for the detailed study of not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in <span class="hlt">Eulerian</span> bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other formulation of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology, focusing on the activation and diffusional growth. Details of the activation</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22482465-lagrangian-flows-within-reflecting-internal-waves-horizontal-free-slip-surface','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22482465-lagrangian-flows-within-reflecting-internal-waves-horizontal-free-slip-surface"><span><span class="hlt">Lagrangian</span> flows within reflecting internal waves at a horizontal free-slip surface</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk; Diamessis, Peter J.</p> <p></p> <p>In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider <span class="hlt">Lagrangian</span> flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking <span class="hlt">Lagrangian</span> fluid particles in direct numerical simulation (DNS) datasets of the <span class="hlt">Eulerian</span> flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that <span class="hlt">Eulerian</span> mean flow due to wave-wave interaction and wave-induced Stokes driftmore » cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero <span class="hlt">Lagrangian</span> mean flow up to that order. However, high-accuracy particle tracking in finite-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean <span class="hlt">Lagrangian</span> flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean <span class="hlt">Lagrangian</span> drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li class="active"><span>7</span></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_7 --> <div id="page_8" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li class="active"><span>8</span></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="141"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CNSNS..20..516I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CNSNS..20..516I"><span>Transport induced by mean-eddy interaction: I. Theory, and relation to <span class="hlt">Lagrangian</span> lobe dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ide, Kayo; Wiggins, Stephen</p> <p>2015-02-01</p> <p>In this paper we develop a method for the estimation of Transport Induced by the Mean-Eddy interaction (TIME) in two-dimensional unsteady flows. The method is based on the dynamical systems approach to fluid transport and can be viewed as a hybrid combination of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> methods. The (<span class="hlt">Eulerian</span>) boundaries across which we consider (<span class="hlt">Lagrangian</span>) transport are kinematically defined by appropriately chosen streamlines of the mean flow. By evaluating the impact of the mean-eddy interaction on transport, the TIME method can be used as a diagnostic tool for transport processes that occur during a specified time interval along a specified boundary segment. We introduce two types of TIME functions: one that quantifies the accumulation of flow properties and another that measures the displacement of the transport geometry. The spatial geometry of transport is described by the so-called pseudo-lobes, and temporal evolution of transport by their dynamics. In the case where the TIME functions are evaluated along a separatrix, the pseudo-lobes have a relationship to the lobes of <span class="hlt">Lagrangian</span> transport theory. In fact, one of the TIME functions is identical to the Melnikov function that is used to measure the distance, at leading order in a small parameter, between the two invariant manifolds that define the <span class="hlt">Lagrangian</span> lobes. We contrast the similarities and differences between the TIME and <span class="hlt">Lagrangian</span> lobe dynamics in detail. An application of the TIME method is carried out for inter-gyre transport in the wind-driven oceanic circulation model and a comparison with the <span class="hlt">Lagrangian</span> transport theory is made.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006JPhy4.133..587K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006JPhy4.133..587K"><span>Modeling NIF experimental designs with adaptive mesh refinement and <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Koniges, A. E.; Anderson, R. W.; Wang, P.; Gunney, B. T. N.; Becker, R.; Eder, D. C.; MacGowan, B. J.; Schneider, M. B.</p> <p>2006-06-01</p> <p>Incorporation of adaptive mesh refinement (AMR) into <span class="hlt">Lagrangian</span> hydrodynamics algorithms allows for the creation of a highly powerful simulation tool effective for complex target designs with three-dimensional structure. We are developing an advanced modeling tool that includes AMR and traditional arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) techniques. Our goal is the accurate prediction of vaporization, disintegration and fragmentation in National Ignition Facility (NIF) experimental target elements. Although our focus is on minimizing the generation of shrapnel in target designs and protecting the optics, the general techniques are applicable to modern advanced targets that include three-dimensional effects such as those associated with capsule fill tubes. Several essential computations in ordinary radiation hydrodynamics need to be redesigned in order to allow for AMR to work well with ALE, including algorithms associated with radiation transport. Additionally, for our goal of predicting fragmentation, we include elastic/plastic flow into our computations. We discuss the integration of these effects into a new ALE-AMR simulation <span class="hlt">code</span>. Applications of this newly developed modeling tool as well as traditional ALE simulations in two and three dimensions are applied to NIF early-light target designs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016TCry...10.1513R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016TCry...10.1513R"><span>Arctic sea-ice diffusion from observed and simulated <span class="hlt">Lagrangian</span> trajectories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rampal, Pierre; Bouillon, Sylvain; Bergh, Jon; Ólason, Einar</p> <p>2016-07-01</p> <p>We characterize sea-ice drift by applying a <span class="hlt">Lagrangian</span> diffusion analysis to buoy trajectories from the International Arctic Buoy Programme (IABP) dataset and from two different models: the standalone <span class="hlt">Lagrangian</span> sea-ice model neXtSIM and the <span class="hlt">Eulerian</span> coupled ice-ocean model used for the TOPAZ reanalysis. By applying the diffusion analysis to the IABP buoy trajectories over the period 1979-2011, we confirm that sea-ice diffusion follows two distinct regimes (ballistic and Brownian) and we provide accurate values for the diffusivity and integral timescale that could be used in <span class="hlt">Eulerian</span> or <span class="hlt">Lagrangian</span> passive tracers models to simulate the transport and diffusion of particles moving with the ice. We discuss how these values are linked to the evolution of the fluctuating displacements variance and how this information could be used to define the size of the search area around the position predicted by the mean drift. By comparing observed and simulated sea-ice trajectories for three consecutive winter seasons (2007-2011), we show how the characteristics of the simulated motion may differ from or agree well with observations. This comparison illustrates the usefulness of first applying a diffusion analysis to evaluate the output of modeling systems that include a sea-ice model before using these in, e.g., oil spill trajectory models or, more generally, to simulate the transport of passive tracers in sea ice.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960049629','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960049629"><span>Atomization simulations using an <span class="hlt">Eulerian-VOF-Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chen, Yen-Sen; Shang, Huan-Min; Liaw, Paul; Chen, C. P.</p> <p>1994-01-01</p> <p>This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a <span class="hlt">Lagrangian</span> tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservations are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present innovative approach by simulating benchmark problems including the coaxial jet atomization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.350...84S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.350...84S"><span>Parallel implementation of a <span class="hlt">Lagrangian</span>-based model on an adaptive mesh in C++: Application to sea-ice</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Samaké, Abdoulaye; Rampal, Pierre; Bouillon, Sylvain; Ólason, Einar</p> <p>2017-12-01</p> <p>We present a parallel implementation framework for a new dynamic/thermodynamic sea-ice model, called neXtSIM, based on the Elasto-Brittle rheology and using an adaptive mesh. The spatial discretisation of the model is done using the finite-element method. The temporal discretisation is semi-implicit and the advection is achieved using either a pure <span class="hlt">Lagrangian</span> scheme or an Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> scheme (ALE). The parallel implementation presented here focuses on the distributed-memory approach using the message-passing library MPI. The efficiency and the scalability of the parallel algorithms are illustrated by the numerical experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM <span class="hlt">code</span> is shown being sufficient to perform simulations for state-of-the-art sea ice forecasting and geophysical process studies over geographical domain of several millions squared kilometers like the Arctic region.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..96l3538A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..96l3538A"><span><span class="hlt">Lagrangian</span> theory of structure formation in relativistic cosmology. IV. <span class="hlt">Lagrangian</span> approach to gravitational waves</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Al Roumi, Fosca; Buchert, Thomas; Wiegand, Alexander</p> <p>2017-12-01</p> <p>The relativistic generalization of the Newtonian <span class="hlt">Lagrangian</span> perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of <span class="hlt">Lagrangian</span>-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the <span class="hlt">Lagrangian</span> perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to <span class="hlt">Eulerian</span> background coordinates with truncation of nonlinear terms.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950049365&hterms=niv&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dniv','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950049365&hterms=niv&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dniv"><span>A comparison of cosmological hydrodynamic <span class="hlt">codes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kang, Hyesung; Ostriker, Jeremiah P.; Cen, Renyue; Ryu, Dongsu; Hernquist, Lars; Evrard, August E.; Bryan, Greg L.; Norman, Michael L.</p> <p>1994-01-01</p> <p>We present a detailed comparison of the simulation results of various hydrodynamic <span class="hlt">codes</span>. Starting with identical initial conditions based on the cold dark matter scenario for the growth of structure, with parameters h = 0.5 Omega = Omega(sub b) = 1, and sigma(sub 8) = 1, we integrate from redshift z = 20 to z = O to determine the physical state within a representative volume of size L(exp 3) where L = 64 h(exp -1) Mpc. Five indenpendent <span class="hlt">codes</span> are compared: three of them <span class="hlt">Eulerian</span> mesh-based and two variants of the smooth particle hydrodynamics 'SPH' <span class="hlt">Lagrangian</span> approach. The <span class="hlt">Eulerian</span> <span class="hlt">codes</span> were run at N(exp 3) = (32(exp 3), 64(exp 3), 128(exp 3), and 256(exp 3)) cells, the SPH <span class="hlt">codes</span> at N(exp 3) = 32(exp 3) and 64(exp 3) particles. Results were then rebinned to a 16(exp 3) grid with the exception that the rebinned data should converge, by all techniques, to a common and correct result as N approaches infinity. We find that global averages of various physical quantities do, as expected, tend to converge in the rebinned model, but that uncertainites in even primitive quantities such as (T), (rho(exp 2))(exp 1/2) persists at the 3%-17% level achieve comparable and satisfactory accuracy for comparable computer time in their treatment of the high-density, high-temeprature regions as measured in the rebinned data; the variance among the five <span class="hlt">codes</span> (at highest resolution) for the mean temperature (as weighted by rho(exp 2) is only 4.5%. Examined at high resolution we suspect that the density resolution is better in the SPH <span class="hlt">codes</span> and the thermal accuracy in low-density regions better in the <span class="hlt">Eulerian</span> <span class="hlt">codes</span>. In the low-density, low-temperature regions the SPH <span class="hlt">codes</span> have poor accuracy due to statiscal effects, and the Jameson <span class="hlt">code</span> gives the temperatures which are too high, due to overuse of artificial viscosity in these high Mach number regions. Overall the comparison allows us to better estimate errors; it points to ways of improving this current generation ofhydrodynamic</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3462029','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3462029"><span><span class="hlt">Lagrangian</span> transport properties of pulmonary interfacial flows</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Smith, Bradford J.; Lukens, Sarah; Yamaguchi, Eiichiro; Gaver, Donald P.</p> <p>2012-01-01</p> <p>Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. Finite-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of <span class="hlt">Lagrangian</span> coherent structures (LCSs) and their effects on transport. The <span class="hlt">Lagrangian</span> perspective of these techniques reveals flow characteristics that are not readily apparent by observing <span class="hlt">Eulerian</span> measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary element method, and measured experimentally with micro particle image velocimetry (μ-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air–liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The <span class="hlt">Lagrangian</span> analysis is applied to velocity data measured with 0.01 mg ml−1 of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the <span class="hlt">Eulerian</span> frame. PMID:23049141</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/10145858-quality-factors-local-adaption-applications-eulerian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/10145858-quality-factors-local-adaption-applications-eulerian-hydrodynamics"><span>Quality factors and local adaption (with applications in <span class="hlt">Eulerian</span> hydrodynamics)</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Crowley, W.P.</p> <p>1992-06-17</p> <p>Adapting the mesh to suit the solution is a technique commonly used for solving both ode`s and pde`s. For <span class="hlt">Lagrangian</span> hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For <span class="hlt">Eulerian</span> hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to <span class="hlt">Eulerian</span> hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh elements. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/6551547-quality-factors-local-adaption-applications-eulerian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/6551547-quality-factors-local-adaption-applications-eulerian-hydrodynamics"><span>Quality factors and local adaption (with applications in <span class="hlt">Eulerian</span> hydrodynamics)</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Crowley, W.P.</p> <p>1992-06-17</p> <p>Adapting the mesh to suit the solution is a technique commonly used for solving both ode's and pde's. For <span class="hlt">Lagrangian</span> hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For <span class="hlt">Eulerian</span> hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to <span class="hlt">Eulerian</span> hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh elements. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24277435','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24277435"><span>Source apportion of atmospheric particulate matter: a joint <span class="hlt">Eulerian/Lagrangian</span> approach.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Riccio, A; Chianese, E; Agrillo, G; Esposito, C; Ferrara, L; Tirimberio, G</p> <p>2014-12-01</p> <p>PM2.5 samples were collected during an annual monitoring campaign (January 2012-January 2013) in the urban area of Naples, one of the major cities in Southern Italy. Samples were collected by means of a standard gravimetric sampler (Tecora Echo model) and characterized from a chemical point of view by ion chromatography. As a result, 143 samples together with their ionic composition have been collected. We extend traditional source apportionment techniques, usually based on multivariate factor analysis, interpreting the chemical analysis results within a <span class="hlt">Lagrangian</span> framework. The Hybrid Single-Particle <span class="hlt">Lagrangian</span> Integrated Trajectory Model (HYSPLIT) model was used, providing linkages to the source regions in the upwind areas. Results were analyzed in order to quantify the relative weight of different source types/areas. Model results suggested that PM concentrations are strongly affected not only by local emissions but also by transboundary emissions, especially from the Eastern and Northern European countries and African Saharan dust episodes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009EGUGA..11.5268B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009EGUGA..11.5268B"><span><span class="hlt">Eulerian</span> velocity reconstruction in ideal atmospheric dynamics using potential vorticity and potential temperature</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Blender, R.</p> <p>2009-04-01</p> <p>An approach for the reconstruction of atmospheric flow is presented which uses space- and time-dependent fields of density ?, potential vorticity Q and potential temperature Î& cedil;[J. Phys. A, 38, 6419 (2005)]. The method is based on the fundamental equations without approximation. The basic idea is to consider the time-dependent continuity equation as a condition for zero divergence of momentum in four dimensions (time and space, with unit velocity in time). This continuity equation is solved by an ansatz for the four-dimensional momentum using three conserved stream functions, the potential vorticity, potential temperature and a third field, denoted as ?-potential. In zonal flows, the ?-potential identifies the initial longitude of particles, whereas potential vorticity and potential temperature identify mainly meridional and vertical positions. Since the <span class="hlt">Lagrangian</span> tracers Q, Î&,cedil; and ? determine the <span class="hlt">Eulerian</span> velocity field, the reconstruction combines the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> view of hydrodynamics. In stationary flows, the ?-potential is related to the Bernoulli function. The approach requires that the gradients of the potential vorticity and potential temperature do not vanish when the velocity remains finite. This behavior indicates a possible interrelation with stability conditions. Examples with analytical solutions are presented for a Rossby wave and zonal and rotational shear flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1084178-multi-phase-cfd-modeling-solid-sorbent-carbon-capture-system','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1084178-multi-phase-cfd-modeling-solid-sorbent-carbon-capture-system"><span>Multi-Phase CFD Modeling of Solid Sorbent Carbon Capture System</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Ryan, Emily M.; DeCroix, David; Breault, Ronald W.</p> <p>2013-07-30</p> <p>Computational fluid dynamics (CFD) simulations are used to investigate a low temperature post-combustion carbon capture reactor. The CFD models are based on a small scale solid sorbent carbon capture reactor design from ADA-ES and Southern Company. The reactor is a fluidized bed design based on a silica-supported amine sorbent. CFD models using both <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> multi-phase modeling methods are developed to investigate the hydrodynamics and adsorption of carbon dioxide in the reactor. Models developed in both FLUENT® and BARRACUDA are presented to explore the strengths and weaknesses of state of the art CFD <span class="hlt">codes</span> for modeling multi-phase carbon capturemore » reactors. The results of the simulations show that the FLUENT® <span class="hlt">Eulerian-Lagrangian</span> simulations (DDPM) are unstable for the given reactor design; while the BARRACUDA <span class="hlt">Eulerian-Lagrangian</span> model is able to simulate the system given appropriate simplifying assumptions. FLUENT® <span class="hlt">Eulerian-Eulerian</span> simulations also provide a stable solution for the carbon capture reactor given the appropriate simplifying assumptions.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.usgs.gov/wri/1986/4145/report.pdf','USGSPUBS'); return false;" href="https://pubs.usgs.gov/wri/1986/4145/report.pdf"><span>Users manual for a one-dimensional <span class="hlt">Lagrangian</span> transport model</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Schoellhamer, D.H.; Jobson, H.E.</p> <p>1986-01-01</p> <p>A Users Manual for the <span class="hlt">Lagrangian</span> Transport Model (LTM) is presented. The LTM uses <span class="hlt">Lagrangian</span> calculations that are based on a reference frame moving with the river flow. The <span class="hlt">Lagrangian</span> reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used <span class="hlt">Eulerian</span> reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014SolED...6.1949T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014SolED...6.1949T"><span>ELEFANT: a user-friendly multipurpose geodynamics <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Thieulot, C.</p> <p>2014-07-01</p> <p>A new finite element <span class="hlt">code</span> for the solution of the Stokes and heat transport equations is presented. It has purposely been designed to address geological flow problems in two and three dimensions at crustal and lithospheric scales. The <span class="hlt">code</span> relies on the Marker-in-Cell technique and <span class="hlt">Lagrangian</span> markers are used to track materials in the simulation domain which allows recording of the integrated history of deformation; their (number) density is variable and dynamically adapted. A variety of rheologies has been implemented including nonlinear thermally activated dislocation and diffusion creep and brittle (or plastic) frictional models. The <span class="hlt">code</span> is built on the Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> kinematic description: the computational grid deforms vertically and allows for a true free surface while the computational domain remains of constant width in the horizontal direction. The solution to the large system of algebraic equations resulting from the finite element discretisation and linearisation of the set of coupled partial differential equations to be solved is obtained by means of the efficient parallel direct solver MUMPS whose performance is thoroughly tested, or by means of the WISMP and AGMG iterative solvers. The <span class="hlt">code</span> accuracy is assessed by means of many geodynamically relevant benchmark experiments which highlight specific features or algorithms, e.g., the implementation of the free surface stabilisation algorithm, the (visco-)plastic rheology implementation, the temperature advection, the capacity of the <span class="hlt">code</span> to handle large viscosity contrasts. A two-dimensional application to salt tectonics presented as case study illustrates the potential of the <span class="hlt">code</span> to model large scale high resolution thermo-mechanically coupled free surface flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcDyn..67.1567C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcDyn..67.1567C"><span>Laboratory experiment on the 3D tide-induced <span class="hlt">Lagrangian</span> residual current using the PIV technique</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chen, Yang; Jiang, Wensheng; Chen, Xu; Wang, Tao; Bian, Changwei</p> <p>2017-12-01</p> <p>The 3D structure of the tide-induced <span class="hlt">Lagrangian</span> residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced <span class="hlt">Lagrangian</span> residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the <span class="hlt">Lagrangian</span> residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> residual currents shows that the <span class="hlt">Eulerian</span> residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22661118-measurements-numerical-viscosity-resistivity-eulerian-mhd-codes','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22661118-measurements-numerical-viscosity-resistivity-eulerian-mhd-codes"><span>On the Measurements of Numerical Viscosity and Resistivity in <span class="hlt">Eulerian</span> MHD <span class="hlt">Codes</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Rembiasz, Tomasz; Obergaulinger, Martin; Cerdá-Durán, Pablo</p> <p>2017-06-01</p> <p>We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any <span class="hlt">Eulerian</span> MHD <span class="hlt">code</span>. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD <span class="hlt">code</span> Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, ofmore » the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012EGUGA..1412096D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012EGUGA..1412096D"><span>Mean <span class="hlt">Lagrangian</span> drift in continental shelf waves</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Drivdal, M.; Weber, J. E. H.</p> <p>2012-04-01</p> <p>The time- and depth-averaged mean drift induced by barotropic continental shelf waves (CSW's) is studied theoretically for idealized shelf topography by calculating the mean volume fluxes to second order in wave amplitude. The waves suffer weak spatial damping due to bottom friction, which leads to radiation stress forcing of the mean fluxes. In terms of the total wave energy density E¯ over the shelf region, the radiation stress tensor component S¯11 for CSW's is found to be different from that of shallow water surface waves in a non-rotating ocean. For CSW's, the ratio ¯S11/¯E depends strongly on the wave number. The mean <span class="hlt">Lagrangian</span> flow forced by the radiation stress can be subdivided into a Stokes drift and a mean <span class="hlt">Eulerian</span> drift current. The magnitude of the latter depends on the ratio between the radiation stress and the bottom stress acting on the mean flow. When the effect of bottom friction acts equally strong on the waves and the mean current, calculations for short CSW's show that the Stokes drift and the friction-dependent wave-induced mean <span class="hlt">Eulerian</span> current varies approximately in anti-phase over the shelf, and that the latter is numerically the largest. For long CSW's they are approximately in phase. In both cases the mean <span class="hlt">Lagrangian</span> current, which is responsible for the net particle drift, has its largest numerical value at the coast on the shallow part of the shelf. Enhancing the effect of bottom friction on the <span class="hlt">Eulerian</span> mean flow, results in a general current speed reduction, as well as a change in spatial structure for long waves. Applying realistic physical parameters for the continental shelf west of Norway, calculations yield along-shelf mean drift velocities for short CSW's that may be important for the transport of biological material, neutral tracers, and underwater plumes of dissolved oil from deep water drilling accidents.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhyA..506..350S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhyA..506..350S"><span>A new <span class="hlt">Eulerian</span> model for viscous and heat conducting compressible flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Svärd, Magnus</p> <p>2018-09-01</p> <p>In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the <span class="hlt">Lagrangian</span> derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely <span class="hlt">Eulerian</span> framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DPPJP8075B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DPPJP8075B"><span>Efficient simulation of pitch angle collisions in a 2+2-D <span class="hlt">Eulerian</span> Vlasov <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Banks, Jeff; Berger, R.; Brunner, S.; Tran, T.</p> <p>2014-10-01</p> <p>Here we discuss pitch angle scattering collisions in the context of the <span class="hlt">Eulerian</span>-based kinetic <span class="hlt">code</span> LOKI that evolves the Vlasov-Poisson system in 2+2-dimensional phase space. The collision operator is discretized using 4th order accurate conservative finite-differencing. The treatment of the Vlasov operator in phase-space uses an approach based on a minimally diffuse, fourth-order-accurate discretization (Banks and Hittinger, IEEE T. Plasma Sci. 39, 2198). The overall scheme is therefore discretely conservative and controls unphysical oscillations. Some details of the numerical scheme will be presented, and the implementation on modern highly concurrent parallel computers will be discussed. We will present results of collisional effects on linear and non-linear Landau damping of electron plasma waves (EPWs). In addition we will present initial results showing the effect of collisions on the evolution of EPWs in two space dimensions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the LDRD program at LLNL under project tracking <span class="hlt">code</span> 12-ERD-061.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li class="active"><span>8</span></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_8 --> <div id="page_9" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li class="active"><span>9</span></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="161"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016E%26ES...49f2008M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016E%26ES...49f2008M"><span>Verification of transport equations in a general purpose commercial CFD <span class="hlt">code</span>.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Melot, Matthieu; Nennemann, Bernd; Deschênes, Claire</p> <p>2016-11-01</p> <p>In this paper, the Verification and Validation methodology is presented. This method aims to increase the reliability and the trust that can be placed into complex CFD simulations. The first step of this methodology, the <span class="hlt">code</span> verification is presented in greater details. The CFD transport equations in steady state, transient and Arbitrary <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> (ALE, used for transient moving mesh) formulations in Ansys CFX are verified. It is shown that the expected spatial and temporal order of convergence are achieved for the steady state and the transient formulations. Unfortunately this is not completely the case for the ALE formulation. As for a lot of other commercial and in-house CFD <span class="hlt">codes</span>, the temporal convergence of the velocity is limited to a first order where a second order would have been expected.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006APS..DPPVP1130L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006APS..DPPVP1130L"><span>Development of a Grid-Based Gyro-Kinetic Simulation <span class="hlt">Code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lapillonne, Xavier; Brunetti, Maura; Tran, Trach-Minh; Brunner, Stephan</p> <p>2006-10-01</p> <p>A grid-based semi-<span class="hlt">Lagrangian</span> <span class="hlt">code</span> using cubic spline interpolation is being developed at CRPP, for solving the electrostatic drift-kinetic equations [M. Brunetti et. al, Comp. Phys. Comm. 163, 1 (2004)] in a cylindrical system. This 4-dim <span class="hlt">code</span>, CYGNE, is part of a project with long term aim of studying microturbulence in toroidal fusion devices, in the more general frame of gyro-kinetic equations. Towards their non-linear phase, the simulations from this <span class="hlt">code</span> are subject to significant overshoot problems, reflected by the development of negative value regions of the distribution function, which leads to bad energy conservation. This has motivated the study of alternative schemes. On the one hand, new time integration algorithms are considered in the semi-<span class="hlt">Lagrangian</span> frame. On the other hand, fully <span class="hlt">Eulerian</span> schemes, which separate time and space discretisation (method of lines), are investigated. In particular, the Essentially Non Oscillatory (ENO) approach, constructed so as to minimize the overshoot problem, has been considered. All these methods have first been tested in the simpler case of the 2-dim guiding-center model for the Kelvin-Helmholtz instability, which enables to address the specific issue of the E xB drift also met in the more complex gyrokinetic-type equations. Based on these preliminary studies, the most promising methods are being implemented and tested in CYGNE.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22393117','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22393117"><span><span class="hlt">Eulerian-Lagrangian</span> analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Umeyama, Motohiko</p> <p>2012-04-13</p> <p>This paper investigates the velocity and the trajectory of water particles under surface waves, which propagate at a constant water depth, using particle image velocimetry (PIV). The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The third-order Stokes wave theory was employed to express the physical quantities. The PIV technique's ability to measure both temporal and spatial variations of the velocity was proved after a series of attempts. This technique was applied to the prediction of particle trajectory in an <span class="hlt">Eulerian</span> scheme. Furthermore, the measured particle path was compared with the positions found theoretically by integrating the <span class="hlt">Eulerian</span> velocity to the higher order of a Taylor series expansion. The profile of average travelling distance is also presented with a solution of zero net mass flux in a closed wave flume.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhA...49g5501W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhA...49g5501W"><span>Vorticity and symplecticity in multi-symplectic, <span class="hlt">Lagrangian</span> gas dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Webb, G. M.; Anco, S. C.</p> <p>2016-02-01</p> <p>The <span class="hlt">Lagrangian</span>, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the <span class="hlt">Lagrangian</span> fluid labels, m i (the <span class="hlt">Lagrangian</span> mass coordinates) and time t are the independent variables, and in which the <span class="hlt">Eulerian</span> position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the <span class="hlt">Lagrangian</span> map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the <span class="hlt">Lagrangian</span> map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The <span class="hlt">Lagrangian</span> is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the <span class="hlt">Lagrangian</span> energy conservation law with respect to the <span class="hlt">Lagrangian</span> mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017WRR....53.3513E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017WRR....53.3513E"><span><span class="hlt">Lagrangian</span> simulation of mixing and reactions in complex geochemical systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Engdahl, Nicholas B.; Benson, David A.; Bolster, Diogo</p> <p>2017-04-01</p> <p>Simulations of detailed geochemical systems have traditionally been restricted to <span class="hlt">Eulerian</span> reactive transport algorithms. This note introduces a <span class="hlt">Lagrangian</span> method for modeling multicomponent reaction systems. The approach uses standard random walk-based methods for the particle motion steps but allows the particles to interact with each other by exchanging mass of their various chemical species. The colocation density of each particle pair is used to calculate the mass transfer rate, which creates a local disequilibrium that is then relaxed back toward equilibrium using the reaction engine PhreeqcRM. The mass exchange is the only step where the particles interact and the remaining transport and reaction steps are entirely independent for each particle. Several validation examples are presented, which reproduce well-known analytical solutions. These are followed by two demonstration examples of a competitive decay chain and an acid-mine drainage system. The source <span class="hlt">code</span>, entitled Complex Reaction on Particles (CRP), and files needed to run these examples are hosted openly on GitHub (https://github.com/nbengdahl/CRP), so as to enable interested readers to readily apply this approach with minimal modifications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22218587-verification-gyrokinetic-microstability-codes-gem-gyro-gs2','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22218587-verification-gyrokinetic-microstability-codes-gem-gyro-gs2"><span>A verification of the gyrokinetic microstability <span class="hlt">codes</span> GEM, GYRO, and GS2</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Bravenec, R. V.; Chen, Y.; Wan, W.</p> <p>2013-10-15</p> <p>A previous publication [R. V. Bravenec et al., Phys. Plasmas 18, 122505 (2011)] presented favorable comparisons of linear frequencies and nonlinear fluxes from the <span class="hlt">Eulerian</span> gyrokinetic <span class="hlt">codes</span> gyro[J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] and gs2[W. Dorland et al., Phys. Rev. Lett. 85, 5579 (2000)]. The motivation was to verify the <span class="hlt">codes</span>, i.e., demonstrate that they correctly solve the gyrokinetic-Maxwell equations. The premise was that it is highly unlikely for both <span class="hlt">codes</span> to yield the same incorrect results. In this work, we add the <span class="hlt">Lagrangian</span> particle-in-cell <span class="hlt">code</span> gem[Y. Chen and S. Parker, J. Comput. Phys.more » 220, 839 (2007)] to the comparisons, not simply to add another <span class="hlt">code</span>, but also to demonstrate that the <span class="hlt">codes</span>' algorithms do not matter. We find good agreement of gem with gyro and gs2 for the plasma conditions considered earlier, thus establishing confidence that the <span class="hlt">codes</span> are verified and that ongoing validation efforts for these plasma parameters are warranted.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28989316','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28989316"><span>Stochastic partial differential fluid equations as a diffusive limit of deterministic <span class="hlt">Lagrangian</span> multi-time dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cotter, C J; Gottwald, G A; Holm, D D</p> <p>2017-09-01</p> <p>In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic <span class="hlt">Lagrangian</span> particle dynamics. Here we show that the same stochastic <span class="hlt">Lagrangian</span> dynamics naturally arises in a multi-scale decomposition of the deterministic <span class="hlt">Lagrangian</span> flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the <span class="hlt">Eulerian</span> formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22047333-tess-relativistic-hydrodynamics-code-moving-voronoi-mesh','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22047333-tess-relativistic-hydrodynamics-code-moving-voronoi-mesh"><span>TESS: A RELATIVISTIC HYDRODYNAMICS <span class="hlt">CODE</span> ON A MOVING VORONOI MESH</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Duffell, Paul C.; MacFadyen, Andrew I., E-mail: pcd233@nyu.edu, E-mail: macfadyen@nyu.edu</p> <p>2011-12-01</p> <p>We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an <span class="hlt">Eulerian</span> formulation. Moving the points at the local fluid velocity makes the formulation effectively <span class="hlt">Lagrangian</span>. We have written the TESS <span class="hlt">code</span> to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluidsmore » on a dynamic Voronoi mesh. When run in <span class="hlt">Lagrangian</span> mode, TESS is significantly less diffusive than fixed mesh <span class="hlt">codes</span> and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5627383','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5627383"><span>Stochastic partial differential fluid equations as a diffusive limit of deterministic <span class="hlt">Lagrangian</span> multi-time dynamics</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Cotter, C. J.</p> <p>2017-01-01</p> <p>In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic <span class="hlt">Lagrangian</span> particle dynamics. Here we show that the same stochastic <span class="hlt">Lagrangian</span> dynamics naturally arises in a multi-scale decomposition of the deterministic <span class="hlt">Lagrangian</span> flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the <span class="hlt">Eulerian</span> formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CoPhC.202..326E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CoPhC.202..326E"><span>High performance computing aspects of a dimension independent semi-<span class="hlt">Lagrangian</span> discontinuous Galerkin <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Einkemmer, Lukas</p> <p>2016-05-01</p> <p>The recently developed semi-<span class="hlt">Lagrangian</span> discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-<span class="hlt">Lagrangian</span> schemes (which are usually based on polynomial or spline interpolation). In this paper, we consider a parallel implementation of a semi-<span class="hlt">Lagrangian</span> discontinuous Galerkin method for distributed memory systems (so-called clusters). Both strong and weak scaling studies are performed on the Vienna Scientific Cluster 2 (VSC-2). In the case of weak scaling we observe a parallel efficiency above 0.8 for both two and four dimensional problems and up to 8192 cores. Strong scaling results show good scalability to at least 512 cores (we consider problems that can be run on a single processor in reasonable time). In addition, we study the scaling of a two dimensional Vlasov-Poisson solver that is implemented using the framework provided. All of the simulations are conducted in the context of worst case communication overhead; i.e., in a setting where the CFL (Courant-Friedrichs-Lewy) number increases linearly with the problem size. The framework introduced in this paper facilitates a dimension independent implementation of scientific <span class="hlt">codes</span> (based on C++ templates) using both an MPI and a hybrid approach to parallelization. We describe the essential ingredients of our implementation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhDT.......215H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhDT.......215H"><span><span class="hlt">Eulerian</span> Formulation of Spatially Constrained Elastic Rods</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Huynen, Alexandre</p> <p></p> <p>Slender elastic rods are ubiquitous in nature and technology. For a vast majority of applications, the rod deflection is restricted by an external constraint and a significant part of the elastic body is in contact with a stiff constraining surface. The research work presented in this doctoral dissertation formulates a computational model for the solution of elastic rods constrained inside or around frictionless tube-like surfaces. The segmentation strategy adopted to cope with this complex class of problems consists in sequencing the global problem into, comparatively simpler, elementary problems either in continuous contact with the constraint or contact-free between their extremities. Within the conventional <span class="hlt">Lagrangian</span> formulation of elastic rods, this approach is however associated with two major drawbacks. First, the boundary conditions specifying the locations of the rod centerline at both extremities of each elementary problem lead to the establishment of isoperimetric constraints, i.e., integral constraints on the unknown length of the rod. Second, the assessment of the unilateral contact condition requires, in principle, the comparison of two curves parametrized by distinct curvilinear coordinates, viz. the rod centerline and the constraint axis. Both conspire to burden the computations associated with the method. To streamline the solution along the elementary problems and rationalize the assessment of the unilateral contact condition, the rod governing equations are reformulated within the <span class="hlt">Eulerian</span> framework of the constraint. The methodical exploration of both types of elementary problems leads to specific formulations of the rod governing equations that stress the profound connection between the mechanics of the rod and the geometry of the constraint surface. The proposed <span class="hlt">Eulerian</span> reformulation, which restates the rod local equilibrium in terms of the curvilinear coordinate associated with the constraint axis, describes the rod deformed configuration</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JCoPh.275..484B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JCoPh.275..484B"><span>A direct Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Boscheri, Walter; Dumbser, Michael</p> <p>2014-10-01</p> <p>In this paper we present a new family of high order accurate Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final <span class="hlt">Lagrangian</span> finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.346..449B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.346..449B"><span>Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Boscheri, Walter; Dumbser, Michael</p> <p>2017-10-01</p> <p>We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018MNRAS.477.2251G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018MNRAS.477.2251G"><span>Well-balanced Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael</p> <p>2018-06-01</p> <p>In this work, we present a novel second-order accurate well-balanced arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFMOS41B..06L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFMOS41B..06L"><span>A Skill Score of Trajectory Model Evaluation Using Reinitialized Series of Normalized Cumulative <span class="hlt">Lagrangian</span> Separation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Y.; Weisberg, R. H.</p> <p>2017-12-01</p> <p>The <span class="hlt">Lagrangian</span> separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as a continental shelf and its adjacent deep ocean. A skill score is proposed based on the cumulative <span class="hlt">Lagrangian</span> separation distances normalized by the associated cumulative trajectory lengths. The new metrics correctly indicates the relative performance of the Global HYCOM in simulating the strong currents of the Gulf of Mexico Loop Current and the weaker currents of the West Florida Shelf in the eastern Gulf of Mexico. In contrast, the <span class="hlt">Lagrangian</span> separation distance alone gives a misleading result. Also, the observed drifter position series can be used to reinitialize the trajectory model and evaluate its performance along the observed trajectory, not just at the drifter end position. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional <span class="hlt">Eulerian</span>-based velocity nor a <span class="hlt">Lagrangian</span>-based probability density function may be estimated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23944559','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23944559"><span><span class="hlt">Lagrangian</span> coherent structures separate dynamically distinct regions in fluid flows.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kelley, Douglas H; Allshouse, Michael R; Ouellette, Nicholas T</p> <p>2013-07-01</p> <p>Using filter-space techniques, we study the scale-to-scale transport of energy in a quasi-two-dimensional, weakly turbulent fluid flow averaged along the trajectories of fluid elements. We find that although the spatial mean of this <span class="hlt">Lagrangian</span>-averaged flux is nearly unchanged from its <span class="hlt">Eulerian</span> counterpart, the spatial structure of the scale-to-scale energy flux changes significantly. In particular, its features appear to correlate with the positions of <span class="hlt">Lagrangian</span> coherent structures (LCS's). We show that the LCS's tend to lie at zeros of the scale-to-scale flux, and therefore that the LCS's separate regions that have qualitatively different dynamics. Since LCS's are also known to be impenetrable barriers to advection and mixing, we therefore find that the fluid on either side of an LCS is both kinematically and dynamically distinct. Our results extend the utility of LCS's by making clear the role they play in the flow dynamics in addition to the kinematics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19910056098&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19910056098&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian"><span>A new <span class="hlt">Lagrangian</span> random choice method for steady two-dimensional supersonic/hypersonic flow</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Loh, C. Y.; Hui, W. H.</p> <p>1991-01-01</p> <p>Glimm's (1965) random choice method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new <span class="hlt">Lagrangian</span> formulation. The method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing <span class="hlt">Eulerian</span> methods. Many computed examples are given.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003AGUFMNG11A0182T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003AGUFMNG11A0182T"><span>Examples of Linking <span class="hlt">Codes</span> Within GeoFramework</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tan, E.; Choi, E.; Thoutireddy, P.; Aivazis, M.; Lavier, L.; Quenette, S.; Gurnis, M.</p> <p>2003-12-01</p> <p>Geological processes usually encompass a broad spectrum of length and time scales. Traditionally, a modeling <span class="hlt">code</span> (solver) is written to solve a problem with specific length and time scales in mind. The utility of the solver beyond the designated purpose is usually limited. Furthermore, two distinct solvers, even if each can solve complementary parts of a new problem, are difficult to link together to solve the problem as a whole. For example, <span class="hlt">Lagrangian</span> deformation model with visco-elastoplastic crust is used to study deformation near plate boundary. Ideally, the driving force of the deformation should be derived from underlying mantle convection, and it requires linking the <span class="hlt">Lagrangian</span> deformation model with a <span class="hlt">Eulerian</span> mantle convection model. As our understanding of geological processes evolves, the need of integrated modeling <span class="hlt">codes</span>, which should reuse existing <span class="hlt">codes</span> as much as possible, begins to surface. GeoFramework project addresses this need by developing a suite of reusable and re-combinable tools for the Earth science community. GeoFramework is based on and extends Pyre, a Python-based modeling framework, recently developed to link solid (<span class="hlt">Lagrangian</span>) and fluid (<span class="hlt">Eulerian</span>) models, as well as mesh generators, visualization packages, and databases, with one another for engineering applications. Under the framework, a solver is aware of the existence of other solvers and can interact with each other via exchanging information across adjacent boundary. A solver needs to conform a standard interface and provide its own implementation for exchanging boundary information. The framework also provides facilities to control the coordination between interacting solvers. We will show an example of linking two solvers within GeoFramework. CitcomS is a finite element <span class="hlt">code</span> which solves for thermal convection within a 3D spherical shell. CitcomS can solve for problems either within a full spherical (global) domain or a restricted (regional) domain of a full sphere by using</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26679833','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26679833"><span><span class="hlt">Lagrangian</span> methods for blood damage estimation in cardiovascular devices--How numerical implementation affects the results.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Marom, Gil; Bluestein, Danny</p> <p>2016-01-01</p> <p>This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using <span class="hlt">Lagrangian</span> methods with <span class="hlt">Eulerian</span> computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of <span class="hlt">Lagrangian</span> models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4932905','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4932905"><span><span class="hlt">Lagrangian</span> methods for blood damage estimation in cardiovascular devices - How numerical implementation affects the results</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Marom, Gil; Bluestein, Danny</p> <p>2016-01-01</p> <p>Summary This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using <span class="hlt">Lagrangian</span> methods with <span class="hlt">Eulerian</span> computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of <span class="hlt">Lagrangian</span> models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed. PMID:26679833</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li class="active"><span>9</span></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_9 --> <div id="page_10" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li class="active"><span>10</span></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="181"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22666212-santa-barbara-cluster-comparison-test-disph','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22666212-santa-barbara-cluster-comparison-test-disph"><span>SANTA BARBARA CLUSTER COMPARISON TEST WITH DISPH</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Saitoh, Takayuki R.; Makino, Junichiro, E-mail: saitoh@elsi.jp</p> <p>2016-06-01</p> <p>The Santa Barbara cluster comparison project revealed that there is a systematic difference between entropy profiles of clusters of galaxies obtained by <span class="hlt">Eulerian</span> mesh and <span class="hlt">Lagrangian</span> smoothed particle hydrodynamics (SPH) <span class="hlt">codes</span>: mesh <span class="hlt">codes</span> gave a core with a constant entropy, whereas SPH <span class="hlt">codes</span> did not. One possible reason for this difference is that mesh <span class="hlt">codes</span> are not Galilean invariant. Another possible reason is the problem of the SPH method, which might give too much “protection” to cold clumps because of the unphysical surface tension induced at contact discontinuities. In this paper, we apply the density-independent formulation of SPH (DISPH), whichmore » can handle contact discontinuities accurately, to simulations of a cluster of galaxies and compare the results with those with the standard SPH. We obtained the entropy core when we adopt DISPH. The size of the core is, however, significantly smaller than those obtained with mesh simulations and is comparable to those obtained with quasi-<span class="hlt">Lagrangian</span> schemes such as “moving mesh” and “mesh free” schemes. We conclude that both the standard SPH without artificial conductivity and <span class="hlt">Eulerian</span> mesh <span class="hlt">codes</span> have serious problems even with such an idealized simulation, while DISPH, SPH with artificial conductivity, and quasi-<span class="hlt">Lagrangian</span> schemes have sufficient capability to deal with it.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005AtmEn..39.7044S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005AtmEn..39.7044S"><span>Evaluation of a <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> air quality model using perfluorocarbon tracers released in Texas for the BRAVO haze study</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Schichtel, Bret A.; Barna, Michael G.; Gebhart, Kristi A.; Malm, William C.</p> <p></p> <p>The Big Bend Regional Aerosol and Visibility Observational (BRAVO) study was designed to determine the sources of haze at Big Bend National Park, Texas, using a combination of source and receptor models. BRAVO included an intensive monitoring campaign from July to October 1999 that included the release of perfluorocarbon tracers from four locations at distances 230-750 km from Big Bend and measured at 24 sites. The tracer measurements near Big Bend were used to evaluate the dispersion mechanisms in the REMSAD <span class="hlt">Eulerian</span> model and the CAPITA Monte Carlo (CMC) <span class="hlt">Lagrangian</span> model used in BRAVO. Both models used 36 km MM5 wind fields as input. The CMC model also used a combination of routinely available 80 and 190 km wind fields from the National Weather Service's National Centers for Environmental Prediction (NCEP) as input. A model's performance is limited by inherent uncertainties due to errors in the tracer concentrations and a model's inability to simulate sub-resolution variability. A range in the inherent uncertainty was estimated by comparing tracer data at nearby monitoring sites. It was found that the REMSAD and CMC models, using the MM5 wind field, produced performance statistics generally within this inherent uncertainty. The CMC simulation using the NCEP wind fields could reproduce the timing of tracer impacts at Big Bend, but not the concentration values, due to a systematic underestimation. It appears that the underestimation was partly due to excessive vertical dilution from high mixing depths. The model simulations were more sensitive to the input wind fields than the models' different dispersion mechanisms. Comparisons of REMSAD to CMC tracer simulations using the MM5 wind fields had correlations between 0.75 and 0.82, depending on the tracer, but the tracer simulations using the two wind fields in the CMC model had correlations between 0.37 and 0.5.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1989umas.reptQ....O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1989umas.reptQ....O"><span><span class="hlt">Lagrangian</span> turbulence near walls: Structures and mixing in admissible model flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ottino, J. M.</p> <p>1989-05-01</p> <p>The general objective of work during this period was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: a perturbed Kelvin cat eyes flow, and prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: production flows capable of producing complex distributions of vorticity, and constructed flow fields, based on solutions of the Navier Stokes equations, which are capable of displaying both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> turbulence.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001APS..DFD.EC008A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001APS..DFD.EC008A"><span>Chaos in an <span class="hlt">Eulerian</span> Based Model of Sickle Cell Blood Flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Apori, Akwasi; Harris, Wesley</p> <p>2001-11-01</p> <p>A novel <span class="hlt">Eulerian</span> model describing the manifestation of sickle cell blood flow in the capillaries has been formulated to study the apparently chaotic onset of sickle cell crises. This <span class="hlt">Eulerian</span> model was based on extending previous models of sickle cell blood flow which were limited due to their <span class="hlt">Lagrangian</span> formulation. Oxygen concentration, red blood cell velocity, cell stiffness, and plasma viscosity were modeled as system state variables. The governing equations of the system were expressed in canonical form. The non-linear coupling of velocity-viscosity and viscosity- stiffness proved to be the origin of chaos in the system. The system was solved with respect to a control parameter representing the unique rheology of the sickle cell erythrocytes. Results of chaos tests proved positive for various ranges of the control parameter. The results included con-tinuous patterns found in the Poincare section, spectral broadening of the Fourier power spectrum, and positive Lyapunov exponent values. The onset of chaos predicted by this sickle cell flow model as the control parameter was varied appeared to coincide with the change from a healthy state to a crisis state in a sickle cell patient. This finding that sickle cell crises may be caused from the well understood change of a solution from a steady state to chaotic could point to new ways in preventing and treating crises and should be validated in clinical trials.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1009440','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1009440"><span>DOE SBIR Phase-1 Report on Hybrid CPU-GPU Parallel Development of the <span class="hlt">Eulerian-Lagrangian</span> Barracuda Multiphase Program</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Dr. Dale M. Snider</p> <p>2011-02-28</p> <p>This report gives the result from the Phase-1 work on demonstrating greater than 10x speedup of the Barracuda computer program using parallel methods and GPU processors (General-Purpose Graphics Processing Unit or Graphics Processing Unit). Phase-1 demonstrated a 12x speedup on a typical Barracuda function using the GPU processor. The problem test case used about 5 million particles and 250,000 <span class="hlt">Eulerian</span> grid cells. The relative speedup, compared to a single CPU, increases with increased number of particles giving greater than 12x speedup. Phase-1 work provided a path for reformatting data structure modifications to give good parallel performance while keeping a friendlymore » environment for new physics development and <span class="hlt">code</span> maintenance. The implementation of data structure changes will be in Phase-2. Phase-1 laid the ground work for the complete parallelization of Barracuda in Phase-2, with the caveat that implemented computer practices for parallel programming done in Phase-1 gives immediate speedup in the current Barracuda serial running <span class="hlt">code</span>. The Phase-1 tasks were completed successfully laying the frame work for Phase-2. The detailed results of Phase-1 are within this document. In general, the speedup of one function would be expected to be higher than the speedup of the entire <span class="hlt">code</span> because of I/O functions and communication between the algorithms. However, because one of the most difficult Barracuda algorithms was parallelized in Phase-1 and because advanced parallelization methods and proposed parallelization optimization techniques identified in Phase-1 will be used in Phase-2, an overall Barracuda <span class="hlt">code</span> speedup (relative to a single CPU) is expected to be greater than 10x. This means that a job which takes 30 days to complete will be done in 3 days. Tasks completed in Phase-1 are: Task 1: Profile the entire Barracuda <span class="hlt">code</span> and select which subroutines are to be parallelized (See Section Choosing a Function to Accelerate) Task 2: Select a GPU consultant</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1430982','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1430982"><span>Surface tension models for a multi-material ALE <span class="hlt">code</span> with AMR</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Liu, Wangyi; Koniges, Alice; Gott, Kevin</p> <p></p> <p>A number of surface tension models have been implemented in a 3D multi-physics multi-material <span class="hlt">code</span>, ALE–AMR, which combines Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR). ALE–AMR is unique in its ability to model hot radiating plasmas, cold fragmenting solids, and most recently, the deformation of molten material. The surface tension models implemented include a diffuse interface approach with special numerical techniques to remove parasitic flow and a height function approach in conjunction with a volume-fraction interface reconstruction package. These surface tension models are benchmarked with a variety of test problems. In conclusion, based on the results, themore » height function approach using volume fractions was chosen to simulate droplet dynamics associated with extreme ultraviolet (EUV) lithography.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1430982-surface-tension-models-multi-material-ale-code-amr','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1430982-surface-tension-models-multi-material-ale-code-amr"><span>Surface tension models for a multi-material ALE <span class="hlt">code</span> with AMR</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Liu, Wangyi; Koniges, Alice; Gott, Kevin; ...</p> <p>2017-06-01</p> <p>A number of surface tension models have been implemented in a 3D multi-physics multi-material <span class="hlt">code</span>, ALE–AMR, which combines Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR). ALE–AMR is unique in its ability to model hot radiating plasmas, cold fragmenting solids, and most recently, the deformation of molten material. The surface tension models implemented include a diffuse interface approach with special numerical techniques to remove parasitic flow and a height function approach in conjunction with a volume-fraction interface reconstruction package. These surface tension models are benchmarked with a variety of test problems. In conclusion, based on the results, themore » height function approach using volume fractions was chosen to simulate droplet dynamics associated with extreme ultraviolet (EUV) lithography.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26826855','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26826855"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Rivera, Michael K; Ecke, Robert E</p> <p>2016-01-01</p> <p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1351187','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1351187"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Rivera, Michael K.; Ecke, Robert E.</p> <p></p> <p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1351187-lagrangian-statistics-weakly-forced-two-dimensional-turbulence','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1351187-lagrangian-statistics-weakly-forced-two-dimensional-turbulence"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Rivera, Michael K.; Ecke, Robert E.</p> <p>2016-01-14</p> <p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1991umas.rept.....O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1991umas.rept.....O"><span><span class="hlt">Lagrangian</span> turbulence: Structures and mixing in admissible model flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ottino, Julio M.</p> <p>1991-12-01</p> <p>The goal of our research was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: (1) a perturbed-Kelvin cat eyes flow, and (2) prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: we have been able to produce flows capable of producing complex distributions of vorticity, and we have been able to construct flowfields, based on solutions of the Navier-Stokes equations, which are capable of displaying both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> turbulence. These results exemplify typical mechanisms of mixing enhancement in transitional flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DPPT11109J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DPPT11109J"><span>Cross-verification of the GENE and XGC <span class="hlt">codes</span> in preparation for their coupling</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jenko, Frank; Merlo, Gabriele; Bhattacharjee, Amitava; Chang, Cs; Dominski, Julien; Ku, Seunghoe; Parker, Scott; Lanti, Emmanuel</p> <p>2017-10-01</p> <p>A high-fidelity Whole Device Model (WDM) of a magnetically confined plasma is a crucial tool for planning and optimizing the design of future fusion reactors, including ITER. Aiming at building such a tool, in the framework of the Exascale Computing Project (ECP) the two existing gyrokinetic <span class="hlt">codes</span> GENE (<span class="hlt">Eulerian</span> delta-f) and XGC (PIC full-f) will be coupled, thus enabling to carry out first principle kinetic WDM simulations. In preparation for this ultimate goal, a benchmark between the two <span class="hlt">codes</span> is carried out looking at ITG modes in the adiabatic electron limit. This verification exercise is also joined by the global <span class="hlt">Lagrangian</span> PIC <span class="hlt">code</span> ORB5. Linear and nonlinear comparisons have been carried out, neglecting for simplicity collisions and sources. A very good agreement is recovered on frequency, growth rate and mode structure of linear modes. A similarly excellent agreement is also observed comparing the evolution of the heat flux and of the background temperature profile during nonlinear simulations. Work supported by the US DOE under the Exascale Computing Project (17-SC-20-SC).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930003501','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930003501"><span>Adaptation of multidimensional group particle tracking and particle wall-boundary condition model to the FDNS <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chen, Y. S.; Farmer, R. C.</p> <p>1992-01-01</p> <p>A particulate two-phase flow CFD model was developed based on the FDNS <span class="hlt">code</span> which is a pressure based predictor plus multi-corrector Navier-Stokes flow solver. Turbulence models with compressibility correction and the wall function models were employed as submodels. A finite-rate chemistry model was used for reacting flow simulation. For particulate two-phase flow simulations, a <span class="hlt">Eulerian-Lagrangian</span> solution method using an efficient implicit particle trajectory integration scheme was developed in this study. Effects of particle-gas reaction and particle size change to agglomeration or fragmentation were not considered in this investigation. At the onset of the present study, a two-dimensional version of FDNS which had been modified to treat <span class="hlt">Lagrangian</span> tracking of particles (FDNS-2DEL) had already been written and was operational. The FDNS-2DEL <span class="hlt">code</span> was too slow for practical use, mainly because it had not been written in a form amenable to vectorization on the Cray, nor was the full three-dimensional form of FDNS utilized. The specific objective of this study was to reorder to calculations into long single arrays for automatic vectorization on the Cray and to implement the full three-dimensional version of FDNS to produce the FDNS-3DEL <span class="hlt">code</span>. Since the FDNS-2DEL <span class="hlt">code</span> was slow, a very limited number of test cases had been run with it. This study was also intended to increase the number of cases simulated to verify and improve, as necessary, the particle tracking methodology <span class="hlt">coded</span> in FDNS.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012APS..DPPJP8110C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012APS..DPPJP8110C"><span>Asymptotic-preserving <span class="hlt">Lagrangian</span> approach for modeling anisotropic transport in magnetized plasmas for arbitrary magnetic fields</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chacon, Luis; Del-Castillo-Negrete, Diego; Hauck, Cory</p> <p>2012-10-01</p> <p>Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (χ/χ˜10^10 in fusion plasmas). Recently, a <span class="hlt">Lagrangian</span> Green's function approach, developed for the purely parallel transport case,footnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011)^,footnotetextD. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, 19, 056112 (2012) has been extended to the anisotropic transport case in the tokamak-ordering limit with constant density.footnotetextL. Chac'on, D. del-Castillo-Negrete, C. Hauck, JCP, submitted (2012) An operator-split algorithm is proposed that allows one to treat <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> components separately. The approach is shown to feature bounded numerical errors for arbitrary χ/χ ratios, which renders it asymptotic-preserving. In this poster, we will present the generalization of the <span class="hlt">Lagrangian</span> approach to arbitrary magnetic fields. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035182&hterms=difference+engine&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Ddifference%2Bengine','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035182&hterms=difference+engine&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Ddifference%2Bengine"><span>Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.; Willis, E. A.</p> <p>1990-01-01</p> <p>A new computer <span class="hlt">code</span> was developed for predicting the turbulent and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, <span class="hlt">Eulerian</span> coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in <span class="hlt">Lagrangian</span> coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900004433','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900004433"><span>Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.; Willis, E. A.</p> <p>1989-01-01</p> <p>A new computer <span class="hlt">code</span> was developed for predicting the turbulent, and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> approach where the unsteady, 3-D Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, <span class="hlt">Eulerian</span> coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in <span class="hlt">Lagrangian</span> coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26578642','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26578642"><span>Segmental Analysis of Cardiac Short-Axis Views Using <span class="hlt">Lagrangian</span> Radial and Circumferential Strain.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ma, Chi; Wang, Xiao; Varghese, Tomy</p> <p>2016-11-01</p> <p>Accurate description of myocardial deformation in the left ventricle is a three-dimensional problem, requiring three normal strain components along its natural axis, that is, longitudinal, radial, and circumferential strains. Although longitudinal strains are best estimated from long-axis views, radial and circumferential strains are best depicted in short-axis views. An algorithm that utilizes a polar grid for short-axis views previously developed in our laboratory for a <span class="hlt">Lagrangian</span> description of tissue deformation is utilized for radial and circumferential displacement and strain estimation. Deformation of the myocardial wall, utilizing numerical simulations with ANSYS, and a finite-element analysis-based canine heart model were adapted as the input to a frequency-domain ultrasound simulation program to generate radiofrequency echo signals. Clinical in vivo data were also acquired from a healthy volunteer. Local displacements estimated along and perpendicular to the ultrasound beam propagation direction are then transformed into radial and circumferential displacements and strains using the polar grid based on a pre-determined centroid location. <span class="hlt">Lagrangian</span> strain variations demonstrate good agreement with the ideal strain when compared with <span class="hlt">Eulerian</span> results. <span class="hlt">Lagrangian</span> radial and circumferential strain estimation results are also demonstrated for experimental data on a healthy volunteer. <span class="hlt">Lagrangian</span> radial and circumferential strain tracking provide accurate results with the assistance of the polar grid, as demonstrated using both numerical simulations and in vivo study. © The Author(s) 2015.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4868801','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4868801"><span>Segmental Analysis of Cardiac Short-Axis Views Using <span class="hlt">Lagrangian</span> Radial and Circumferential Strain</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Ma, Chi; Wang, Xiao; Varghese, Tomy</p> <p>2016-01-01</p> <p>Accurate description of myocardial deformation in the left ventricle is a three-dimensional problem, requiring three normal strain components along its natural axis, that is, longitudinal, radial, and circumferential strains. Although longitudinal strains are best estimated from long-axis views, radial and circumferential strains are best depicted in short-axis views. An algorithm that utilizes a polar grid for short-axis views previously developed in our laboratory for a <span class="hlt">Lagrangian</span> description of tissue deformation is utilized for radial and circumferential displacement and strain estimation. Deformation of the myocardial wall, utilizing numerical simulations with ANSYS, and a finite-element analysis–based canine heart model were adapted as the input to a frequency-domain ultrasound simulation program to generate radiofrequency echo signals. Clinical in vivo data were also acquired from a healthy volunteer. Local displacements estimated along and perpendicular to the ultrasound beam propagation direction are then transformed into radial and circumferential displacements and strains using the polar grid based on a pre-determined centroid location. <span class="hlt">Lagrangian</span> strain variations demonstrate good agreement with the ideal strain when compared with <span class="hlt">Eulerian</span> results. <span class="hlt">Lagrangian</span> radial and circumferential strain estimation results are also demonstrated for experimental data on a healthy volunteer. <span class="hlt">Lagrangian</span> radial and circumferential strain tracking provide accurate results with the assistance of the polar grid, as demonstrated using both numerical simulations and in vivo study. PMID:26578642</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.usgs.gov/wri/1986/4144/report.pdf','USGSPUBS'); return false;" href="https://pubs.usgs.gov/wri/1986/4144/report.pdf"><span>Programmers manual for a one-dimensional <span class="hlt">Lagrangian</span> transport model</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Schoellhamer, D.H.; Jobson, H.E.</p> <p>1986-01-01</p> <p>A one-dimensional <span class="hlt">Lagrangian</span> transport model for simulating water-quality constituents such as temperature, dissolved oxygen , and suspended sediment in rivers is presented in this Programmers Manual. <span class="hlt">Lagrangian</span> transport modeling techniques, the model 's subroutines, and the user-written decay-coefficient subroutine are discussed in detail. Appendices list the program <span class="hlt">codes</span>. The Programmers Manual is intended for the model user who needs to modify <span class="hlt">code</span> either to adapt the model to a particular need or to use reaction kinetics not provided with the model. (Author 's abstract)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1913844L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1913844L"><span>Estimating <span class="hlt">Eulerian</span> spectra from pairs of drifters</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>LaCasce, Joe</p> <p>2017-04-01</p> <p>GPS-tracked surface drifters offer the possibility of sampling energetic variations at the ocean surface on scales of only 10s of meters, much less than that resolved by satellite. Here we investigate whether velocity differences between pairs of drifters can be used to estimate kinetic energy spectra. Theoretical relations between the spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived. The structure function is a natural statistic for particle pairs and is easily calculated. However it integrates contributions across wavenumber, and this tends to obscure the spectral dependencies when turbulent inertial ranges are of finite extent. Nevertheless, the transform from spectrum to structure function is robust, as illustrated with <span class="hlt">Eulerian</span> data collected from aircraft. The inverse transform, from structure function to spectrum, is much less robust, yielding poor results in particular at large wavenumbers. This occurs because the transform involves a filter function which magnifies contributions from large pair separations, which tend to be noisy. Fitting the structure function to a polynomial improves the spectral estimate, but not sufficiently to distinguish correct inertial range dependencies. Thus with <span class="hlt">Lagrangian</span> data, it is appears preferable to focus on structure functions, despite their shortcomings.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li class="active"><span>10</span></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_10 --> <div id="page_11" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li class="active"><span>11</span></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="201"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4833750','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4833750"><span>Investigation of particle inertial migration in high particle concentration suspension flow by multi-electrodes sensing and <span class="hlt">Eulerian-Lagrangian</span> simulation in a square microchannel</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Zhao, Tong; Liu, Kai; Takei, Masahiro</p> <p>2016-01-01</p> <p>The inertial migration of neutrally buoyant spherical particles in high particle concentration (αpi > 3%) suspension flow in a square microchannel was investigated by means of the multi-electrodes sensing method which broke through the limitation of conventional optical measurement techniques in the high particle concentration suspensions due to interference from the large particle numbers. Based on the measured particle concentrations near the wall and at the corner of the square microchannel, particle cross-sectional migration ratios are calculated to quantitatively estimate the migration degree. As a result, particle migration to four stable equilibrium positions near the centre of each face of the square microchannel is found only in the cases of low initial particle concentration up to 5.0 v/v%, while the migration phenomenon becomes partial as the initial particle concentration achieves 10.0 v/v% and disappears in the cases of the initial particle concentration αpi ≥ 15%. In order to clarify the influential mechanism of particle-particle interaction on particle migration, an <span class="hlt">Eulerian-Lagrangian</span> numerical model was proposed by employing the Lennard-Jones potential as the inter-particle potential, while the inertial lift coefficient is calculated by a pre-processed semi-analytical simulation. Moreover, based on the experimental and simulation results, a dimensionless number named migration index was proposed to evaluate the influence of the initial particle concentration on the particle migration phenomenon. The migration index less than 0.1 is found to denote obvious particle inertial migration, while a larger migration index denotes the absence of it. This index is helpful for estimation of the maximum initial particle concentration for the design of inertial microfluidic devices. PMID:27158288</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20170004568','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20170004568"><span>A Decadal Inversion of CO2 Using the Global <span class="hlt">Eulerian-Lagrangian</span> Coupled Atmospheric Model (GELCA): Sensitivity to the Ground-Based Observation Network</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shirai, T.; Ishizawa, M.; Zhuravlev, R.; Ganshin, A.; Belikov, D.; Saito, M.; Oda, T.; Valsala, V.; Gomez-Pelaez, A. J.; Langenfelds, R.; <a style="text-decoration: none; " href="javascript:void(0); " onClick="displayelement('author_20170004568'); toggleEditAbsImage('author_20170004568_show'); toggleEditAbsImage('author_20170004568_hide'); "> <img style="display:inline; width:12px; height:12px; " src="images/arrow-up.gif" width="12" height="12" border="0" alt="hide" id="author_20170004568_show"> <img style="width:12px; height:12px; display:none; " src="images/arrow-down.gif" width="12" height="12" border="0" alt="hide" id="author_20170004568_hide"></p> <p>2017-01-01</p> <p>We present an assimilation system for atmospheric carbon dioxide (CO2) using a Global <span class="hlt">Eulerian-Lagrangian</span> Coupled Atmospheric model (GELCA), and demonstrate its capability to capture the observed atmospheric CO2 mixing ratios and to estimate CO2 fluxes. With the efficient data handling scheme in GELCA, our system assimilates non-smoothed CO2 data from observational data products such as the Observation Package (ObsPack) data products as constraints on surface fluxes. We conducted sensitivity tests to examine the impact of the site selections and the prior uncertainty settings of observation on the inversion results. For these sensitivity tests, we made five different sitedata selections from the ObsPack product. In all cases, the time series of the global net CO2 flux to the atmosphere stayed close to values calculated from the growth rate of the observed global mean atmospheric CO2 mixing ratio. At regional scales, estimated seasonal CO2 fluxes were altered, depending on the CO2 data selected for assimilation. Uncertainty reductions (URs) were determined at the regional scale and compared among cases. As measures of the model-data mismatch, we used the model-data bias, root-mean-square error, and the linear correlation. For most observation sites, the model-data mismatch was reasonably small. Regarding regional flux estimates, tropical Asia was one of the regions that showed a significant impact from the observation network settings. We found that the surface fluxes in tropical Asia were the most sensitive to the use of aircraft measurements over the Pacific, and the seasonal cycle agreed better with the results of bottom-up studies when the aircraft measurements were assimilated. These results confirm the importance of these aircraft observations, especially for constraining surface fluxes in the tropics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22572306-numerical-methods-weakly-compressible-generalized-langevin-model-eulerian-reference-frame','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22572306-numerical-methods-weakly-compressible-generalized-langevin-model-eulerian-reference-frame"><span>Numerical methods for the weakly compressible Generalized Langevin Model in <span class="hlt">Eulerian</span> reference frame</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Azarnykh, Dmitrii, E-mail: d.azarnykh@tum.de; Litvinov, Sergey; Adams, Nikolaus A.</p> <p>2016-06-01</p> <p>A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a <span class="hlt">Lagrangian</span> reference frame, typically solvedmore » by particle methods. A representation in a <span class="hlt">Eulerian</span> reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a <span class="hlt">Eulerian</span>-frame numerical flow solver. GLM in a <span class="hlt">Eulerian</span> frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered finite-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JGRD..11810243H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JGRD..11810243H"><span>Identification and uncertainty estimation of vertical reflectivity profiles using a <span class="hlt">Lagrangian</span> approach to support quantitative precipitation measurements by weather radar</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hazenberg, P.; Torfs, P. J. J. F.; Leijnse, H.; Delrieu, G.; Uijlenhoet, R.</p> <p>2013-09-01</p> <p>This paper presents a novel approach to estimate the vertical profile of reflectivity (VPR) from volumetric weather radar data using both a traditional <span class="hlt">Eulerian</span> as well as a newly proposed <span class="hlt">Lagrangian</span> implementation. For this latter implementation, the recently developed Rotational Carpenter Square Cluster Algorithm (RoCaSCA) is used to delineate precipitation regions at different reflectivity levels. A piecewise linear VPR is estimated for either stratiform or neither stratiform/convective precipitation. As a second aspect of this paper, a novel approach is presented which is able to account for the impact of VPR uncertainty on the estimated radar rainfall variability. Results show that implementation of the VPR identification and correction procedure has a positive impact on quantitative precipitation estimates from radar. Unfortunately, visibility problems severely limit the impact of the <span class="hlt">Lagrangian</span> implementation beyond distances of 100 km. However, by combining this procedure with the global <span class="hlt">Eulerian</span> VPR estimation procedure for a given rainfall type (stratiform and neither stratiform/convective), the quality of the quantitative precipitation estimates increases up to a distance of 150 km. Analyses of the impact of VPR uncertainty shows that this aspect accounts for a large fraction of the differences between weather radar rainfall estimates and rain gauge measurements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980197321','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980197321"><span>EUPDF: An <span class="hlt">Eulerian</span>-Based Monte Carlo Probability Density Function (PDF) Solver. User's Manual</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.</p> <p>1998-01-01</p> <p>EUPDF is an <span class="hlt">Eulerian</span>-based Monte Carlo PDF solver developed for application with sprays, combustion, parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and spray solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type. The manual provides the user with the <span class="hlt">coding</span> required to couple the PDF <span class="hlt">code</span> to any given flow <span class="hlt">code</span> and a basic understanding of the EUPDF <span class="hlt">code</span> structure as well as the models involved in the PDF formulation. The source <span class="hlt">code</span> of EUPDF will be available with the release of the National Combustion <span class="hlt">Code</span> (NCC) as a complete package.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920010138','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920010138"><span>A computer <span class="hlt">code</span> for multiphase all-speed transient flows in complex geometries. MAST version 1.0</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chen, C. P.; Jiang, Y.; Kim, Y. M.; Shang, H. M.</p> <p>1991-01-01</p> <p>The operation of the MAST <span class="hlt">code</span>, which computes transient solutions to the multiphase flow equations applicable to all-speed flows, is described. Two-phase flows are formulated based on the <span class="hlt">Eulerian</span>-Lagrange scheme in which the continuous phase is described by the Navier-Stokes equation (or Reynolds equations for turbulent flows). Dispersed phase is formulated by a <span class="hlt">Lagrangian</span> tracking scheme. The numerical solution algorithms utilized for fluid flows is a newly developed pressure-implicit algorithm based on the operator-splitting technique in generalized nonorthogonal coordinates. This operator split allows separate operation on each of the variable fields to handle pressure-velocity coupling. The obtained pressure correction equation has the hyperbolic nature and is effective for Mach numbers ranging from the incompressible limit to supersonic flow regimes. The present <span class="hlt">code</span> adopts a nonstaggered grid arrangement; thus, the velocity components and other dependent variables are collocated at the same grid. A sequence of benchmark-quality problems, including incompressible, subsonic, transonic, supersonic, gas-droplet two-phase flows, as well as spray-combustion problems, were performed to demonstrate the robustness and accuracy of the present <span class="hlt">code</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA596022','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA596022"><span>Blast Fragmentation Modeling and Analysis</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2010-10-31</p> <p>weapons device containing a multiphase blast explosive (MBX). 1. INTRODUCTION The ARL Survivability Lethality and Analysis Directorate (SLAD) is...velocity. In order to simulate the highly complex phenomenon, the exploding cylinder is modeled with the hydrodynamics <span class="hlt">code</span> ALE3D , an arbitrary...<span class="hlt">Lagrangian-Eulerian</span> multiphysics <span class="hlt">code</span>, developed at Lawrence Livermore National Laboratory. ALE3D includes physical properties, constitutive models for</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29435676','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29435676"><span>Vortex dynamics and <span class="hlt">Lagrangian</span> statistics in a model for active turbulence.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>James, Martin; Wilczek, Michael</p> <p>2018-02-14</p> <p>Cellular suspensions such as dense bacterial flows exhibit a turbulence-like phase under certain conditions. We study this phenomenon of "active turbulence" statistically by using numerical tools. Following Wensink et al. (Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012)), we model active turbulence by means of a generalized Navier-Stokes equation. Two-point velocity statistics of active turbulence, both in the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> frame, is explored. We characterize the scale-dependent features of two-point statistics in this system. Furthermore, we extend this statistical study with measurements of vortex dynamics in this system. Our observations suggest that the large-scale statistics of active turbulence is close to Gaussian with sub-Gaussian tails.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016WRR....52.8561Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016WRR....52.8561Z"><span>Bounded fractional diffusion in geological media: Definition and <span class="hlt">Lagrangian</span> approximation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang</p> <p>2016-11-01</p> <p>Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a <span class="hlt">Lagrangian</span> solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New <span class="hlt">Lagrangian</span> schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or <span class="hlt">Eulerian</span> solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded <span class="hlt">Lagrangian</span> solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2814836','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2814836"><span>Using hyperbolic <span class="hlt">Lagrangian</span> coherent structures to investigate vortices in bioinspired fluid flows</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Green, Melissa A.; Rowley, Clarence W.; Smits, Alexander J.</p> <p>2010-01-01</p> <p>We use direct Lyapunov exponents to identify <span class="hlt">Lagrangian</span> coherent structures (LCSs) in a bioinspired fluid flow: the wakes of rigid pitching panels with a trapezoidal planform geometry chosen to model idealized fish caudal fins. When compared with commonly used <span class="hlt">Eulerian</span> criteria, the <span class="hlt">Lagrangian</span> method has previously exhibited the ability to define structure boundaries without relying on a preselected threshold. In addition, qualitative changes in the LCS have previously been shown to correspond to physical changes in the vortex structure. For this paper, digital particle image velocimetry experiments were performed to obtain the time-resolved velocity fields for Strouhal numbers of 0.17 and 0.27. A classic reverse von Kármán vortex street pattern was observed along the midspan of the near wake at low Strouhal number, but at higher Strouhal number the complexity of the wake increased downstream of the trailing edge. The spanwise vortices spread transversely across the wake and lose coherence, and this event was shown to correspond to a qualitative change in the LCS at the same time and location. PMID:20370300</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.356..174C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.356..174C"><span>A purely <span class="hlt">Lagrangian</span> method for simulating the shallow water equations on a sphere using smooth particle hydrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Capecelatro, Jesse</p> <p>2018-03-01</p> <p>It has long been suggested that a purely <span class="hlt">Lagrangian</span> solution to global-scale atmospheric/oceanic flows can potentially outperform tradition <span class="hlt">Eulerian</span> schemes. Meanwhile, a demonstration of a scalable and practical framework remains elusive. Motivated by recent progress in particle-based methods when applied to convection dominated flows, this work presents a fully <span class="hlt">Lagrangian</span> method for solving the inviscid shallow water equations on a rotating sphere in a smooth particle hydrodynamics framework. To avoid singularities at the poles, the governing equations are solved in Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the surface of the sphere. An underlying grid in spherical coordinates is used to facilitate efficient neighbor detection and parallelization. The method is applied to a suite of canonical test cases, and conservation, accuracy, and parallel performance are assessed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1919137F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1919137F"><span>Evaluation of the HF-Radar network system around Taiwan using normalized cumulative <span class="hlt">Lagrangian</span> separation.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fredj, Erick; Kohut, Josh; Roarty, Hugh; Lai, Jian-Wu</p> <p>2017-04-01</p> <p>The <span class="hlt">Lagrangian</span> separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as over continental shelves and the adjacent deep ocean. A skill score described in detail by (Lui et.al. 2011) was applied to estimate the cumulative <span class="hlt">Lagrangian</span> separation distances normalized by the associated cumulative trajectory lengths. In contrast, the <span class="hlt">Lagrangian</span> separation distance alone gives a misleading result. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional <span class="hlt">Eulerian</span>-based velocity nor a <span class="hlt">Lagrangian</span> based probability density function may be estimated. The skill score assesses The Taiwan Ocean Radar Observing System (TOROS) performance. TOROS consists of 17 SeaSonde type radars around the Taiwan Island. The currents off Taiwan are significantly influenced by the nearby Kuroshio current. The main stream of the Kuroshio flows along the east coast of Taiwan to the north throughout the year. Sometimes its branch current also bypasses the south end of Taiwan and goes north along the west coast of Taiwan. The Kuroshio is also prone to seasonal change in its speed of flow, current capacity, distribution width, and depth. The evaluations of HF-Radar National Taiwanese network performance using <span class="hlt">Lagrangian</span> drifter records demonstrated the high quality and robustness of TOROS HF-Radar data using a purely trajectory-based non-dimensional index. Yonggang Liu and Robert H. Weisberg, "Evaluation of trajectory modeling in different dynamic regions using normalized cumulative <span class="hlt">Lagrangian</span> separation", Journal of Geophysical Research, Vol. 116, C09013, doi:10.1029/2010JC006837, 2011</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcMod.113..185A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcMod.113..185A"><span>Corrigenda of 'explicit wave-averaged primitive equations using a generalized <span class="hlt">Lagrangian</span> Mean'</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ardhuin, F.; Rascle, N.; Belibassakis, K. A.</p> <p>2017-05-01</p> <p>Ardhuin et al. (2008) gave a second-order approximation in the wave slope of the exact Generalized <span class="hlt">Lagrangian</span> Mean (GLM) equations derived by Andrews and McIntyre (1978), and also performed a coordinate transformation, going from GLM to a 'GLMz' set of equations. That latter step removed the wandering of the GLM mean sea level away from the <span class="hlt">Eulerian</span>-mean sea level, making the GLMz flow non-divergent. That step contained some inaccuarate statements about the coordinate transformation, while the rest of the paper contained an error on the surface dynamic boundary condition for viscous stresses. I am thankful to Mathias Delpey and Hidenori Aiki for pointing out these errors, which are corrected below.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA590591','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA590591"><span>Hybrid <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Simulation of Steep and Breaking Waves and Surface Fluxes in High Winds</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2012-09-30</p> <p><span class="hlt">Lagrangian</span> methods for free - surface turbulence and wave simulation . In the far field, coupled wind and wave simulations are used to obtain wind...to conserve the mass precisely. When the wave breaks, the flow at the free surface may become very violent, air and water may be highly mixed...fluids free - surface flows that can be used to study the fundamental physics of wave breaking. The research will improve the understanding of air-sea</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26317686','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26317686"><span>Particle transport in the human respiratory tract: formulation of a nodal inverse distance weighted <span class="hlt">Eulerian-Lagrangian</span> transport and implementation of the Wind-Kessel algorithm for an oral delivery.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kannan, Ravishekar; Guo, Peng; Przekwas, Andrzej</p> <p>2016-06-01</p> <p>This paper is the first in a series wherein efficient computational methods are developed and implemented to accurately quantify the transport, deposition, and clearance of the microsized particles (range of interest: 2 to 10 µm) in the human respiratory tract. In particular, this paper (part I) deals with (i) development of a detailed 3D computational finite volume mesh comprising of the NOPL (nasal, oral, pharyngeal and larynx), trachea and several airway generations; (ii) use of CFD Research Corporation's finite volume Computational Biology (CoBi) flow solver to obtain the flow physics for an oral inhalation simulation; (iii) implement a novel and accurate nodal inverse distance weighted <span class="hlt">Eulerian-Lagrangian</span> formulation to accurately obtain the deposition, and (iv) development of Wind-Kessel boundary condition algorithm. This new Wind-Kessel boundary condition algorithm allows the 'escaped' particles to reenter the airway through the outlets, thereby to an extent accounting for the drawbacks of having a finite number of lung generations in the computational mesh. The deposition rates in the NOPL, trachea, the first and second bifurcation were computed, and they were in reasonable accord with the Typical Path Length model. The quantitatively validated results indicate that these developments will be useful for (i) obtaining depositions in diseased lungs (because of asthma and COPD), for which there are no empirical models, and (ii) obtaining the secondary clearance (mucociliary clearance) of the deposited particles. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1437781-lagrangian-ocean-analysis-fundamentals-practices','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1437781-lagrangian-ocean-analysis-fundamentals-practices"><span><span class="hlt">Lagrangian</span> ocean analysis: Fundamentals and practices</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; ...</p> <p>2017-11-24</p> <p><span class="hlt">Lagrangian</span> analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the <span class="hlt">Lagrangian</span> approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. A variety of tools and methods for this purpose have emerged, over several decades. Here, we review the state of the art in the field of <span class="hlt">Lagrangian</span> analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolvedmore » physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. Our overall goal of this review paper is to reconcile some of the different techniques and methods in <span class="hlt">Lagrangian</span> ocean analysis, while recognising the rich diversity of <span class="hlt">codes</span> that have and continue to emerge, and the challenges of the coming age of petascale computing.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018OcMod.121...49V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018OcMod.121...49V"><span><span class="hlt">Lagrangian</span> ocean analysis: Fundamentals and practices</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan; Adams, Thomas P.; Berloff, Pavel; Biastoch, Arne; Blanke, Bruno; Chassignet, Eric P.; Cheng, Yu; Cotter, Colin J.; Deleersnijder, Eric; Döös, Kristofer; Drake, Henri F.; Drijfhout, Sybren; Gary, Stefan F.; Heemink, Arnold W.; Kjellsson, Joakim; Koszalka, Inga Monika; Lange, Michael; Lique, Camille; MacGilchrist, Graeme A.; Marsh, Robert; Mayorga Adame, C. Gabriela; McAdam, Ronan; Nencioli, Francesco; Paris, Claire B.; Piggott, Matthew D.; Polton, Jeff A.; Rühs, Siren; Shah, Syed H. A. M.; Thomas, Matthew D.; Wang, Jinbo; Wolfram, Phillip J.; Zanna, Laure; Zika, Jan D.</p> <p>2018-01-01</p> <p><span class="hlt">Lagrangian</span> analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the <span class="hlt">Lagrangian</span> approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of <span class="hlt">Lagrangian</span> analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in <span class="hlt">Lagrangian</span> ocean analysis, while recognising the rich diversity of <span class="hlt">codes</span> that have and continue to emerge, and the challenges of the coming age of petascale computing.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1437781-lagrangian-ocean-analysis-fundamentals-practices','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1437781-lagrangian-ocean-analysis-fundamentals-practices"><span><span class="hlt">Lagrangian</span> ocean analysis: Fundamentals and practices</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>van Sebille, Erik; Griffies, Stephen M.; Abernathey, Ryan</p> <p></p> <p><span class="hlt">Lagrangian</span> analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the <span class="hlt">Lagrangian</span> approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. A variety of tools and methods for this purpose have emerged, over several decades. Here, we review the state of the art in the field of <span class="hlt">Lagrangian</span> analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolvedmore » physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. Our overall goal of this review paper is to reconcile some of the different techniques and methods in <span class="hlt">Lagrangian</span> ocean analysis, while recognising the rich diversity of <span class="hlt">codes</span> that have and continue to emerge, and the challenges of the coming age of petascale computing.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDH23005V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDH23005V"><span>Estimates of <span class="hlt">Lagrangian</span> particle transport by wave groups: forward transport by Stokes drift and backward transport by the return flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>van den Bremer, Ton S.; Taylor, Paul H.</p> <p>2014-11-01</p> <p>Although the literature has examined Stokes drift, the net <span class="hlt">Lagrangian</span> transport by particles due to of surface gravity waves, in great detail, the motion of fluid particles transported by surface gravity wave groups has received considerably less attention. In practice nevertheless, the wave field on the open sea often has a group-like structure. The motion of particles is different, as particles at sufficient depth are transported backwards by the <span class="hlt">Eulerian</span> return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for wave groups ensuring the (irrotational) mass balance holds. We use WKB theory to study the variation of the <span class="hlt">Lagrangian</span> transport by the return current with depth distinguishing two-dimensional seas, three-dimensional seas, infinite depth and finite depth. We then provide dimensional estimates of the net horizontal <span class="hlt">Lagrangian</span> transport by the Stokes drift on the one hand and the return flow on the other hand for realistic sea states in all four cases. Finally we propose a simple scaling relationship for the transition depth: the depth above which <span class="hlt">Lagrangian</span> particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhPl...24e6115T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhPl...24e6115T"><span>Verification of Gyrokinetic <span class="hlt">codes</span>: Theoretical background and applications</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tronko, Natalia; Bottino, Alberto; Görler, Tobias; Sonnendrücker, Eric; Told, Daniel; Villard, Laurent</p> <p>2017-05-01</p> <p>In fusion plasmas, the strong magnetic field allows the fast gyro-motion to be systematically removed from the description of the dynamics, resulting in a considerable model simplification and gain of computational time. Nowadays, the gyrokinetic (GK) <span class="hlt">codes</span> play a major role in the understanding of the development and the saturation of turbulence and in the prediction of the subsequent transport. Naturally, these <span class="hlt">codes</span> require thorough verification and validation. Here, we present a new and generic theoretical framework and specific numerical applications to test the faithfulness of the implemented models to theory and to verify the domain of applicability of existing GK <span class="hlt">codes</span>. For a sound verification process, the underlying theoretical GK model and the numerical scheme must be considered at the same time, which has rarely been done and therefore makes this approach pioneering. At the analytical level, the main novelty consists in using advanced mathematical tools such as variational formulation of dynamics for systematization of basic GK <span class="hlt">code</span>'s equations to access the limits of their applicability. The verification of the numerical scheme is proposed via the benchmark effort. In this work, specific examples of <span class="hlt">code</span> verification are presented for two GK <span class="hlt">codes</span>: the multi-species electromagnetic ORB5 (PIC) and the radially global version of GENE (<span class="hlt">Eulerian</span>). The proposed methodology can be applied to any existing GK <span class="hlt">code</span>. We establish a hierarchy of reduced GK Vlasov-Maxwell equations implemented in the ORB5 and GENE <span class="hlt">codes</span> using the <span class="hlt">Lagrangian</span> variational formulation. At the computational level, detailed verifications of global electromagnetic test cases developed from the CYCLONE Base Case are considered, including a parametric β-scan covering the transition from ITG to KBM and the spectral properties at the nominal β value.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li class="active"><span>11</span></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_11 --> <div id="page_12" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li class="active"><span>12</span></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="221"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22608639-eulerian-frequency-analysis-structural-vibrations-from-high-speed-video','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22608639-eulerian-frequency-analysis-structural-vibrations-from-high-speed-video"><span><span class="hlt">Eulerian</span> frequency analysis of structural vibrations from high-speed video</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Venanzoni, Andrea; Siemens Industry Software NV, Interleuvenlaan 68, B-3001 Leuven; De Ryck, Laurent</p> <p></p> <p>An approach for the analysis of the frequency content of structural vibrations from high-speed video recordings is proposed. The techniques and tools proposed rely on an <span class="hlt">Eulerian</span> approach, that is, using the time history of pixels independently to analyse structural motion, as opposed to <span class="hlt">Lagrangian</span> approaches, where the motion of the structure is tracked in time. The starting point is an existing <span class="hlt">Eulerian</span> motion magnification method, which consists in decomposing the video frames into a set of spatial scales through a so-called Laplacian pyramid [1]. Each scale — or level — can be amplified independently to reconstruct a magnified motionmore » of the observed structure. The approach proposed here provides two analysis tools or pre-amplification steps. The first tool provides a representation of the global frequency content of a video per pyramid level. This may be further enhanced by applying an angular filter in the spatial frequency domain to each frame of the video before the Laplacian pyramid decomposition, which allows for the identification of the frequency content of the structural vibrations in a particular direction of space. This proposed tool complements the existing <span class="hlt">Eulerian</span> magnification method by amplifying selectively the levels containing relevant motion information with respect to their frequency content. This magnifies the displacement while limiting the noise contribution. The second tool is a holographic representation of the frequency content of a vibrating structure, yielding a map of the predominant frequency components across the structure. In contrast to the global frequency content representation of the video, this tool provides a local analysis of the periodic gray scale intensity changes of the frame in order to identify the vibrating parts of the structure and their main frequencies. Validation cases are provided and the advantages and limits of the approaches are discussed. The first validation case consists of the frequency</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA192285','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA192285"><span>MACH2: A Two-Dimensional Magnetohydrodynamic Simulation <span class="hlt">Code</span> for Complex Experimental Configurations.</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1987-09-01</p> <p><span class="hlt">Eulerian</span> or <span class="hlt">Lagrangian</span> flow problems, use of real equations of state and transport properties from the Los Alamos National Laboratory SESAME package...permissible problem geometries; time differencing; and spatial discretization, centering, and differ- encing of MACH2. /. I." - Magnetohydrodynamics...R-A & Y7 24 9 5.2 THE IDEAL COORDINATE SYSTEM DTIC TAB 13 24 5.3 THE MATERIAL DERIVATIVE Uannounoed 0 26 Justifloatlo- 6. TIME DIFFERENCING 31 6.1</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1995JCoPh.122..291L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1995JCoPh.122..291L"><span>A Shock-Adaptive Godunov Scheme Based on the Generalised <span class="hlt">Lagrangian</span> Formulation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lepage, C. Y.; Hui, W. H.</p> <p>1995-12-01</p> <p>Application of the Godunov scheme to the Euler equations of gas dynamics based on the <span class="hlt">Eulerian</span> formulation of flow smears discontinuities, sliplines especially, over several computational cells, while the accuracy in the smooth flow region is of the order O( h), where h is the cell width. Based on the generalised <span class="hlt">Lagrangian</span> formulation (GLF) of Hui et al., the Godunov scheme yields superior accuracy. By the use of coordinate streamlines in the GLF, the slipline—itself a streamline—is resolved crisply. Infinite shock resolution is achieved through the splitting of shock-cells. An improved entropy-conservation formulation of the governing equations is also proposed for computations in smooth flow regions. Finally, the use of the GLF substantially simplifies the programming logic resulting in a very robust, accurate, and efficient scheme.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1128909-multi-phase-cfd-modeling-solid-sorbent-carbon-capture-system','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1128909-multi-phase-cfd-modeling-solid-sorbent-carbon-capture-system"><span>Multi-phase CFD modeling of solid sorbent carbon capture system</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Ryan, E. M.; DeCroix, D.; Breault, R.</p> <p>2013-07-01</p> <p>Computational fluid dynamics (CFD) simulations are used to investigate a low temperature post-combustion carbon capture reactor. The CFD models are based on a small scale solid sorbent carbon capture reactor design from ADA-ES and Southern Company. The reactor is a fluidized bed design based on a silica-supported amine sorbent. CFD models using both Eulerian–<span class="hlt">Eulerian</span> and Eulerian–<span class="hlt">Lagrangian</span> multi-phase modeling methods are developed to investigate the hydrodynamics and adsorption of carbon dioxide in the reactor. Models developed in both FLUENT® and BARRACUDA are presented to explore the strengths and weaknesses of state of the art CFD <span class="hlt">codes</span> for modeling multi-phase carbon capturemore » reactors. The results of the simulations show that the FLUENT® Eulerian–<span class="hlt">Lagrangian</span> simulations (DDPM) are unstable for the given reactor design; while the BARRACUDA Eulerian–<span class="hlt">Lagrangian</span> model is able to simulate the system given appropriate simplifying assumptions. FLUENT® Eulerian–<span class="hlt">Eulerian</span> simulations also provide a stable solution for the carbon capture reactor given the appropriate simplifying assumptions.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1198063-assessing-effects-data-compression-simulations-using-physically-motivated-metrics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1198063-assessing-effects-data-compression-simulations-using-physically-motivated-metrics"><span>Assessing the Effects of Data Compression in Simulations Using Physically Motivated Metrics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Laney, Daniel; Langer, Steven; Weber, Christopher; ...</p> <p>2014-01-01</p> <p>This paper examines whether lossy compression can be used effectively in physics simulations as a possible strategy to combat the expected data-movement bottleneck in future high performance computing architectures. We show that, for the <span class="hlt">codes</span> and simulations we tested, compression levels of 3–5X can be applied without causing significant changes to important physical quantities. Rather than applying signal processing error metrics, we utilize physics-based metrics appropriate for each <span class="hlt">code</span> to assess the impact of compression. We evaluate three different simulation <span class="hlt">codes</span>: a <span class="hlt">Lagrangian</span> shock-hydrodynamics <span class="hlt">code</span>, an <span class="hlt">Eulerian</span> higher-order hydrodynamics turbulence modeling <span class="hlt">code</span>, and an <span class="hlt">Eulerian</span> coupled laser-plasma interaction <span class="hlt">code</span>. Wemore » compress relevant quantities after each time-step to approximate the effects of tightly coupled compression and study the compression rates to estimate memory and disk-bandwidth reduction. We find that the error characteristics of compression algorithms must be carefully considered in the context of the underlying physics being modeled.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA019968','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA019968"><span>LYNX: A Linked <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> <span class="hlt">Code</span>. Volume II. LYNX Computer Listing</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1975-11-01</p> <p>177« 178« 179» ISO* 18|» 182« 183» IBM * 185* 1B6« 187» 198« 189« 190« |f|i 192» 193« 194» 195» 196« 197» 198» 199* 200» 201...XPLC ID) ,Y(JD) ,TAUI ID) ,YB(IJD) .FBI IJD) ,T 1 3B ( ID ) • XCT I IJD) »VOBUjD» ,ZZ(NN0IM) ,VV(NND1M) »OBFUL •BETA tAP •OTCP iTP ...CELL CONTAINING PARTICLE NO I. •OB IOUFUL •BETA »AP •UTCP iTP •COMPEN ,SHEN •YP1 »YP2 •KMAX ,KBAR • 1JMA< ,IK»UX</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004PhR...392..279S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004PhR...392..279S"><span><span class="hlt">Lagrangian</span> fluid description with simple applications in compressible plasma and gas dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Schamel, Hans</p> <p>2004-03-01</p> <p>The <span class="hlt">Lagrangian</span> fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid elements, not only presents an alternative to the more common <span class="hlt">Eulerian</span> description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as <span class="hlt">Lagrangian</span> <span class="hlt">codes</span> and experimental techniques are developed utilizing the <span class="hlt">Lagrangian</span> point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in finite time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the <span class="hlt">Lagrangian</span> fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the <span class="hlt">Lagrangian</span> flow velocity is given by its initial value and hence the <span class="hlt">Lagrangian</span> velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1415468-netl-mfix-suite-multiphase-flow-models-brief-review-recent-applications-mfix-tfm-fossil-energy-technologies','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1415468-netl-mfix-suite-multiphase-flow-models-brief-review-recent-applications-mfix-tfm-fossil-energy-technologies"><span>The NETL MFiX Suite of multiphase flow models: A brief review and recent applications of MFiX-TFM to fossil energy technologies</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Li, Tingwen; Rogers, William A.; Syamlal, Madhava; ...</p> <p>2016-07-29</p> <p>Here, the MFiX suite of multiphase computational fluid dynamics (CFD) <span class="hlt">codes</span> is being developed at U.S. Department of Energy's National Energy Technology Laboratory (NETL). It includes several different approaches to multiphase simulation: MFiX-TFM, a two-fluid (Eulerian–<span class="hlt">Eulerian</span>) model; MFiX-DEM, an <span class="hlt">Eulerian</span> fluid model with a <span class="hlt">Lagrangian</span> Discrete Element Model for the solids phase; and MFiX-PIC, <span class="hlt">Eulerian</span> fluid model with <span class="hlt">Lagrangian</span> particle ‘parcels’ representing particle groups. These models are undergoing continuous development and application, with verification, validation, and uncertainty quantification (VV&UQ) as integrated activities. After a brief summary of recent progress in the verification, validation and uncertainty quantification (VV&UQ), this article highlightsmore » two recent accomplishments in the application of MFiX-TFM to fossil energy technology development. First, recent application of MFiX to the pilot-scale KBR TRIG™ Transport Gasifier located at DOE's National Carbon Capture Center (NCCC) is described. Gasifier performance over a range of operating conditions was modeled and compared to NCCC operational data to validate the ability of the model to predict parametric behavior. Second, comparison of <span class="hlt">code</span> predictions at a detailed fundamental scale is presented studying solid sorbents for the post-combustion capture of CO 2 from flue gas. Specifically designed NETL experiments are being used to validate hydrodynamics and chemical kinetics for the sorbent-based carbon capture process.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19890059396&hterms=nozzle+failure&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dnozzle%2Bfailure','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19890059396&hterms=nozzle+failure&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dnozzle%2Bfailure"><span>A combined <span class="hlt">Eulerian-Lagrangian</span> two-phase flow analysis of SSME HPOTP nozzle plug trajectories. II - Results</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Mcconnaughey, P. K.; Garcia, R.; Dejong, F. J.; Sabnis, J. S.; Pribik, D. A.</p> <p>1989-01-01</p> <p>An analysis of Space Shuttle Main Engine high-pressure oxygen turbopump nozzle plug trajectories has been performed, using a <span class="hlt">Lagrangian</span> method to track nozzle plug particles expelled from a turbine through a high Reynolds number flow in a turnaround duct with turning vanes. Axisymmetric and parametric analyses reveal that if nozzle plugs exited the turbine they would probably impact the LOX heat exchanger with impact velocities which are significantly less than the penetration velocity. The finding that only slight to moderate damage will result from nozzle plug failure in flight is supported by the results of a hot-fire engine test with induced nozzle plug failures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22482601','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22482601"><span><span class="hlt">Lagrangian</span> displacement tracking using a polar grid between endocardial and epicardial contours for cardiac strain imaging.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ma, Chi; Varghese, Tomy</p> <p>2012-04-01</p> <p>Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires <span class="hlt">Lagrangian</span> description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time. <span class="hlt">Lagrangian</span> based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polar-grid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure <span class="hlt">Lagrangian</span> description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time. A finite element based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the finite element model and our <span class="hlt">Lagrangian</span> approach to strain estimation. Traditional <span class="hlt">Eulerian</span> based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented. <span class="hlt">Lagrangian</span> displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both finite element and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/5708333-larc-computer-codes-lagrangian-analysis-stress-gauge-data-obtain-decomposition-rates-through-correlation-thermodynamic-variables','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/5708333-larc-computer-codes-lagrangian-analysis-stress-gauge-data-obtain-decomposition-rates-through-correlation-thermodynamic-variables"><span>LARC: computer <span class="hlt">codes</span> for <span class="hlt">Lagrangian</span> analysis of stress-gauge data to obtain decomposition rates through correlation to thermodynamic variables</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Anderson, A.B.; Wackerle, J.</p> <p>1983-07-01</p> <p>This report describes a package of five computer <span class="hlt">codes</span> for analyzing stress-gauge data from shock-wave experiments on reactive materials. The aim of the analysis is to obtain rate laws from experiment. A <span class="hlt">Lagrangian</span> analysis of the stress records, performed by program LANAL, provides flow histories of particle velocity, density, and energy. Three postprocessing programs, LOOKIT, LOOK1, and LOOK2, are included in the package of <span class="hlt">codes</span> for producing graphical output of the results of LANAL. Program RATE uses the flow histories in conjunction with an equation of state to calculate reaction-rate histories. RATE can be programmed to examine correlations between themore » rate histories and thermodynamic variables. Observed correlations can be incorporated into an appropriately parameterized rate law. Program RATE determines the values of these parameters that best reproduce the observed rate histories. The procedure is illustrated with a sample problem.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19990097981','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19990097981"><span><span class="hlt">Eulerian</span> Time-Domain Filtering for Spatial LES</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Pruett, C. David</p> <p>1997-01-01</p> <p><span class="hlt">Eulerian</span> time-domain filtering seems to be appropriate for LES (large eddy simulation) of flows whose large coherent structures convect approximately at a common characteristic velocity; e.g., mixing layers, jets, and wakes. For these flows, we develop an approach to LES based on an explicit second-order digital Butterworth filter, which is applied in,the time domain in an <span class="hlt">Eulerian</span> context. The approach is validated through a priori and a posteriori analyses of the simulated flow of a heated, subsonic, axisymmetric jet.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AIPC.1376...29S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AIPC.1376...29S"><span>Multiphase Fluid Dynamics for Spacecraft Applications</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shyy, W.; Sim, J.</p> <p>2011-09-01</p> <p>Multiphase flows involving moving interfaces between different fluids/phases are observed in nature as well as in a wide range of engineering applications. With the recent development of high fidelity computational techniques, a number of challenging multiphase flow problems can now be computed. We introduce the basic notion of the main categories of multiphase flow computation; <span class="hlt">Lagrangian</span>, <span class="hlt">Eulerian</span>, and <span class="hlt">Eulerian-Lagrangian</span> techniques to represent and follow interface, and sharp and continuous interface methods to model interfacial dynamics. The marker-based adaptive <span class="hlt">Eulerian-Lagrangian</span> method, which is one of the most popular methods, is highlighted with microgravity and space applications including droplet collision and spacecraft liquid fuel tank surface stability.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvF...3d4303M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvF...3d4303M"><span>Topology of two-dimensional turbulent flows of dust and gas</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mitra, Dhrubaditya; Perlekar, Prasad</p> <p>2018-04-01</p> <p>We perform direct numerical simulations (DNS) of passive heavy inertial particles (dust) in homogeneous and isotropic two-dimensional turbulent flows (gas) for a range of Stokes number, St<1 . We solve for the particles using both a <span class="hlt">Lagrangian</span> and an <span class="hlt">Eulerian</span> approach (with a shock-capturing scheme). In the latter, the particles are described by a dust-density field and a dust-velocity field. We find the following: the dust-density field in our <span class="hlt">Eulerian</span> simulations has the same correlation dimension d2 as obtained from the clustering of particles in the <span class="hlt">Lagrangian</span> simulations for St<1 ; the cumulative probability distribution function of the dust density coarse grained over a scale r , in the inertial range, has a left tail with a power-law falloff indicating the presence of voids; the energy spectrum of the dust velocity has a power-law range with an exponent that is the same as the gas-velocity spectrum except at very high Fourier modes; the compressibility of the dust-velocity field is proportional to St2. We quantify the topological properties of the dust velocity and the gas velocity through their gradient matrices, called A and B , respectively. Our DNS confirms that the statistics of topological properties of B are the same in <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> frames only if the <span class="hlt">Eulerian</span> data are weighed by the dust density. We use this correspondence to study the statistics of topological properties of A in the <span class="hlt">Lagrangian</span> frame from our <span class="hlt">Eulerian</span> simulations by calculating density-weighted probability distribution functions. We further find that in the <span class="hlt">Lagrangian</span> frame, the mean value of the trace of A is negative and its magnitude increases with St approximately as exp(-C /St) with a constant C ≈0.1 . The statistical distribution of different topological structures that appear in the dust flow is different in <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> (density-weighted <span class="hlt">Eulerian</span>) cases, particularly for St close to unity. In both of these cases, for small St the topological structures</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1996AIPC..370..993L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1996AIPC..370..993L"><span>A strong shock tube problem calculated by different numerical schemes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lee, Wen Ho; Clancy, Sean P.</p> <p>1996-05-01</p> <p>Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA <span class="hlt">code</span>, (2) UNICORN <span class="hlt">code</span>, (3) Schulz hydro, and (4) modified TVD scheme. The first two <span class="hlt">codes</span> are written in <span class="hlt">Eulerian</span> coordinates, whereas methods (3) and (4) are in <span class="hlt">Lagrangian</span> coordinates. MESA and UNICORN <span class="hlt">codes</span> are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. <span class="hlt">Code</span> (3) uses typical artificial viscosity for inviscid flow, whereas <span class="hlt">code</span> (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressure ratio of 109 and density ratio of 103 in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the <span class="hlt">Lagrangian</span> methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20140002508','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20140002508"><span>Very Large Eddy Simulations of a Jet-A Spray Reacting Flow in a Single Element LDI Injector With and Without Invoking an <span class="hlt">Eulerian</span> Scalar DWFDF Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shih, Tsan-Hsing; Liu, Nan-Suey</p> <p>2013-01-01</p> <p>This paper presents the very large eddy simulations (VLES) of a Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion <span class="hlt">Code</span> (NCC) with and without invoking the <span class="hlt">Eulerian</span> scalar DWFDF method, in which DWFDF is defined as the density weighted time filtered fine grained probability density function. The flow field is calculated by using the time filtered compressible Navier-Stokes equations (TFNS) with nonlinear subscale turbulence models, and when the <span class="hlt">Eulerian</span> scalar DWFDF method is invoked, the energy and species mass fractions are calculated by solving the equation of DWFDF. A nonlinear subscale model for closing the convection term of the <span class="hlt">Eulerian</span> scalar DWFDF equation is used and will be briefly described in this paper. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the <span class="hlt">Eulerian</span> scalar DWFDF method in both improving the simulation quality and maintaining economic computing cost are observed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28425587','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28425587"><span>Hybrid finite difference/finite element immersed boundary method.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>E Griffith, Boyce; Luo, Xiaoyu</p> <p>2017-12-01</p> <p>The immersed boundary method is an approach to fluid-structure interaction that uses a <span class="hlt">Lagrangian</span> description of the structural deformations, stresses, and forces along with an <span class="hlt">Eulerian</span> description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require <span class="hlt">Lagrangian</span> meshes that are finer than the <span class="hlt">Eulerian</span> grid. This work introduces a coupling scheme for the immersed boundary method to link the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the <span class="hlt">Eulerian</span> variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed <span class="hlt">Eulerian</span> grid spacing, coarser <span class="hlt">Lagrangian</span> structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The <span class="hlt">Lagrangian-Eulerian</span> coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015EGUGA..1713527P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015EGUGA..1713527P"><span>Inverse constraints for emission fluxes of atmospheric tracers estimated from concentration measurements and <span class="hlt">Lagrangian</span> transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pisso, Ignacio; Patra, Prabir; Breivik, Knut</p> <p>2015-04-01</p> <p><span class="hlt">Lagrangian</span> transport models based on times series of <span class="hlt">Eulerian</span> fields provide a computationally affordable way of achieving very high resolution for limited areas and time periods. This makes them especially suitable for the analysis of point-wise measurements of atmospheric tracers. We present an application illustrated with examples of greenhouse gases from anthropogenic emissions in urban areas and biogenic emissions in Japan and of pollutants in the Arctic. We asses the algorithmic complexity of the numerical implementation as well as the use of non-procedural techniques such as Object-Oriented programming. We discuss aspects related to the quantification of uncertainty from prior information in the presence of model error and limited number of observations. The case of non-linear constraints is explored using direct numerical optimisation methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PhFl...25g3302D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PhFl...25g3302D"><span>Stochastic-field cavitation model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dumond, J.; Magagnato, F.; Class, A.</p> <p>2013-07-01</p> <p>Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo <span class="hlt">codes</span> based on <span class="hlt">Lagrangian</span> "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on <span class="hlt">Eulerian</span> fields has been proposed which eliminates the necessity to mix <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFD.L2010Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFD.L2010Z"><span>Dual domain material point method for multiphase flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhang, Duan</p> <p>2017-11-01</p> <p>Although the particle-in-cell method was first invented in the 60's for fluid computations, one of its later versions, the material point method, is mostly used for solid calculations. Recent development of the multi-velocity formulations for multiphase flows and fluid-structure interactions requires the <span class="hlt">Lagrangian</span> capability of the method be combined with <span class="hlt">Eulerian</span> calculations for fluids. Because of different numerical representations of the materials, additional numerical schemes are needed to ensure continuity of the materials. New applications of the method to compute fluid motions have revealed numerical difficulties in various versions of the method. To resolve these difficulties, the dual domain material point method is introduced and improved. Unlike other particle based methods, the material point method uses both <span class="hlt">Lagrangian</span> particles and <span class="hlt">Eulerian</span> mesh, therefore it avoids direct communication between particles. With this unique property and the <span class="hlt">Lagrangian</span> capability of the method, it is shown that a multiscale numerical scheme can be efficiently built based on the dual domain material point method. In this talk, the theoretical foundation of the method will be introduced. Numerical examples will be shown. Work sponsored by the next generation <span class="hlt">code</span> project of LANL.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li class="active"><span>12</span></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_12 --> <div id="page_13" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li class="active"><span>13</span></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="241"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70164424','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70164424"><span>On tide-induced <span class="hlt">Lagrangian</span> residual current and residual transport: 2. Residual transport with application in south San Francisco Bay, California</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi</p> <p>1986-01-01</p> <p>The transports of solutes and other tracers are fundamental to estuarine processes. The apparent transport mechanisms are convection by tidal current and current-induced shear effect dispersion for processes which take place in a time period of the order of a tidal cycle. However, as emphasis is shifted toward the effects of intertidal processes, the net transport is mainly determined by tide-induced residual circulation and by residual circulation due to other processes. The commonly used intertidal conservation equation takes the form of a convection-dispersion equation in which the convective velocity is the <span class="hlt">Eulerian</span> residual current, and the dispersion terms are often referred to as the phase effect dispersion or, sometimes, as the “tidal dispersion.” The presence of these dispersion terms is merely the result of a Fickian type hypothesis. Since the actual processes are not Fickian, thus a Fickian hypothesis obscures the physical significance of this equation. Recent research results on residual circulation have suggested that long-term transport phenomena are closely related to the <span class="hlt">Lagrangian</span> residual current or the <span class="hlt">Lagrangian</span> residual transport. In this paper a new formulation of an intertidal conservation equation is presented and examined in detail. In a weakly nonlinear tidal estuary the resultant intertidal transport equation also takes the form of a convection-dispersion equation without the ad hoc introduction of phase effect dispersion in a form of dispersion tensor. The convective velocity in the resultant equation is the first-order <span class="hlt">Lagrangian</span> residual current (the sum of the <span class="hlt">Eulerian</span> residual current and the Stokes drift). The remaining dispersion terms are important only in higher-order solutions; they are due to shear effect dispersion and turbulent mixing. There exists a dispersion boundary layer adjacent to shoreline boundaries. An order of magnitude estimate of the properties in the dispersion boundary layer is given. The present treatment</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930065904&hterms=lean&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dlean','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930065904&hterms=lean&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dlean"><span>Computations of spray, fuel-air mixing, and combustion in a lean-premixed-prevaporized combustor</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dasgupta, A.; Li, Z.; Shih, T. I.-P.; Kundu, K.; Deur, J. M.</p> <p>1993-01-01</p> <p>A <span class="hlt">code</span> was developed for computing the multidimensional flow, spray, combustion, and pollutant formation inside gas turbine combustors. The <span class="hlt">code</span> developed is based on a <span class="hlt">Lagrangian-Eulerian</span> formulation and utilizes an implicit finite-volume method. The focus of this paper is on the spray part of the <span class="hlt">code</span> (both formulation and algorithm), and a number of issues related to the computation of sprays and fuel-air mixing in a lean-premixed-prevaporized combustor. The issues addressed include: (1) how grid spacings affect the diffusion of evaporated fuel, and (2) how spurious modes can arise through modelling of the spray in the <span class="hlt">Lagrangian</span> computations. An upwind interpolation scheme is proposed to account for some effects of grid spacing on the artificial diffusion of the evaporated fuel. Also, some guidelines are presented to minimize errors associated with the spurious modes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035993&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035993&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary-layer separation. I - General theory</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Van Dommelen, Leon L.; Cowley, Stephen J.</p> <p>1990-01-01</p> <p>Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of <span class="hlt">Eulerian</span> coordinates, a <span class="hlt">Lagrangian</span> approach may have significant analytical and computational advantages. In <span class="hlt">Lagrangian</span> coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDQ36002K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDQ36002K"><span>Verification of <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> simulations for fluid-particle flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kong, Bo; Patel, Ravi G.; Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney O.</p> <p>2017-11-01</p> <p>In this work, we study the performance of three simulation techniques for fluid-particle flows: (1) a volume-filtered Euler-Lagrange approach (EL), (2) a quadrature-based moment method using the anisotropic Gaussian closure (AG), and (3) a traditional two-fluid model. By simulating two problems: particles in frozen homogeneous isotropic turbulence (HIT), and cluster-induced turbulence (CIT), the convergence of the methods under grid refinement is found to depend on the simulation method and the specific problem, with CIT simulations facing fewer difficulties than HIT. Although EL converges under refinement for both HIT and CIT, its statistical results exhibit dependence on the techniques used to extract statistics for the particle phase. For HIT, converging both EE methods (TFM and AG) poses challenges, while for CIT, AG and EL produce similar results. Overall, all three methods face challenges when trying to extract converged, parameter-independent statistics due to the presence of shocks in the particle phase. National Science Foundation and National Energy Technology Laboratory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.329...48D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.329...48D"><span>A semi-<span class="hlt">Lagrangian</span> transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Doisneau, François; Arienti, Marco; Oefelein, Joseph C.</p> <p>2017-01-01</p> <p>For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the <span class="hlt">Eulerian</span> formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-<span class="hlt">Lagrangian</span> schemes, developed for Gas Dynamics. We show how semi-<span class="hlt">Lagrangian</span> formulations are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of <span class="hlt">Eulerian</span> fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22622237-semi-lagrangian-transport-method-kinetic-problems-application-dense-dilute-polydisperse-reacting-spray-flows','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22622237-semi-lagrangian-transport-method-kinetic-problems-application-dense-dilute-polydisperse-reacting-spray-flows"><span>A semi-<span class="hlt">Lagrangian</span> transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Doisneau, François, E-mail: fdoisne@sandia.gov; Arienti, Marco, E-mail: marient@sandia.gov; Oefelein, Joseph C., E-mail: oefelei@sandia.gov</p> <p></p> <p>For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier–Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the <span class="hlt">Eulerian</span> formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-<span class="hlt">Lagrangian</span> schemes, developed for Gas Dynamics. We show how semi-<span class="hlt">Lagrangian</span> formulations are relevant for a disperse phase far from equilibrium and where the particle–particle coupling barelymore » influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of <span class="hlt">Eulerian</span> fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011PhyS...83c5007N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011PhyS...83c5007N"><span>Some <span class="hlt">Lagrangians</span> for systems without a <span class="hlt">Lagrangian</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nucci, M. C.; Leach, P. G. L.</p> <p>2011-03-01</p> <p>We demonstrate how to construct many different <span class="hlt">Lagrangians</span> for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a <span class="hlt">Lagrangian</span>. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1432627-constrained-optimization-framework-interface-aware-sub-scale-dynamics-models-voids-closure-lagrangian-hydrodynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1432627-constrained-optimization-framework-interface-aware-sub-scale-dynamics-models-voids-closure-lagrangian-hydrodynamics"><span>Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Barlow, Andrew; Klima, Matej; Shashkov, Mikhail</p> <p>2018-04-02</p> <p>In hydrocodes, voids are used to represent vacuum and model free boundaries between vacuum and real materials. We give a systematic description of a new treatment of void closure in the framework of the multimaterial arbitrary Lagrangian–<span class="hlt">Eulerian</span> (ALE) methods. This includes a new formulation of the interface-aware sub-scale-dynamics (IA-SSD) closure model for multimaterial cells with voids, which is used in the <span class="hlt">Lagrangian</span> stage of our indirect ALE scheme. The results of the comprehensive testing of the new model are presented for one- and two-dimensional multimaterial calculations in the presence of voids. Finally, we also present a sneak peek of amore » realistic shaped charge calculation in the presence of voids and solids.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1432627-constrained-optimization-framework-interface-aware-sub-scale-dynamics-models-voids-closure-lagrangian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1432627-constrained-optimization-framework-interface-aware-sub-scale-dynamics-models-voids-closure-lagrangian-hydrodynamics"><span>Constrained optimization framework for interface-aware sub-scale dynamics models for voids closure in <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Barlow, Andrew; Klima, Matej; Shashkov, Mikhail</p> <p></p> <p>In hydrocodes, voids are used to represent vacuum and model free boundaries between vacuum and real materials. We give a systematic description of a new treatment of void closure in the framework of the multimaterial arbitrary Lagrangian–<span class="hlt">Eulerian</span> (ALE) methods. This includes a new formulation of the interface-aware sub-scale-dynamics (IA-SSD) closure model for multimaterial cells with voids, which is used in the <span class="hlt">Lagrangian</span> stage of our indirect ALE scheme. The results of the comprehensive testing of the new model are presented for one- and two-dimensional multimaterial calculations in the presence of voids. Finally, we also present a sneak peek of amore » realistic shaped charge calculation in the presence of voids and solids.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014EGUGA..1611016B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..1611016B"><span>Development of CO2 inversion system based on the adjoint of the global coupled transport model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Belikov, Dmitry; Maksyutov, Shamil; Chevallier, Frederic; Kaminski, Thomas; Ganshin, Alexander; Blessing, Simon</p> <p>2014-05-01</p> <p>We present the development of an inverse modeling system employing an adjoint of the global coupled transport model consisting of the National Institute for Environmental Studies (NIES) <span class="hlt">Eulerian</span> transport model (TM) and the <span class="hlt">Lagrangian</span> plume diffusion model (LPDM) FLEXPART. NIES TM is a three-dimensional atmospheric transport model, which solves the continuity equation for a number of atmospheric tracers on a grid spanning the entire globe. Spatial discretization is based on a reduced latitude-longitude grid and a hybrid sigma-isentropic coordinate in the vertical. NIES TM uses a horizontal resolution of 2.5°×2.5°. However, to resolve synoptic-scale tracer distributions and to have the ability to optimize fluxes at resolutions of 0.5° and higher we coupled NIES TM with the <span class="hlt">Lagrangian</span> model FLEXPART. The <span class="hlt">Lagrangian</span> component of the forward and adjoint models uses precalculated responses of the observed concentration to the surface fluxes and 3-D concentrations field simulated with the FLEXPART model. NIES TM and FLEXPART are driven by JRA-25/JCDAS reanalysis dataset. Construction of the adjoint of the <span class="hlt">Lagrangian</span> part is less complicated, as LPDMs calculate the sensitivity of measurements to the surrounding emissions field by tracking a large number of "particles" backwards in time. Developing of the adjoint to <span class="hlt">Eulerian</span> part was performed with automatic differentiation tool the Transformation of Algorithms in Fortran (TAF) software (http://www.FastOpt.com). This method leads to the discrete adjoint of NIES TM. The main advantage of the discrete adjoint is that the resulting gradients of the numerical cost function are exact, even for nonlinear algorithms. The overall advantages of our method are that: 1. No <span class="hlt">code</span> modification of <span class="hlt">Lagrangian</span> model is required, making it applicable to combination of global NIES TM and any <span class="hlt">Lagrangian</span> model; 2. Once run, the <span class="hlt">Lagrangian</span> output can be applied to any chemically neutral gas; 3. High-resolution results can be obtained over</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22410329-relativistic-eulerian-vlasov-simulations-amplification-seed-pulses-brillouin-backscattering-plasmas','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22410329-relativistic-eulerian-vlasov-simulations-amplification-seed-pulses-brillouin-backscattering-plasmas"><span>Relativistic <span class="hlt">Eulerian</span> Vlasov simulations of the amplification of seed pulses by Brillouin backscattering in plasmas</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Shoucri, M., E-mail: Shoucri.Magdi@ireq.ca; Matte, J.-P.; Vidal, F.</p> <p></p> <p>We apply an <span class="hlt">Eulerian</span> Vlasov <span class="hlt">code</span> to study the amplification by Brillouin scattering of a short seed laser pulse by a long pump laser pulse in an underdense plasma. The stimulated Brillouin backscattering interaction is the coupling of the pump and seed electromagnetic waves propagating in opposite directions, and the ion plasma wave. The <span class="hlt">code</span> solves the one-dimensional relativistic Vlasov-Maxwell set of equations. Large amplitude ion waves are generated. In the simulations we present, the density plateau of the plasma is n{sub e}=0.3 n{sub c} (n{sub c} is the critical density), which excludes spurious stimulated Raman scattering amplification (which can occurmore » only if n{sub e}« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24229270','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24229270"><span><span class="hlt">Lagrangian</span> statistics across the turbulent-nonturbulent interface in a turbulent plane jet.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Taveira, Rodrigo R; Diogo, José S; Lopes, Diogo C; da Silva, Carlos B</p> <p>2013-10-01</p> <p><span class="hlt">Lagrangian</span> statistics from millions of particles are used to study the turbulent entrainment mechanism in a direct numerical simulation of a turbulent plane jet at Re(λ) ≈ 110. The particles (tracers) are initially seeded at the irrotational region of the jet near the turbulent shear layer and are followed as they are drawn into the turbulent region across the turbulent-nonturbulent interface (TNTI), allowing the study of the enstrophy buildup and thereby characterizing the turbulent entrainment mechanism in the jet. The use of <span class="hlt">Lagrangian</span> statistics following fluid particles gives a more correct description of the entrainment mechanism than in previous works since the statistics in relation to the TNTI position involve data from the trajectories of the entraining fluid particles. The <span class="hlt">Lagrangian</span> statistics for the particles show the existence of a velocity jump and a characteristic vorticity jump (with a thickness which is one order of magnitude greater than the Kolmogorov microscale), in agreement with previous results using <span class="hlt">Eulerian</span> statistics. The particles initially acquire enstrophy by viscous diffusion and later by enstrophy production, which becomes "active" only deep inside the turbulent region. Both enstrophy diffusion and production near the TNTI differ substantially from inside the turbulent region. Only about 1% of all particles find their way into pockets of irrotational flow engulfed into the turbulent shear layer region, indicating that "engulfment" is not significant for the present flow, indirectly suggesting that the entrainment is largely due to "nibbling" small-scale mechanisms acting along the entire TNTI surface. Probability density functions of particle positions suggests that the particles spend more time crossing the region near the TNTI than traveling inside the turbulent region, consistent with the particles moving tangent to the interface around the time they cross it.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDD19001F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDD19001F"><span><span class="hlt">Lagrangian</span> particle drift and surface deformation in a rotating wave on a free liquid surface</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fontana, Paul W.; Francois, Nicolas; Xia, Hua; Punzmann, Horst; Shats, Michael</p> <p>2017-11-01</p> <p>A nonlinear model of a rotating wave on the free surface of a liquid is presented. The flow is assumed to be inviscid and irrotational. The wave is constructed as a superposition of two perpendicular, monochromatic standing Stokes waves and is standing-wave-like, but with ``antinodes'' or cells consisting of rotating surface gradients of alternating polarity. <span class="hlt">Lagrangian</span> fluid particle trajectories show a rotational drift about each cell in the direction of wave rotation, corresponding to a rotating Stokes drift. Each cell therefore has a circulating flow and localized angular momentum even though the <span class="hlt">Eulerian</span> flow is irrotational. Meanwhile, the wave sets up a static displacement of the free surface, making a trough in each cell. This static surface gradient provides a centripetal force that may account for additional rotation seen in experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992JCoPh.100..143B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992JCoPh.100..143B"><span>Momentum Advection on a Staggered Mesh</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Benson, David J.</p> <p>1992-05-01</p> <p><span class="hlt">Eulerian</span> and ALE (arbitrary <span class="hlt">Lagrangian-Eulerian</span>) hydrodynamics programs usually split a timestep into two parts. The first part is a <span class="hlt">Lagrangian</span> step, which calculates the incremental motion of the material. The second part is referred to as the <span class="hlt">Eulerian</span> step, the advection step, or the remap step, and it accounts for the transport of material between cells. In most finite difference and finite element formulations, all the solution variables except the velocities are cell-centered while the velocities are edge- or vertex-centered. As a result, the advection algorithm for the momentum is, by necessity, different than the algorithm used for the other variables. This paper reviews three momentum advection methods and proposes a new one. One method, pioneered in YAQUI, creates a new staggered mesh, while the other two, used in SALE and SHALE, are cell-centered. The new method is cell-centered and its relationship to the other methods is discussed. Both pure advection and strong shock calculations are presented to substantiate the mathematical analysis. From the standpoint of numerical accuracy, both the staggered mesh and the cell-centered algorithms can give good results, while the computational costs are highly dependent on the overall architecture of a <span class="hlt">code</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890014450','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890014450"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary layer separation. Part 1: General theory</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Vandommelen, Leon L.; Cowley, Stephen J.</p> <p>1989-01-01</p> <p>Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of <span class="hlt">Eulerian</span> coordinates, a <span class="hlt">Lagrangian</span> approach may have significant analytical and computational advantages. In <span class="hlt">Lagrangian</span> coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018ascl.soft04015Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018ascl.soft04015Y"><span>NR-<span class="hlt">code</span>: Nonlinear reconstruction <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yu, Yu; Pen, Ue-Li; Zhu, Hong-Ming</p> <p>2018-04-01</p> <p>NR-<span class="hlt">code</span> applies nonlinear reconstruction to the dark matter density field in redshift space and solves for the nonlinear mapping from the initial <span class="hlt">Lagrangian</span> positions to the final redshift space positions; this reverses the large-scale bulk flows and improves the precision measurement of the baryon acoustic oscillations (BAO) scale.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCHyd.172...48T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCHyd.172...48T"><span>Modeling coupled nanoparticle aggregation and transport in porous media: A <span class="hlt">Lagrangian</span> approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Taghavy, Amir; Pennell, Kurt D.; Abriola, Linda M.</p> <p>2015-01-01</p> <p>Changes in nanoparticle size and shape due to particle-particle interactions (i.e., aggregation or agglomeration) may significantly alter particle mobility and retention in porous media. To date, however, few modeling studies have considered the coupling of transport and particle aggregation processes. The majority of particle transport models employ an <span class="hlt">Eulerian</span> modeling framework and are, consequently, limited in the types of collisions and aggregate sizes that can be considered. In this work, a more general <span class="hlt">Lagrangian</span> modeling framework is developed and implemented to explore coupled nanoparticle aggregation and transport processes. The model was verified through comparison of model simulations to published results of an experimental and <span class="hlt">Eulerian</span> modeling study (Raychoudhury et al., 2012) of carboxymethyl cellulose (CMC)-modified nano-sized zero-valent iron particle (nZVI) transport and retention in water-saturated sand columns. A model sensitivity analysis reveals the influence of influent particle concentration (ca. 70 to 700 mg/L), primary particle size (10-100 nm) and pore water velocity (ca. 1-6 m/day) on particle-particle, and, consequently, particle-collector interactions. Model simulations demonstrate that, when environmental conditions promote particle-particle interactions, neglecting aggregation effects can lead to under- or over-estimation of nanoparticle mobility. Results also suggest that the extent to which higher order particle-particle collisions influence aggregation kinetics will increase with the fraction of primary particles. This work demonstrates the potential importance of time-dependent aggregation processes on nanoparticle mobility and provides a numerical model capable of capturing/describing these interactions in water-saturated porous media.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25437227','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25437227"><span>Modeling coupled nanoparticle aggregation and transport in porous media: a <span class="hlt">Lagrangian</span> approach.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Taghavy, Amir; Pennell, Kurt D; Abriola, Linda M</p> <p>2015-01-01</p> <p>Changes in nanoparticle size and shape due to particle-particle interactions (i.e., aggregation or agglomeration) may significantly alter particle mobility and retention in porous media. To date, however, few modeling studies have considered the coupling of transport and particle aggregation processes. The majority of particle transport models employ an <span class="hlt">Eulerian</span> modeling framework and are, consequently, limited in the types of collisions and aggregate sizes that can be considered. In this work, a more general <span class="hlt">Lagrangian</span> modeling framework is developed and implemented to explore coupled nanoparticle aggregation and transport processes. The model was verified through comparison of model simulations to published results of an experimental and <span class="hlt">Eulerian</span> modeling study (Raychoudhury et al., 2012) of carboxymethyl cellulose (CMC)-modified nano-sized zero-valent iron particle (nZVI) transport and retention in water-saturated sand columns. A model sensitivity analysis reveals the influence of influent particle concentration (ca. 70 to 700 mg/L), primary particle size (10-100 nm) and pore water velocity (ca. 1-6 m/day) on particle-particle, and, consequently, particle-collector interactions. Model simulations demonstrate that, when environmental conditions promote particle-particle interactions, neglecting aggregation effects can lead to under- or over-estimation of nanoparticle mobility. Results also suggest that the extent to which higher order particle-particle collisions influence aggregation kinetics will increase with the fraction of primary particles. This work demonstrates the potential importance of time-dependent aggregation processes on nanoparticle mobility and provides a numerical model capable of capturing/describing these interactions in water-saturated porous media. Copyright © 2014 Elsevier B.V. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/561813-strong-shock-tube-problem-calculated-different-numerical-schemes','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/561813-strong-shock-tube-problem-calculated-different-numerical-schemes"><span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Lee, W.H.; Clancy, S.P.</p> <p></p> <p>Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA <span class="hlt">code</span>, (2) UNICORN <span class="hlt">code</span>, (3) Schulz hydro, and (4) modified TVD scheme. The first two <span class="hlt">codes</span> are written in <span class="hlt">Eulerian</span> coordinates, whereas methods (3) and (4) are in <span class="hlt">Lagrangian</span> coordinates. MESA and UNICORN <span class="hlt">codes</span> are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. <span class="hlt">Code</span> (3) uses typical artificial viscosity for inviscid flow, whereas <span class="hlt">code</span> (4) uses a modified TVD scheme. The test problem is a strong shock tube problem with a pressuremore » ratio of 10{sup 9} and density ratio of 10{sup 3} in an ideal gas. For no mass-matching case, Schulz hydro is better than TVD scheme. In the case of mass-matching, there is no difference between them. MESA and UNICORN results are nearly the same. However, the computed positions such as the contact discontinuity (i.e. the material interface) are not as accurate as the <span class="hlt">Lagrangian</span> methods. {copyright} {ital 1996 American Institute of Physics.}« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009AGUSM.A34A..01S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009AGUSM.A34A..01S"><span>Implications of <span class="hlt">Lagrangian</span> Tracer Transport for Coupled Chemistry-Climate Simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Stenke, A.</p> <p>2009-05-01</p> <p>Today's coupled chemistry-climate models (CCM) consider a large number of trace species and feedback processes. Due to the radiative effect of some species, errors in simulated tracer distributions can feed back to model dynamics. Thus, shortcomings of the applied transport schemes can have severe implications for the overall model performance. Traditional <span class="hlt">Eulerian</span> approaches show a satisfactory performance in case of homogeneously distributed trace species, but they can lead to severe problems when applied to highly inhomogeneous tracer distributions. In case of sharp gradients many schemes show a considerable numerical diffusion. <span class="hlt">Lagrangian</span> approaches, on the other hand, combine a number of favourable numerical properties: They are strictly mass-conserving and do not suffer from numerical diffusion. Therefore they are able to maintain steeper gradients. A further advantage is that they allow the transport of a large number of tracers without being prohibitively expensive. A variety of benefits for stratospheric dynamics and chemistry resulting from a <span class="hlt">Lagrangian</span> transport algorithm are demonstrated by the example of the CCM E39C. In an updated version of E39C, called E39C-A, the operational semi-<span class="hlt">Lagrangian</span> advection scheme has been replaced with the purely <span class="hlt">Lagrangian</span> scheme ATTILA. It will be shown that several model deficiencies can be cured by the choice of an appropriate transport algorithm. The most important advancement concerns the reduction of a pronounced wet bias in the extra- tropical lowermost stratosphere. In turn, the associated temperature error ("cold bias") is significantly reduced. Stratospheric wind variations are now in better agreement with observations, e.g. E39C-A is able to reproduce the stratospheric wind reversal in the Southern Hemisphere in summer which was not captured by the previous model version. Resulting changes in wave propagation and dissipation lead to a weakening of the simulated mean meridional circulation and therefore a more</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li class="active"><span>13</span></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_13 --> <div id="page_14" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li class="active"><span>14</span></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="261"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26672054','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26672054"><span>Learn the <span class="hlt">Lagrangian</span>: A Vector-Valued RKHS Approach to Identifying <span class="hlt">Lagrangian</span> Systems.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cheng, Ching-An; Huang, Han-Pang</p> <p>2016-12-01</p> <p>We study the modeling of <span class="hlt">Lagrangian</span> systems with multiple degrees of freedom. Based on system dynamics, canonical parametric models require ad hoc derivations and sometimes simplification for a computable solution; on the other hand, due to the lack of prior knowledge in the system's structure, modern nonparametric models in machine learning face the curse of dimensionality, especially in learning large systems. In this paper, we bridge this gap by unifying the theories of <span class="hlt">Lagrangian</span> systems and vector-valued reproducing kernel Hilbert space. We reformulate <span class="hlt">Lagrangian</span> systems with kernels that embed the governing Euler-Lagrange equation-the <span class="hlt">Lagrangian</span> kernels-and show that these kernels span a subspace capturing the <span class="hlt">Lagrangian</span>'s projection as inverse dynamics. By such property, our model uses only inputs and outputs as in machine learning and inherits the structured form as in system dynamics, thereby removing the need for the mundane derivations for new systems as well as the generalization problem in learning from scratches. In effect, it learns the system's <span class="hlt">Lagrangian</span>, a simpler task than directly learning the dynamics. To demonstrate, we applied the proposed kernel to identify the robot inverse dynamics in simulations and experiments. Our results present a competitive novel approach to identifying <span class="hlt">Lagrangian</span> systems, despite using only inputs and outputs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JHyDy..30..122C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JHyDy..30..122C"><span>3-D <span class="hlt">Lagrangian</span>-based investigations of the time-dependent cloud cavitating flows around a Clark-Y hydrofoil with special emphasis on shedding process analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cheng, Huai-yu; Long, Xin-ping; Ji, Bin; Liu, Qi; Bai, Xiao-rui</p> <p>2018-02-01</p> <p>In the present paper, the unsteady cavitating flow around a 3-D Clark-Y hydrofoil is numerically investigated with the filter-based density correction model (FBDCM), a turbulence model and the Zwart-Gerber-Belamri (ZGB) cavitation model. A reasonable agreement is obtained between the numerical and experimental results. To study the complex flow structures more straightforwardly, a 3-D <span class="hlt">Lagrangian</span> technology is developed, which can provide the particle tracks and the 3-D <span class="hlt">Lagrangian</span> coherent structures (LCSs). Combined with the traditional methods based on the <span class="hlt">Eulerian</span> viewpoint, this technology is used to analyze the attached cavity evolution and the re-entrant jet behavior in detail. At stage I, the collapse of the previous shedding cavity and the growth of a new attached cavity, the significant influence of the collapse both on the suction and pressure sides are captured quite well by the 3-D LCSs, which is underestimated by the traditional methods like the iso-surface of Q-criteria. As a kind of special LCSs, the arching LCSs are observed in the wake, induced by the counter-rotating vortexes. At stage II, with the development of the re-entrant jet, the influence of the cavitation on the pressure side is still not negligible. And with this 3-D <span class="hlt">Lagrangian</span> technology, the tracks of the re-entrant jet are visualized clearly, moving from the trailing edge to the leading edge. Finally, at stage III, the re-entrant jet collides with the mainstream and finally induces the shedding. The cavitation evolution and the re-entrant jet movement in the whole cycle are well visualized with the 3-D <span class="hlt">Lagrangian</span> technology. Moreover, the comparison between the LCSs obtained with 2-D and 3-D <span class="hlt">Lagrangian</span> technologies indicates the advantages of the latter. It is demonstrated that the 3-D <span class="hlt">Lagrangian</span> technology is a promising tool in the investigation of complex cavitating flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19730006017','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19730006017"><span><span class="hlt">Lagrangian</span> description of warm plasmas</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kim, H.</p> <p>1970-01-01</p> <p>Efforts are described to extend the averaged <span class="hlt">Lagrangian</span> method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic <span class="hlt">Lagrangian</span> is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic <span class="hlt">Lagrangian</span>. In the first of these, the <span class="hlt">Lagrangian</span> is obtained by velocity integration of the exact microscopic <span class="hlt">Lagrangian</span>. In the second, the expanded hydrodynamic <span class="hlt">Lagrangian</span> is obtained directly from the expanded microscopic <span class="hlt">Lagrangian</span>. As applications of the microscopic <span class="hlt">Lagrangian</span>, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22311051-stochastic-field-cavitation-model','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22311051-stochastic-field-cavitation-model"><span>Stochastic-field cavitation model</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Dumond, J., E-mail: julien.dumond@areva.com; AREVA GmbH, Erlangen, Paul-Gossen-Strasse 100, D-91052 Erlangen; Magagnato, F.</p> <p>2013-07-15</p> <p>Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo <span class="hlt">codes</span> based on <span class="hlt">Lagrangian</span> “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on <span class="hlt">Eulerian</span> fields has been proposed which eliminates the necessity to mix <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-fieldmore » cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1993MsT.........23L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1993MsT.........23L"><span>A second-order shock-adaptive Godunov scheme based on the generalized <span class="hlt">Lagrangian</span> formulation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lepage, Claude</p> <p></p> <p>Application of the Godunov scheme to the Euler equations of gas dynamics, based on the <span class="hlt">Eulerian</span> formulation of flow, smears discontinuities (especially sliplines) over several computational cells, while the accuracy in the smooth flow regions is of the order of a function of the cell width. Based on the generalized <span class="hlt">Lagrangian</span> formulation (GLF), the Godunov scheme yields far superior results. By the use of coordinate streamlines in the GLF, the slipline (itself a streamline) is resolved crisply. Infinite shock resolution is achieved through the splitting of shock cells, while the accuracy in the smooth flow regions is improved using a nonconservative formulation of the governing equations coupled to a second order extension of the Godunov scheme. Furthermore, GLF requires no grid generation for boundary value problems and the simple structure of the solution to the Riemann problem in the GLF is exploited in the numerical implementation of the shock adaptive scheme. Numerical experiments reveal high efficiency and unprecedented resolution of shock and slipline discontinuities.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JGRC..123.1994T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JGRC..123.1994T"><span>Transformation of Deep Water Masses Along <span class="hlt">Lagrangian</span> Upwelling Pathways in the Southern Ocean</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tamsitt, V.; Abernathey, R. P.; Mazloff, M. R.; Wang, J.; Talley, L. D.</p> <p>2018-03-01</p> <p>Upwelling of northern deep waters in the Southern Ocean is fundamentally important for the closure of the global meridional overturning circulation and delivers carbon and nutrient-rich deep waters to the sea surface. We quantify water mass transformation along upwelling pathways originating in the Atlantic, Indian, and Pacific and ending at the surface of the Southern Ocean using <span class="hlt">Lagrangian</span> trajectories in an eddy-permitting ocean state estimate. Recent related work shows that upwelling in the interior below about 400 m depth is localized at hot spots associated with major topographic features in the path of the Antarctic Circumpolar Current, while upwelling through the surface layer is more broadly distributed. In the ocean interior upwelling is largely isopycnal; Atlantic and to a lesser extent Indian Deep Waters cool and freshen while Pacific deep waters are more stable, leading to a homogenization of water mass properties. As upwelling water approaches the mixed layer, there is net strong transformation toward lighter densities due to mixing of freshwater, but there is a divergence in the density distribution as Upper Circumpolar Deep Water tends become lighter and dense Lower Circumpolar Deep Water tends to become denser. The spatial distribution of transformation shows more rapid transformation at eddy hot spots associated with major topography where density gradients are enhanced; however, the majority of cumulative density change along trajectories is achieved by background mixing. We compare the <span class="hlt">Lagrangian</span> analysis to diagnosed <span class="hlt">Eulerian</span> water mass transformation to attribute the mechanisms leading to the observed transformation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/510351','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/510351"><span>An incompressible two-dimensional multiphase particle-in-cell model for dense particle flows</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Snider, D.M.; O`Rourke, P.J.; Andrews, M.J.</p> <p>1997-06-01</p> <p>A two-dimensional, incompressible, multiphase particle-in-cell (MP-PIC) method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a <span class="hlt">Lagrangian</span> model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to a <span class="hlt">Eulerian</span> grid and then mapping back computed stress tensors to particle positions. This approach utilizes the best of <span class="hlt">Eulerian/Eulerian</span> continuum models and <span class="hlt">Eulerian/Lagrangian</span> discrete models. The solution scheme allows for distributions of types, sizes, and density of particles,more » with no numerical diffusion from the <span class="hlt">Lagrangian</span> particle calculations. The computational method is implicit with respect to pressure, velocity, and volume fraction in the continuum solution thus avoiding courant limits on computational time advancement. MP-PIC simulations are compared with one-dimensional problems that have analytical solutions and with two-dimensional problems for which there are experimental data.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950049298&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950049298&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DLagrangian"><span><span class="hlt">Lagrangian</span> mixed layer modeling of the western equatorial Pacific</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shinoda, Toshiaki; Lukas, Roger</p> <p>1995-01-01</p> <p>Processes that control the upper ocean thermohaline structure in the western equatorial Pacific are examined using a <span class="hlt">Lagrangian</span> mixed layer model. The one-dimensional bulk mixed layer model of Garwood (1977) is integrated along the trajectories derived from a nonlinear 1 1/2 layer reduced gravity model forced with actual wind fields. The Global Precipitation Climatology Project (GPCP) data are used to estimate surface freshwater fluxes for the mixed layer model. The wind stress data which forced the 1 1/2 layer model are used for the mixed layer model. The model was run for the period 1987-1988. This simple model is able to simulate the isothermal layer below the mixed layer in the western Pacific warm pool and its variation. The subduction mechanism hypothesized by Lukas and Lindstrom (1991) is evident in the model results. During periods of strong South Equatorial Current, the warm and salty mixed layer waters in the central Pacific are subducted below the fresh shallow mixed layer in the western Pacific. However, this subduction mechanism is not evident when upwelling Rossby waves reach the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific or when a prominent deepening of the mixed layer occurs in the western equatorial Pacific due to episodes of strong wind and light precipitation associated with the El Nino-Southern Oscillation. Comparison of the results between the <span class="hlt">Lagrangian</span> mixed layer model and a locally forced <span class="hlt">Eulerian</span> mixed layer model indicated that horizontal advection of salty waters from the central Pacific strongly affects the upper ocean salinity variation in the western Pacific, and that this advection is necessary to maintain the upper ocean thermohaline structure in this region.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20180002538','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20180002538"><span>Acoustic Radiation Pressure</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Cantrell, John H.</p> <p>2018-01-01</p> <p>The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in <span class="hlt">Lagrangian</span> coordinates (not <span class="hlt">Eulerian</span> coordinates) and that the terms in the BST are not the momentum flux density and mean excess <span class="hlt">Eulerian</span> stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in <span class="hlt">Eulerian</span> coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean <span class="hlt">Eulerian</span> pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the <span class="hlt">Eulerian</span> pressure. It is shown that the transformation between <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the <span class="hlt">Lagrangian</span> radiation pressure in the propagation direction is equal to (2K) and the BST result that the <span class="hlt">Eulerian</span> radiation pressure in that direction</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.358..173F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.358..173F"><span>Enhancement of a 2D front-tracking algorithm with a non-uniform distribution of <span class="hlt">Lagrangian</span> markers</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Febres, Mijail; Legendre, Dominique</p> <p>2018-04-01</p> <p>The 2D front tracking method is enhanced to control the development of spurious velocities for non-uniform distributions of markers. The hybrid formulation of Shin et al. (2005) [7] is considered. A new tangent calculation is proposed for the calculation of the tension force at markers. A new reconstruction method is also proposed to manage non-uniform distributions of markers. We show that for both the static and the translating spherical drop test case the spurious currents are reduced to the machine precision. We also show that the ratio of the <span class="hlt">Lagrangian</span> grid size Δs over the <span class="hlt">Eulerian</span> grid size Δx has to satisfy Δs / Δx > 0.2 for ensuring such low level of spurious velocity. The method is found to provide very good agreement with benchmark test cases from the literature.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22069184-about-non-standard-lagrangians-cosmology','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22069184-about-non-standard-lagrangians-cosmology"><span>About non standard <span class="hlt">Lagrangians</span> in cosmology</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Dimitrijevic, Dragoljub D.; Milosevic, Milan</p> <p></p> <p>A review of non standard <span class="hlt">Lagrangians</span> present in modern cosmological models will be considered. Well known example of non standard <span class="hlt">Lagrangian</span> is Dirac-Born-Infeld (DBI) type <span class="hlt">Lagrangian</span> for tachyon field. Another type of non standard <span class="hlt">Lagrangian</span> under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory <span class="hlt">Lagrangian</span>. We will investigate homogenous cases of both DBI and p-adic fields and obtain <span class="hlt">Lagrangians</span> of the standard type which have the same equations of motions as aforementioned non standard one.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22391168-numerical-modeling-pulsed-laser-material-interaction-laser-plume-dynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22391168-numerical-modeling-pulsed-laser-material-interaction-laser-plume-dynamics"><span>Numerical modeling of pulsed laser-material interaction and of laser plume dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Zhao, Qiang; Shi, Yina</p> <p>2015-03-10</p> <p>We have developed two-dimensional Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) <span class="hlt">code</span> which is used to study the physical processes, the plasma absorption, the crater profile, and the temperature distribution on metallic target and below the surface. The ALE method overcomes problems with <span class="hlt">Lagrangian</span> moving mesh distortion by mesh smoothing and conservative quantities remapping from <span class="hlt">Lagrangian</span> mesh to smoothed one. A new second order accurate diffusion solver has been implemented for the thermal conduction and radiation transport on distorted mesh. The results of numerical simulation of pulsed laser ablation are presented. The influences of different processes, such as time evolution of the surfacemore » temperature, interspecies interactions (elastic collisions, recombination-dissociation reaction), interaction with an ambient gas are examined. The study presents particular interest for the analysis of experimental results obtained during pulsed laser ablation.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22600073-intercode-comparison-gyrokinetic-global-electromagnetic-modes','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22600073-intercode-comparison-gyrokinetic-global-electromagnetic-modes"><span>Intercode comparison of gyrokinetic global electromagnetic modes</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Görler, T., E-mail: tobias.goerler@ipp.mpg.de; Tronko, N.; Hornsby, W. A.</p> <p></p> <p>Aiming to fill a corresponding lack of sophisticated test cases for global electromagnetic gyrokinetic <span class="hlt">codes</span>, a new hierarchical benchmark is proposed. Starting from established test sets with adiabatic electrons, fully gyrokinetic electrons, and electrostatic fluctuations are taken into account before finally studying the global electromagnetic micro-instabilities. Results from up to five <span class="hlt">codes</span> involving representatives from different numerical approaches as particle-in-cell methods, <span class="hlt">Eulerian</span> and Semi-<span class="hlt">Lagrangian</span> are shown. By means of spectrally resolved growth rates and frequencies and mode structure comparisons, agreement can be confirmed on ion-gyro-radius scales, thus providing confidence in the correct implementation of the underlying equations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004AIPC..706..375L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004AIPC..706..375L"><span>Implementation of a High Explosive Equation of State into an <span class="hlt">Eulerian</span> Hydrocode</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Littlefield, David L.; Baker, Ernest L.</p> <p>2004-07-01</p> <p>The implementation of a high explosive equation of state into the <span class="hlt">Eulerian</span> hydrocode CTH is described. The equation of state is an extension to JWL referred to as JWLB, and is intended to model the thermodynamic state of detonation products from a high explosive reaction. The EOS was originally cast in a form p = p(ρ, e), where p is the pressure, ρ is the density and e is the internal energy. However, the target application <span class="hlt">code</span> requires an EOS of the form p = p(ρ, T), where T is the temperature, so it was necessary to reformulate the EOS in a thermodynamically consistent manner. A Helmholtz potential, developed from the original EOS, insures this consistency. Example calculations are shown that illustrate the veracity of this implementation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JCoPh.237..251S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JCoPh.237..251S"><span>A cell-centered <span class="hlt">Lagrangian</span> finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.</p> <p>2013-03-01</p> <p>A finite volume cell-centered <span class="hlt">Lagrangian</span> formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> hydrocodes in addition to analytical and experimental results are made to validate the current approach.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19750023590','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19750023590"><span>An investigation of turbulent transport in the extreme lower atmosphere</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Koper, C. A., Jr.; Sadeh, W. Z.</p> <p>1975-01-01</p> <p>A model in which the <span class="hlt">Lagrangian</span> autocorrelation is expressed by a domain integral over a set of usual <span class="hlt">Eulerian</span> autocorrelations acquired concurrently at all points within a turbulence box is proposed along with a method for ascertaining the statistical stationarity of turbulent velocity by creating an equivalent ensemble to investigate the flow in the extreme lower atmosphere. Simultaneous measurements of turbulent velocity on a turbulence line along the wake axis were carried out utilizing a longitudinal array of five hot-wire anemometers remotely operated. The stationarity test revealed that the turbulent velocity is approximated as a realization of a weakly self-stationary random process. Based on the <span class="hlt">Lagrangian</span> autocorrelation it is found that: (1) large diffusion time predominated; (2) ratios of <span class="hlt">Lagrangian</span> to <span class="hlt">Eulerian</span> time and spatial scales were smaller than unity; and, (3) short and long diffusion time scales and diffusion spatial scales were constrained within their <span class="hlt">Eulerian</span> counterparts.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20120013786','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20120013786"><span>Simulations of Spray Reacting Flows in a Single Element LDI Injector With and Without Invoking an <span class="hlt">Eulerian</span> Scalar PDF Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shih, Tsan-Hsing; Liu, Nan-Suey</p> <p>2012-01-01</p> <p>This paper presents the numerical simulations of the Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion <span class="hlt">Code</span> (NCC) with and without invoking the <span class="hlt">Eulerian</span> scalar probability density function (PDF) method. The flow field is calculated by using the Reynolds averaged Navier-Stokes equations (RANS and URANS) with nonlinear turbulence models, and when the scalar PDF method is invoked, the energy and compositions or species mass fractions are calculated by solving the equation of an ensemble averaged density-weighted fine-grained probability density function that is referred to here as the averaged probability density function (APDF). A nonlinear model for closing the convection term of the scalar APDF equation is used in the presented simulations and will be briefly described. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the <span class="hlt">Eulerian</span> scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JCoPh.229.8231C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JCoPh.229.8231C"><span>Differential geometry based solvation model I: <span class="hlt">Eulerian</span> formulation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chen, Zhan; Baker, Nathan A.; Wei, G. W.</p> <p>2010-11-01</p> <p>This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a <span class="hlt">Lagrangian</span> formulation of the surface energy into an <span class="hlt">Eulerian</span> formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2951687','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2951687"><span>Differential geometry based solvation model I: <span class="hlt">Eulerian</span> formulation</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Chen, Zhan; Baker, Nathan A.; Wei, G. W.</p> <p>2010-01-01</p> <p>This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a <span class="hlt">Lagrangian</span> formulation of the surface energy into an <span class="hlt">Eulerian</span> formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013IJCFD..27...32C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013IJCFD..27...32C"><span>Hyperviscosity for unstructured ALE meshes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cook, Andrew W.; Ulitsky, Mark S.; Miller, Douglas S.</p> <p>2013-01-01</p> <p>An artificial viscosity, originally designed for <span class="hlt">Eulerian</span> schemes, is adapted for use in arbitrary <span class="hlt">Lagrangian-Eulerian</span> simulations. Changes to the <span class="hlt">Eulerian</span> model (dubbed 'hyperviscosity') are discussed, which enable it to work within a <span class="hlt">Lagrangian</span> framework. New features include a velocity-weighted grid scale and a generalised filtering procedure, applicable to either structured or unstructured grids. The model employs an artificial shear viscosity for treating small-scale vorticity and an artificial bulk viscosity for shock capturing. The model is based on the Navier-Stokes form of the viscous stress tensor, including the diagonal rate-of-expansion tensor. A second-order version of the model is presented, in which Laplacian operators act on the velocity divergence and the grid-weighted strain-rate magnitude to ensure that the velocity field remains smooth at the grid scale. Unlike sound-speed-based artificial viscosities, the hyperviscosity model is compatible with the low Mach number limit. The new model outperforms a commonly used <span class="hlt">Lagrangian</span> artificial viscosity on a variety of test problems.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li class="active"><span>14</span></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_14 --> <div id="page_15" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li class="active"><span>15</span></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="281"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA588350','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA588350"><span>Nonlinear <span class="hlt">Eulerian</span> Thermoelasticity for Anisotropic Crystals</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2013-08-01</p> <p>the applied pressure. However, some crystalline materials such as ceramics and hard minerals may retain significant shear strength at finite strain...which elastic properties have been measured. Benefits of using <span class="hlt">Eulerian</span> strain measures for nonlinear elasticity of isotropic materials were extolled by...highly symmetric anharmonic properties . Deviations may be expected for highly anisotropic materials , as shown in Section 4. This work is focused</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940019171','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940019171"><span>Solution of mixed convection heat transfer from isothermal in-line fins</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Khalilollahi, Amir</p> <p>1993-01-01</p> <p>Transient and steady state combined natural and forced convective flows over two in-line finite thickness fins (louvers) in a vertical channel are numerically solved using two methods. The first method of solution is based on the 'Simple Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span>' (SALE) technique which incorporates mainly two computational phases: (1) a <span class="hlt">Lagrangian</span> phase in which the velocity field is updated by the effects of all forces, and (2) an <span class="hlt">Eulerian</span> phase that executes all advective fluxes of mass, momentum and energy. The second method of solution uses the finite element <span class="hlt">code</span> entitled FIDAP. In the first part, comparison of the results by FIDAP, SALE, and available experimental work were done and discussed for steady state forced convection over louvered fins. Good agreements were deduced between the three sets of results especially for the flow over a single fin. In the second part and in the absence of experimental literature, the numerical predictions were extended to the transient transports and to the opposing flow where pressure drop is reversed. Results are presented and discussed for heat transfer and pressure drop in assisting and opposing mixed convection flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1341976-multi-material-closure-model-high-order-finite-element-lagrangian-hydrodynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1341976-multi-material-closure-model-high-order-finite-element-lagrangian-hydrodynamics"><span>Multi-Material Closure Model for High-Order Finite Element <span class="hlt">Lagrangian</span> Hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.; ...</p> <p>2016-04-27</p> <p>We present a new closure model for single fluid, multi-material <span class="hlt">Lagrangian</span> hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–<span class="hlt">Eulerian</span> calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1341976','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1341976"><span>Multi-Material Closure Model for High-Order Finite Element <span class="hlt">Lagrangian</span> Hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.</p> <p></p> <p>We present a new closure model for single fluid, multi-material <span class="hlt">Lagrangian</span> hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–<span class="hlt">Eulerian</span> calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/966578','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/966578"><span>Laser Ray Tracing in a Parallel Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Adaptive Mesh Refinement Hydrocode</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Masters, N D; Kaiser, T B; Anderson, R W</p> <p>2009-09-28</p> <p>ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray-tracing in ALE-AMR. We present the equations of laser ray tracing, our approach to efficient traversal of the adaptive mesh hierarchy in which we propagate computational rays through a virtual composite mesh consisting of the finest resolution representation of the modeled space, and anticipate simulations that will be compared to experiments for <span class="hlt">code</span> validation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1985AmJPh..53..982J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1985AmJPh..53..982J"><span>Form of the manifestly covariant <span class="hlt">Lagrangian</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Johns, Oliver Davis</p> <p>1985-10-01</p> <p>The preferred form for the manifestly covariant <span class="hlt">Lagrangian</span> function of a single, charged particle in a given electromagnetic field is the subject of some disagreement in the textbooks. Some authors use a ``homogeneous'' <span class="hlt">Lagrangian</span> and others use a ``modified'' form in which the covariant Hamiltonian function is made to be nonzero. We argue in favor of the ``homogeneous'' form. We show that the covariant <span class="hlt">Lagrangian</span> theories can be understood only if one is careful to distinguish quantities evaluated on the varied (in the sense of the calculus of variations) world lines from quantities evaluated on the unvaried world lines. By making this distinction, we are able to derive the Hamilton-Jacobi and Klein-Gordon equations from the ``homogeneous'' <span class="hlt">Lagrangian</span>, even though the covariant Hamiltonian function is identically zero on all world lines. The derivation of the Klein-Gordon equation in particular gives <span class="hlt">Lagrangian</span> theoretical support to the derivations found in standard quantum texts, and is also shown to be consistent with the Feynman path-integral method. We conclude that the ``homogeneous'' <span class="hlt">Lagrangian</span> is a completely adequate basis for covariant <span class="hlt">Lagrangian</span> theory both in classical and quantum mechanics. The article also explores the analogy with the Fermat theorem of optics, and illustrates a simple invariant notation for the <span class="hlt">Lagrangian</span> and other four-vector equations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.5284P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.5284P"><span>A <span class="hlt">Lagrangian</span> stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Parsakhoo, Zahra; Shao, Yaping</p> <p>2017-04-01</p> <p>Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in <span class="hlt">Eulerian</span> models directly. We have developed a <span class="hlt">Lagrangian</span> stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different <span class="hlt">Lagrangian</span> time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19840024358','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19840024358"><span>Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Przekwas, A. J.; Singhal, A. K.; Tam, L. T.</p> <p>1984-01-01</p> <p>The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> approach to simulate two phase spray flow, evaporation and combustion. The modified <span class="hlt">code</span> is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.A51A2030N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A51A2030N"><span>Understanding spatial and temporal behavior of sea spray droplets in the marine atmospheric boundary layer using an <span class="hlt">Eulerian-Lagrangian</span> model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nissanka, I. D.; Richter, D. H.</p> <p>2017-12-01</p> <p>Previous studies have shown that sea spray droplets can play a significant role in air-sea heat and moisture exchange. The larger spray droplets have potential to transfer considerable amount of mass, momentum and heat, however they remain closer to surface and their residence times are shorter due to the faster settling. On the other hand, smaller droplets have high vertical mobility which allows sufficient time for droplets to adjust to ambient conditions. Hence, to study the heat and moisture characteristics of sea spray droplets it is important to understand how different droplet sizes behave in the Marine Atmospheric Boundary Layer (MABL), especially their temporal evolutions. In this study sea spray droplet transport in the MABL is simulated using Large Eddy Simulation combined with a <span class="hlt">Lagrangian</span> Particle model which represents spray droplets of varying size. The individual droplets are tracked while their radius and temperature evolve based on local ambient conditions. The particles are advected based on the local resolved velocities and the particle dispersion due to sub-filtered scale motions are modeled using a <span class="hlt">Lagrangian</span> stochastic model. In this study a series of simulations are conducted with the focus of understanding fundamental droplet microphysics, which will help characterize and quantify the lifetime and airborne concentrations of spray droplets in the MABL, thus elucidating ongoing knowledge gaps which are impossible to fill using observations alone. We measure the size resolved spray droplet vertical concentrations, particle residence times, and temporal evolution of droplet radius and temperature to explain the behavior of sea spry droplets in MABL. The PDF of residence time of different initial droplet sizes and joint PDFs of droplet life time and radius and temperature for different droplet sizes are calculated to further quantify the temporal and spatial behavior of sea spray droplets in the MABL, which can be used as inputs into bulk models</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007JCoPh.225..464J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007JCoPh.225..464J"><span>A purely <span class="hlt">Lagrangian</span> method for computing linearly-perturbed flows in spherical geometry</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jaouen, Stéphane</p> <p>2007-07-01</p> <p>In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in <span class="hlt">Lagrangian</span> coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the <span class="hlt">Lagrangian</span> perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, <span class="hlt">Lagrangian</span> systems of conservation laws. Invariance properties of <span class="hlt">Lagrangian</span> systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, <span class="hlt">Lagrangian</span> gas dynamics in two dimensions and <span class="hlt">Lagrangian</span> systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations <span class="hlt">Code</span> (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/18518379','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/18518379"><span>Extreme <span class="hlt">Lagrangian</span> acceleration in confined turbulent flow.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kadoch, Benjamin; Bos, Wouter J T; Schneider, Kai</p> <p>2008-05-09</p> <p>A <span class="hlt">Lagrangian</span> study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the <span class="hlt">Lagrangian</span> dynamics. It is found that the <span class="hlt">Lagrangian</span> acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the <span class="hlt">Lagrangian</span> acceleration as a function of the radius shows that the influence of the wall on the <span class="hlt">Lagrangian</span> dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the <span class="hlt">Lagrangian</span> statistics between this region, not directly influenced by the walls, and a critical radius which defines a <span class="hlt">Lagrangian</span> boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27176403','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27176403"><span>Turbulent transport with intermittency: Expectation of a scalar concentration.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Rast, Mark Peter; Pinton, Jean-François; Mininni, Pablo D</p> <p>2016-04-01</p> <p>Scalar transport by turbulent flows is best described in terms of <span class="hlt">Lagrangian</span> parcel motions. Here we measure the <span class="hlt">Eulerian</span> distance travel along <span class="hlt">Lagrangian</span> trajectories in a simple point vortex flow to determine the probabilistic impulse response function for scalar transport in the absence of molecular diffusion. As expected, the mean squared <span class="hlt">Eulerian</span> displacement scales ballistically at very short times and diffusively for very long times, with the displacement distribution at any given time approximating that of a random walk. However, significant deviations in the displacement distributions from Rayleigh are found. The probability of long distance transport is reduced over inertial range time scales due to spatial and temporal intermittency. This can be modeled as a series of trapping events with durations uniformly distributed below the <span class="hlt">Eulerian</span> integral time scale. The probability of long distance transport is, on the other hand, enhanced beyond that of the random walk for both times shorter than the <span class="hlt">Lagrangian</span> integral time and times longer than the <span class="hlt">Eulerian</span> integral time. The very short-time enhancement reflects the underlying <span class="hlt">Lagrangian</span> velocity distribution, while that at very long times results from the spatial and temporal variation of the flow at the largest scales. The probabilistic impulse response function, and with it the expectation value of the scalar concentration at any point in space and time, can be modeled using only the evolution of the lowest spatial wave number modes (the mean and the lowest harmonic) and an eddy based constrained random walk that captures the essential velocity phase relations associated with advection by vortex motions. Preliminary examination of <span class="hlt">Lagrangian</span> tracers in three-dimensional homogeneous isotropic turbulence suggests that transport in that setting can be similarly modeled.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26551100','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26551100"><span>"<span class="hlt">Lagrangian</span>" for a Non-<span class="hlt">Lagrangian</span> Field Theory with N=2 Supersymmetry.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Gadde, Abhijit; Razamat, Shlomo S; Willett, Brian</p> <p>2015-10-23</p> <p>We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 <span class="hlt">Lagrangian</span> description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a <span class="hlt">Lagrangian</span> description was previously unavailable. We utilize this description to compute several supersymmetric partition functions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcMod.119...45G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcMod.119...45G"><span>Attribution of horizontal and vertical contributions to spurious mixing in an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> ocean model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gibson, Angus H.; Hogg, Andrew McC.; Kiss, Andrew E.; Shakespeare, Callum J.; Adcroft, Alistair</p> <p>2017-11-01</p> <p>We examine the separate contributions to spurious mixing from horizontal and vertical processes in an ALE ocean model, MOM6, using reference potential energy (RPE). The RPE is a global diagnostic which changes only due to mixing between density classes. We extend this diagnostic to a sub-timestep timescale in order to individually separate contributions to spurious mixing through horizontal (tracer advection) and vertical (regridding/remapping) processes within the model. We both evaluate the overall spurious mixing in MOM6 against previously published output from other models (MOM5, MITGCM and MPAS-O), and investigate impacts on the components of spurious mixing in MOM6 across a suite of test cases: a lock exchange, internal wave propagation, and a baroclinically-unstable eddying channel. The split RPE diagnostic demonstrates that the spurious mixing in a lock exchange test case is dominated by horizontal tracer advection, due to the spatial variability in the velocity field. In contrast, the vertical component of spurious mixing dominates in an internal waves test case. MOM6 performs well in this test case owing to its quasi-<span class="hlt">Lagrangian</span> implementation of ALE. Finally, the effects of model resolution are examined in a baroclinic eddies test case. In particular, the vertical component of spurious mixing dominates as horizontal resolution increases, an important consideration as global models evolve towards higher horizontal resolutions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.681a2001I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.681a2001I"><span>Surface 3D nanostructuring by tightly focused laser pulse: simulations by <span class="hlt">Lagrangian</span> <span class="hlt">code</span> and molecular dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Inogamov, Nail A.; Zhakhovsky, Vasily V.</p> <p>2016-02-01</p> <p>There are many important applications in which the ultrashort diffraction-limited and therefore tightly focused laser pulses irradiates metal films mounted on dielectric substrate. Here we present the detailed picture of laser peeling and 3D structure formation of the thin (relative to a depth of a heat affected zone in the bulk targets) gold films on glass substrate. The underlying physics of such diffraction-limited laser peeling was not well understood previously. Our approach is based on a physical model which takes into consideration the new calculations of the two-temperature (2T) equation of state (2T EoS) and the two-temperature transport coefficients together with the coupling parameter between electron and ion subsystems. The usage of the 2T EoS and the kinetic coefficients is required because absorption of an ultrashort pulse with duration of 10-1000 fs excites electron subsystem of metal and transfers substance into the 2T state with hot electrons (typical electron temperatures 1-3 eV) and much colder ions. It is shown that formation of submicrometer-sized 3D structures is a result of the electron-ion energy transfer, melting, and delamination of film from substrate under combined action of electron and ion pressures, capillary deceleration of the delaminated liquid metal or semiconductor, and ultrafast freezing of molten material. We found that the freezing is going in non-equilibrium regime with strongly overcooled liquid phase. In this case the Stefan approximation is non-applicable because the solidification front speed is limited by the diffusion rate of atoms in the molten material. To solve the problem we have developed the 2T <span class="hlt">Lagrangian</span> <span class="hlt">code</span> including all this reach physics in. We also used the high-performance combined Monte- Carlo and molecular dynamics <span class="hlt">code</span> for simulation of surface 3D nanostructuring at later times after completion of electron-ion relaxation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=158803&keyword=nitrate+AND+multiscale&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=158803&keyword=nitrate+AND+multiscale&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>LINKING THE CMAQ AND HYSPLIT MODELING SYSTEM INTERFACE PROGRAM AND EXAMPLE APPLICATION</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>A new software tool has been developed to link the <span class="hlt">Eulerian</span>-based Community Multiscale Air Quality (CMAQ) modeling system with the <span class="hlt">Lagrangian</span>-based HYSPLIT (HYbrid Single-Particle <span class="hlt">Lagrangian</span> Integrated Trajectory) model. Both models require many of the same hourly meteorological...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29684700','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29684700"><span>How physiological and physical processes contribute to the phenology of cyanobacterial blooms in large shallow lakes: A new Euler-<span class="hlt">Lagrangian</span> coupled model.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Feng, Tao; Wang, Chao; Wang, Peifang; Qian, Jin; Wang, Xun</p> <p>2018-09-01</p> <p>Cyanobacterial blooms have emerged as one of the most severe ecological problems affecting large and shallow freshwater lakes. To improve our understanding of the factors that influence, and could be used to predict, surface blooms, this study developed a novel Euler-<span class="hlt">Lagrangian</span> coupled approach combining the <span class="hlt">Eulerian</span> model with agent-based modelling (ABM). The approach was subsequently verified based on monitoring datasets and MODIS data in a large shallow lake (Lake Taihu, China). The <span class="hlt">Eulerian</span> model solves the <span class="hlt">Eulerian</span> variables and physiological parameters, whereas ABM generates the complete life cycle and transport processes of cyanobacterial colonies. This model ensemble performed well in fitting historical data and predicting the dynamics of cyanobacterial biomass, bloom distribution, and area. Based on the calculated physical and physiological characteristics of surface blooms, principal component analysis (PCA) captured the major processes influencing surface bloom formation at different stages (two bloom clusters). Early bloom outbreaks were influenced by physical processes (horizontal transport and vertical turbulence-induced mixing), whereas buoyancy-controlling strategies were essential for mature bloom outbreaks. Canonical correlation analysis (CCA) revealed the combined actions of multiple environment variables on different bloom clusters. The effects of buoyancy-controlling strategies (ISP), vertical turbulence-induced mixing velocity of colony (VMT) and horizontal drift velocity of colony (HDT) were quantitatively compared using scenario simulations in the coupled model. VMT accounted for 52.9% of bloom formations and maintained blooms over long periods, thus demonstrating the importance of wind-induced turbulence in shallow lakes. In comparison, HDT and buoyancy controlling strategies influenced blooms at different stages. In conclusion, the approach developed here presents a promising tool for understanding the processes of onshore/offshore algal</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/21418120-backward-phase-flow-fbi-transform-based-eulerian-gaussian-beams-schroedinger-equation','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/21418120-backward-phase-flow-fbi-transform-based-eulerian-gaussian-beams-schroedinger-equation"><span>The backward phase flow and FBI-transform-based <span class="hlt">Eulerian</span> Gaussian beams for the Schroedinger equation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Leung Shingyu, E-mail: masyleung@ust.h; Qian Jianliang, E-mail: qian@math.msu.ed</p> <p>2010-11-20</p> <p>We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based <span class="hlt">Eulerian</span> Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of <span class="hlt">Eulerian</span> Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the <span class="hlt">Eulerian</span> Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the <span class="hlt">Eulerian</span> Gaussian beam framework. Essentially we reinitialize beam propagation by applying themore » FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017RSPSA.47370558O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017RSPSA.47370558O"><span><span class="hlt">Lagrangian</span> averaging with geodesic mean</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Oliver, Marcel</p> <p>2017-11-01</p> <p>This paper revisits the derivation of the <span class="hlt">Lagrangian</span> averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy <span class="hlt">Lagrangian</span> of an ideal fluid yields the LAE <span class="hlt">Lagrangian</span>. The derivation presented here assumes a Euclidean spatial domain without boundaries.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29225505','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29225505"><span><span class="hlt">Lagrangian</span> averaging with geodesic mean.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Oliver, Marcel</p> <p>2017-11-01</p> <p>This paper revisits the derivation of the <span class="hlt">Lagrangian</span> averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy <span class="hlt">Lagrangian</span> of an ideal fluid yields the LAE <span class="hlt">Lagrangian</span>. The derivation presented here assumes a Euclidean spatial domain without boundaries.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li class="active"><span>15</span></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_15 --> <div id="page_16" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li class="active"><span>16</span></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="301"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20364958','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20364958"><span>Asymptotic shape of the region visited by an <span class="hlt">Eulerian</span> walker.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kapri, Rajeev; Dhar, Deepak</p> <p>2009-11-01</p> <p>We study an <span class="hlt">Eulerian</span> walker on a square lattice, starting from an initial randomly oriented background using Monte Carlo simulations. We present evidence that, for a large number of steps N , the asymptotic shape of the set of sites visited by the walker is a perfect circle. The radius of the circle increases as N1/3, for large N , and the width of the boundary region grows as Nalpha/3, with alpha=0.40+/-0.06 . If we introduce stochasticity in the evolution rules, the mean-square displacement of the walker, <RN2> approximately <RN2> approximately N2nu, shows a crossover from the <span class="hlt">Eulerian</span> (nu=1/3) to a simple random-walk (nu=1/2) behavior.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUFMEP42A..04G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUFMEP42A..04G"><span>Modeling Sediment Transport Using a <span class="hlt">Lagrangian</span> Particle Tracking Algorithm Coupled with High-Resolution Large Eddy Simulations: a Critical Analysis of Model Limits and Sensitivity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Garcia, M. H.</p> <p>2016-12-01</p> <p>Modeling Sediment Transport Using a <span class="hlt">Lagrangian</span> Particle Tracking Algorithm Coupled with High-Resolution Large Eddy Simulations: a Critical Analysis of Model Limits and Sensitivity Som Dutta1, Paul Fischer2, Marcelo H. Garcia11Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Il, 61801 2Department of Computer Science and Department of MechSE, University of Illinois at Urbana-Champaign, Urbana, Il, 61801 Since the seminal work of Niño and Garcia [1994], one-way coupled <span class="hlt">Lagrangian</span> particle tracking has been used extensively for modeling sediment transport. Over time, the <span class="hlt">Lagrangian</span> particle tracking method has been coupled with <span class="hlt">Eulerian</span> flow simulations, ranging from Reynolds Averaged Navier-Stokes (RANS) based models to Detached Eddy Simulations (DES) [Escauriaza and Sotiropoulos, 2011]. Advent of high performance computing (HPC) platforms and faster algorithms have resulted in the work of Dutta et al. [2016], where <span class="hlt">Lagrangian</span> particle tracking was coupled with high-resolution Large Eddy Simulations (LES) to model the complex and highly non-linear phenomenon of Bulle-Effect at diversions. Despite all the advancements in using <span class="hlt">Lagrangian</span> particle tracking, there has not been a study that looks in detail at the limits of the model in the context of sediment transport, and also analyzes the sensitivity of the various force formulation in the force balance equation of the particles. Niño and Garcia [1994] did a similar analysis, but the vertical flow velocity distribution was modeled as the log-law. The current study extends the analysis by modeling the flow using high-resolution LES at a Reynolds number comparable to experiments of Niño et al. [1994]. Dutta et al., (2016), Large Eddy Simulation (LES) of flow and bedload transport at an idealized 90-degree diversion: insight into Bulle-Effect, River Flow 2016 - Constantinescu, Garcia & Hanes (Eds), Taylor & Francis Group, London, 101-109. Escauriaza and Sotiropoulos</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20010062151','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20010062151"><span>Impact Cratering Calculations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ahrens, Thomas J.</p> <p>2001-01-01</p> <p>This research is computational /theoretical and complements the Caltech experimental program. We have developed an understanding of the basic physical processes and produced computational models and implemented these into <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> finite element <span class="hlt">codes</span>. The key issues we have addressed include the conditions required for: faulting (strain localization), elastic moduli weakening, dynamic weakening (layering elastic instabilities and fluidization), bulking (creation of porosity at zero pressure) and compaction of pores, frictional melting (creation of pseudotachylytes), partial and selective devolatilization of materials (e.g. CaCO3, water/ice mixtures), and debris flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20010028951','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20010028951"><span><span class="hlt">Lagrangian</span> Approach to Jet Mixing and Optimization of the Reactor for Production of Carbon Nanotubes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Povitsky, Alex; Salas, Manuel D.</p> <p>2001-01-01</p> <p>This study was motivated by an attempt to optimize the High Pressure carbon oxide (HiPco) process for the production of carbon nanotubes from gaseous carbon oxide, The goal is to achieve rapid and uniform heating of catalyst particles by an optimal arrangement of jets. A mixed <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> approach is implemented to track the temperature of catalyst particles along their trajectories as a function of time. The FLUENT CFD software with second-order upwind approximation of convective terms and an algebraic multigrid-based solver is used. The poor performance of the original reactor configuration is explained in terms of features of particle trajectories. The trajectories most exposed to the hot jets appear to be the most problematic for heating because they either bend towards the cold jet interior or rotate upwind of the mixing zone. To reduce undesirable slow and/or oscillatory heating of catalyst particles, a reactor configuration with three central jets is proposed and the optimal location of the central and peripheral nozzles is determined.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20120003371','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20120003371"><span>LSPRAY-IV: A <span class="hlt">Lagrangian</span> Spray Module</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.</p> <p>2012-01-01</p> <p>LSPRAY-IV is a <span class="hlt">Lagrangian</span> spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray. Some important research areas covered as a part of the <span class="hlt">code</span> development are: (1) the extension of combined CFD/scalar-Monte- Carlo-PDF method to spray modeling, (2) the multi-component liquid spray modeling, and (3) the assessment of various atomization models used in spray calculations. The current version contains the extension to the modeling of superheated sprays. The manual provides the user with an understanding of various models involved in the spray formulation, its <span class="hlt">code</span> structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017GMD....10.4175L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017GMD....10.4175L"><span>Parcels v0.9: prototyping a <span class="hlt">Lagrangian</span> ocean analysis framework for the petascale age</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lange, Michael; van Sebille, Erik</p> <p>2017-11-01</p> <p>As ocean general circulation models (OGCMs) move into the petascale age, where the output of single simulations exceeds petabytes of storage space, tools to analyse the output of these models will need to scale up too. <span class="hlt">Lagrangian</span> ocean analysis, where virtual particles are tracked through hydrodynamic fields, is an increasingly popular way to analyse OGCM output, by mapping pathways and connectivity of biotic and abiotic particulates. However, the current software stack of <span class="hlt">Lagrangian</span> ocean analysis <span class="hlt">codes</span> is not dynamic enough to cope with the increasing complexity, scale and need for customization of use-cases. Furthermore, most community <span class="hlt">codes</span> are developed for stand-alone use, making it a nontrivial task to integrate virtual particles at runtime of the OGCM. Here, we introduce the new Parcels <span class="hlt">code</span>, which was designed from the ground up to be sufficiently scalable to cope with petascale computing. We highlight its API design that combines flexibility and customization with the ability to optimize for HPC workflows, following the paradigm of domain-specific languages. Parcels is primarily written in Python, utilizing the wide range of tools available in the scientific Python ecosystem, while generating low-level C <span class="hlt">code</span> and using just-in-time compilation for performance-critical computation. We show a worked-out example of its API, and validate the accuracy of the <span class="hlt">code</span> against seven idealized test cases. This version 0.9 of Parcels is focused on laying out the API, with future work concentrating on support for curvilinear grids, optimization, efficiency and at-runtime coupling with OGCMs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20150023469','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20150023469"><span>LSPRAY-V: A <span class="hlt">Lagrangian</span> Spray Module</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.</p> <p>2015-01-01</p> <p>LSPRAY-V is a <span class="hlt">Lagrangian</span> spray solver developed for application with unstructured grids and massively parallel computers. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray encountered over a wide range of operating conditions in modern aircraft engine development. It could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The manual provides the user with an understanding of various models involved in the spray formulation, its <span class="hlt">code</span> structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-V, we have advanced the state-of-the-art in spray computations in several important ways.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/21044884-assessment-eulerian-particle-flamelet-model-nonpremixed-turbulent-jet-flames','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/21044884-assessment-eulerian-particle-flamelet-model-nonpremixed-turbulent-jet-flames"><span>Assessment of the <span class="hlt">Eulerian</span> particle flamelet model for nonpremixed turbulent jet flames</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Kim, Seong-Ku; Kim, Yongmo</p> <p>2008-07-15</p> <p>Although the <span class="hlt">Eulerian</span> particle flamelet model (EPFM) recently proposed by Barths et al. [Proc. Combust. Inst. 27 (1998) 1841-1847] has shown the potential capabilities to realistically predict detailed pollutant (NO{sub x}, soot) formation in a turbulent reacting flow occurring within practical combustion devices, there still exists room to improve the predicative capability in terms of local flame structure and turbulence-chemistry interaction. In this study, the EPFM approach was applied to simulate two turbulent nonpremixed jet flames of CO/H{sub 2}/N{sub 2} fuel having the same jet Reynolds number but different nozzle diameters, and the capability of predicting the NO{sub x} formationmore » as well as both similarity of major species and sensitivity of minor species to fluid-dynamic scaling for the two flames has been assessed deeply in terms of both conditional and unconditional mean structures. The present results indicate that the original EPFM substantially overpredicts the conditional scalar dissipation rate at the downstream region and consequently underpredicts the streamwise decay of superequilibrium radical concentrations to the equilibrium state. In this study, in order to correctly estimate the averaged conditional scalar dissipation rate, a new modeling of the conditional scalar dissipation rate based on a least-squares fit through a mass weighted spatial distribution has been devised. In terms of both conditional and unconditional means, the EPFM utilizing this new procedure yields nearly the same results as the <span class="hlt">Lagrangian</span> flamelet model, and provides closer agreement with experimental data than the original EPFM approach. (author)« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=85010&Lab=NERL&keyword=Network+AND+security&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=85010&Lab=NERL&keyword=Network+AND+security&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>QUANTIFYING SUBGRID POLLUTANT VARIABILITY IN <span class="hlt">EULERIAN</span> AIR QUALITY MODELS</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>In order to properly assess human risk due to exposure to hazardous air pollutants or air toxics, detailed information is needed on the location and magnitude of ambient air toxic concentrations. Regional scale <span class="hlt">Eulerian</span> air quality models are typically limited to relatively coar...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25059889','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25059889"><span><span class="hlt">Lagrangian</span> postprocessing of computational hemodynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Shadden, Shawn C; Arzani, Amirhossein</p> <p>2015-01-01</p> <p>Recent advances in imaging, modeling, and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries, and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform <span class="hlt">Lagrangian</span> particle tracking, and other <span class="hlt">Lagrangian</span>-based postprocessing. As described herein, <span class="hlt">Lagrangian</span> methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review <span class="hlt">Lagrangian</span> methods that have been used in post-processing velocity data of cardiovascular flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4289096','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4289096"><span><span class="hlt">Lagrangian</span> postprocessing of computational hemodynamics</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Shadden, Shawn C.; Arzani, Amirhossein</p> <p>2014-01-01</p> <p>Recent advances in imaging, modeling and computing have rapidly expanded our capabilities to model hemodynamics in the large vessels (heart, arteries and veins). This data encodes a wealth of information that is often under-utilized. Modeling (and measuring) blood flow in the large vessels typically amounts to solving for the time-varying velocity field in a region of interest. Flow in the heart and larger arteries is often complex, and velocity field data provides a starting point for investigating the hemodynamics. This data can be used to perform <span class="hlt">Lagrangian</span> particle tracking, and other <span class="hlt">Lagrangian</span>-based postprocessing. As described herein, <span class="hlt">Lagrangian</span> methods are necessary to understand inherently transient hemodynamic conditions from the fluid mechanics perspective, and to properly understand the biomechanical factors that lead to acute and gradual changes of vascular function and health. The goal of the present paper is to review <span class="hlt">Lagrangian</span> methods that have been used in post-processing velocity data of cardiovascular flows. PMID:25059889</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EGUGA..15.8041M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..15.8041M"><span>Testing of a new dense gas approach in the <span class="hlt">Lagrangian</span> Dispersion Model SPRAY.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mortarini, Luca; Alessandrini, Stefano; Ferrero, Enrico; Anfossi, Domenico; Manfrin, Massimiliano</p> <p>2013-04-01</p> <p>A new original method for the dispersion of a positively and negatively buoyant plume is proposed. The buoyant pollutant movement is treated introducing a fictitious scalar inside the <span class="hlt">Lagrangian</span> Stochastic Particle Model SPRAY. The method is based on the same idea of Alessandrini and Ferrero (Phys. A 388:1375-1387, 2009) for the treatment of a background substance entrainment into the plume. In this application, the fictitious scalar is the density and momentum difference between the plume portions and the environment air that naturally takes into account the interaction between the plume and the environment. As a consequence, no more particles than those inside the plume have to be released to simulate the entrainment of the background air temperature. In this way the entrainment is properly simulated and the plume sink is calculated from the local property of the flow. This new approach is wholly <span class="hlt">Lagrangian</span> in the sense that the <span class="hlt">Eulerian</span> grid is only used to compute the propriety of a portion of the plume from the particles contained in every cell. No equation of the bulk plume is solved on a fixed grid. To thoroughly test the turbulent velocity field calculated by the model, the latter is compared with a water tank experiment carried out in the TURLAB laboratory in Turin (Italy). A vertical density driven current was created releasing a saline solution (salt and water) in a water tank with no mean flow. The experiment reproduces in physical similarity, based on the density Froud number, the release of a dense gas in the planetary boundary layer and the Particle Image Velocimetry technique has been used to analyze the buoyancy generated velocity field. The high temporal and spatial resolution of the measurements gives a deep insight to the problems of the bouncing of the dense gas and of the creation of the outflow velocity at the ground.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1013753','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1013753"><span>Forecasting Future Sea Ice Conditions: A <span class="hlt">Lagrangian</span> Approach</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2015-09-30</p> <p>1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Forecasting Future Sea Ice Conditions: A <span class="hlt">Lagrangian</span> ...GCMs participating in IPCC AR5 agree with observed source region patterns from the satellite- derived dataset. 4- Compare <span class="hlt">Lagrangian</span> ice... <span class="hlt">Lagrangian</span> sea-ice back trajectories to estimate thermodynamic and dynamic (advection) ice loss. APPROACH We use a <span class="hlt">Lagrangian</span> trajectory model to</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhyA..393..337B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhyA..393..337B"><span>Option volatility and the acceleration <span class="hlt">Lagrangian</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Baaquie, Belal E.; Cao, Yang</p> <p>2014-01-01</p> <p>This paper develops a volatility formula for option on an asset from an acceleration <span class="hlt">Lagrangian</span> model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent <span class="hlt">Lagrangian</span>. The acceleration <span class="hlt">Lagrangian</span> is defined, and the classical solution of the system in Euclidean time is solved by choosing proper boundary conditions. The conditional probability distribution of final position given the initial position is obtained from the transition amplitude. The volatility is the standard deviation of the conditional probability distribution. Using the conditional probability and the path integral method, the martingale condition is applied, and one of the parameters in the <span class="hlt">Lagrangian</span> is fixed. The call option price is obtained using the conditional probability and the path integral method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002APS..DFD.AK010R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002APS..DFD.AK010R"><span>Stochastic modeling of <span class="hlt">Lagrangian</span> accelerations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Reynolds, Andy</p> <p>2002-11-01</p> <p>It is shown how Sawford's second-order <span class="hlt">Lagrangian</span> stochastic model (Phys. Fluids A 3, 1577-1586, 1991) for fluid-particle accelerations can be combined with a model for the evolution of the dissipation rate (Pope and Chen, Phys. Fluids A 2, 1437-1449, 1990) to produce a <span class="hlt">Lagrangian</span> stochastic model that is consistent with both the measured distribution of <span class="hlt">Lagrangian</span> accelerations (La Porta et al., Nature 409, 1017-1019, 2001) and Kolmogorov's similarity theory. The later condition is found not to be satisfied when a constant dissipation rate is employed and consistency with prescribed acceleration statistics is enforced through fulfilment of a well-mixed condition.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010AIPC.1301..476G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AIPC.1301..476G"><span>Studying an <span class="hlt">Eulerian</span> Computer Model on Different High-performance Computer Platforms and Some Applications</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Georgiev, K.; Zlatev, Z.</p> <p>2010-11-01</p> <p>The Danish <span class="hlt">Eulerian</span> Model (DEM) is an <span class="hlt">Eulerian</span> model for studying the transport of air pollutants on large scale. Originally, the model was developed at the National Environmental Research Institute of Denmark. The model computational domain covers Europe and some neighbour parts belong to the Atlantic Ocean, Asia and Africa. If DEM model is to be applied by using fine grids, then its discretization leads to a huge computational problem. This implies that such a model as DEM must be run only on high-performance computer architectures. The implementation and tuning of such a complex large-scale model on each different computer is a non-trivial task. Here, some comparison results of running of this model on different kind of vector (CRAY C92A, Fujitsu, etc.), parallel computers with distributed memory (IBM SP, CRAY T3E, Beowulf clusters, Macintosh G4 clusters, etc.), parallel computers with shared memory (SGI Origin, SUN, etc.) and parallel computers with two levels of parallelism (IBM SMP, IBM BlueGene/P, clusters of multiprocessor nodes, etc.) will be presented. The main idea in the parallel version of DEM is domain partitioning approach. Discussions according to the effective use of the cache and hierarchical memories of the modern computers as well as the performance, speed-ups and efficiency achieved will be done. The parallel <span class="hlt">code</span> of DEM, created by using MPI standard library, appears to be highly portable and shows good efficiency and scalability on different kind of vector and parallel computers. Some important applications of the computer model output are presented in short.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20050180395&hterms=lecture&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dlecture','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20050180395&hterms=lecture&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dlecture"><span>3 Lectures: "<span class="hlt">Lagrangian</span> Models", "Numerical Transport Schemes", and "Chemical and Transport Models"</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Douglass, A.</p> <p>2005-01-01</p> <p>The topics for the three lectures for the Canadian Summer School are <span class="hlt">Lagrangian</span> Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the <span class="hlt">Lagrangian</span> model (a trajectory <span class="hlt">code</span> and a photochemical <span class="hlt">code</span>), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29507245','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29507245"><span>Coherent <span class="hlt">Lagrangian</span> swirls among submesoscale motions.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Beron-Vera, F J; Hadjighasem, A; Xia, Q; Olascoaga, M J; Haller, G</p> <p>2018-03-05</p> <p>The emergence of coherent <span class="hlt">Lagrangian</span> swirls (CLSs) among submesoscale motions in the ocean is illustrated. This is done by applying recent nonlinear dynamics tools for <span class="hlt">Lagrangian</span> coherence detection on a surface flow realization produced by a data-assimilative submesoscale-permitting ocean general circulation model simulation of the Gulf of Mexico. Both mesoscale and submesoscale CLSs are extracted. These extractions prove the relevance of coherent <span class="hlt">Lagrangian</span> eddies detected in satellite-altimetry-based geostrophic flow data for the arguably more realistic ageostrophic multiscale flow.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JPhA...43R5204S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JPhA...43R5204S"><span>Alternative kinetic energy metrics for <span class="hlt">Lagrangian</span> systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sarlet, W.; Prince, G.</p> <p>2010-11-01</p> <p>We examine <span class="hlt">Lagrangian</span> systems on \\ {R}^n with standard kinetic energy terms for the possibility of additional, alternative <span class="hlt">Lagrangians</span> with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such <span class="hlt">Lagrangians</span>. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous <span class="hlt">Lagrangians</span> for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002JMP....43.1441N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002JMP....43.1441N"><span>Multi-<span class="hlt">Lagrangians</span> for integrable systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nutku, Y.; Pavlov, M. V.</p> <p>2002-03-01</p> <p>We propose a general scheme to construct multiple <span class="hlt">Lagrangians</span> for completely integrable nonlinear evolution equations that admit multi-Hamiltonian structure. The recursion operator plays a fundamental role in this construction. We use a conserved quantity higher/lower than the Hamiltonian in the potential part of the new <span class="hlt">Lagrangian</span> and determine the corresponding kinetic terms by generating the appropriate momentum map. This leads to some remarkable new developments. We show that nonlinear evolutionary systems that admit N-fold first order local Hamiltonian structure can be cast into variational form with 2N-1 <span class="hlt">Lagrangians</span> which will be local functionals of Clebsch potentials. This number increases to 3N-2 when the Miura transformation is invertible. Furthermore we construct a new <span class="hlt">Lagrangian</span> for polytropic gas dynamics in 1+1 dimensions which is a free, local functional of the physical field variables, namely density and velocity, thus dispensing with the necessity of introducing Clebsch potentials entirely. This is a consequence of bi-Hamiltonian structure with a compatible pair of first and third order Hamiltonian operators derived from Sheftel's recursion operator.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li class="active"><span>16</span></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_16 --> <div id="page_17" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li class="active"><span>17</span></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="321"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JCoPh.229.8888L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JCoPh.229.8888L"><span>The backward phase flow and FBI-transform-based <span class="hlt">Eulerian</span> Gaussian beams for the Schrödinger equation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Leung, Shingyu; Qian, Jianliang</p> <p>2010-11-01</p> <p>We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based <span class="hlt">Eulerian</span> Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of <span class="hlt">Eulerian</span> Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the <span class="hlt">Eulerian</span> Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the <span class="hlt">Eulerian</span> Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010CompM..46..147S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010CompM..46..147S"><span>Full <span class="hlt">Eulerian</span> simulations of biconcave neo-Hookean particles in a Poiseuille flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sugiyama, Kazuyasu; , Satoshi, II; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro</p> <p>2010-03-01</p> <p>For a given initial configuration of a multi-component geometry represented by voxel-based data on a fixed Cartesian mesh, a full <span class="hlt">Eulerian</span> finite difference method facilitates solution of dynamic interaction problems between Newtonian fluid and hyperelastic material. The solid volume fraction, and the left Cauchy-Green deformation tensor are temporally updated on the <span class="hlt">Eulerian</span> frame, respectively, to distinguish the fluid and solid phases, and to describe the solid deformation. The simulation method is applied to two- and three-dimensional motions of two biconcave neo-Hookean particles in a Poiseuille flow. Similar to the numerical study on the red blood cell motion in a circular pipe (Gong et al. in J Biomech Eng 131:074504, 2009), in which Skalak’s constitutive laws of the membrane are considered, the deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. The present <span class="hlt">Eulerian</span> approach is demonstrated that it has the potential to be easily extended to larger system problems involving a large number of particles of complicated geometries.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2000JFM...402..291B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2000JFM...402..291B"><span>On hydrostatic flows in isentropic coordinates</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bokhove, Onno</p> <p>2000-01-01</p> <p>The hydrostatic primitive equations of motion which have been used in large-scale weather prediction and climate modelling over the last few decades are analysed with variational methods in an isentropic <span class="hlt">Eulerian</span> framework. The use of material isentropic coordinates for the <span class="hlt">Eulerian</span> hydrostatic equations is known to have distinct conceptual advantages since fluid motion is, under inviscid and statically stable circumstances, confined to take place on quasi-horizontal isentropic surfaces. First, an <span class="hlt">Eulerian</span> isentropic Hamilton's principle, expressed in terms of fluid parcel variables, is therefore derived by transformation of a <span class="hlt">Lagrangian</span> Hamilton's principle to an <span class="hlt">Eulerian</span> one. This <span class="hlt">Eulerian</span> principle explicitly describes the boundary dynamics of the time-dependent domain in terms of advection of boundary isentropes sB; these are the values the isentropes have at their intersection with the (lower) boundary. A partial Legendre transform for only the interior variables yields an <span class="hlt">Eulerian</span> ‘action’ principle. Secondly, Noether's theorem is used to derive energy and potential vorticity conservation from the <span class="hlt">Eulerian</span> Hamilton's principle. Thirdly, these conservation laws are used to derive a wave-activity invariant which is second-order in terms of small-amplitude disturbances relative to a resting or moving basic state. Linear stability criteria are derived but only for resting basic states. In mid-latitudes a time- scale separation between gravity and vortical modes occurs. Finally, this time-scale separation suggests that conservative geostrophic and ageostrophic approximations can be made to the <span class="hlt">Eulerian</span> action principle for hydrostatic flows. Approximations to <span class="hlt">Eulerian</span> variational principles may be more advantageous than approximations to <span class="hlt">Lagrangian</span> ones because non-dimensionalization and scaling tend to be based on <span class="hlt">Eulerian</span> estimates of the characteristic scales involved. These approximations to the stratified hydrostatic formulation extend previous</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22039394-method-coupling-dynamical-collisional-evolution-dust-circumstellar-disks-effect-dead-zone','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22039394-method-coupling-dynamical-collisional-evolution-dust-circumstellar-disks-effect-dead-zone"><span>A METHOD FOR COUPLING DYNAMICAL AND COLLISIONAL EVOLUTION OF DUST IN CIRCUMSTELLAR DISKS: THE EFFECT OF A DEAD ZONE</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Charnoz, Sebastien; Taillifet, Esther, E-mail: charnoz@cea.fr</p> <p></p> <p>Dust is a major component of protoplanetary and debris disks as it is the main observable signature of planetary formation. However, since dust dynamics are size-dependent (because of gas drag or radiation pressure) any attempt to understand the full dynamical evolution of circumstellar dusty disks that neglect the coupling of collisional evolution with dynamical evolution is thwarted because of the feedback between these two processes. Here, a new hybrid <span class="hlt">Lagrangian/Eulerian</span> <span class="hlt">code</span> is presented that overcomes some of these difficulties. The particles representing 'dust clouds' are tracked individually in a <span class="hlt">Lagrangian</span> way. This system is then mapped on an <span class="hlt">Eulerian</span> spatialmore » grid, inside the cells of which the local collisional evolutions are computed. Finally, the system is remapped back in a collection of discrete <span class="hlt">Lagrangian</span> particles, keeping their number constant. An application example of dust growth in a turbulent protoplanetary disk at 1 AU is presented. First, the growth of dust is considered in the absence of a dead zone and the vertical distribution of dust is self-consistently computed. It is found that the mass is rapidly dominated by particles about a fraction of a millimeter in size. Then the same case with an embedded dead zone is investigated and it is found that coagulation is much more efficient and produces, in a short timescale, 1-10 cm dust pebbles that dominate the mass. These pebbles may then be accumulated into embryo-sized objects inside large-scale turbulent structures as shown recently.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1993PhDT........38Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1993PhDT........38Y"><span>Parallel Decomposition of the Fictitious <span class="hlt">Lagrangian</span> Algorithm and its Accuracy for Molecular Dynamics Simulations of Semiconductors.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yeh, Mei-Ling</p> <p></p> <p>We have performed a parallel decomposition of the fictitious <span class="hlt">Lagrangian</span> method for molecular dynamics with tight-binding total energy expression into the hypercube computer. This is the first time in literature that the dynamical simulation of semiconducting systems containing more than 512 silicon atoms has become possible with the electrons treated as quantum particles. With the utilization of the Intel Paragon system, our timing analysis predicts that our <span class="hlt">code</span> is expected to perform realistic simulations on very large systems consisting of thousands of atoms with time requirements of the order of tens of hours. Timing results and performance analysis of our parallel <span class="hlt">code</span> are presented in terms of calculation time, communication time, and setup time. The accuracy of the fictitious <span class="hlt">Lagrangian</span> method in molecular dynamics simulation is also investigated, especially the energy conservation of the total energy of ions. We find that the accuracy of the fictitious <span class="hlt">Lagrangian</span> scheme in small silicon cluster and very large silicon system simulations is good for as long as the simulations proceed, even though we quench the electronic coordinates to the Born-Oppenheimer surface only in the beginning of the run. The kinetic energy of electrons does not increase as time goes on, and the energy conservation of the ionic subsystem remains very good. This means that, as far as the ionic subsystem is concerned, the electrons are on the average in the true quantum ground states. We also tie up some odds and ends regarding a few remaining questions about the fictitious <span class="hlt">Lagrangian</span> method, such as the difference between the results obtained from the Gram-Schmidt and SHAKE method of orthonormalization, and differences between simulations where the electrons are quenched to the Born -Oppenheimer surface only once compared with periodic quenching.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27739805','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27739805"><span>Target <span class="hlt">Lagrangian</span> kinematic simulation for particle-laden flows.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Murray, S; Lightstone, M F; Tullis, S</p> <p>2016-09-01</p> <p>The target <span class="hlt">Lagrangian</span> kinematic simulation method was motivated as a stochastic <span class="hlt">Lagrangian</span> particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target <span class="hlt">Lagrangian</span> integral timescale. In addition to recovering the expected <span class="hlt">Lagrangian</span> properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26827193','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26827193"><span>Communication: A simplified coupled-cluster <span class="hlt">Lagrangian</span> for polarizable embedding.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Krause, Katharina; Klopper, Wim</p> <p>2016-01-28</p> <p>A simplified coupled-cluster <span class="hlt">Lagrangian</span>, which is linear in the <span class="hlt">Lagrangian</span> multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the <span class="hlt">Lagrangian</span> multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the <span class="hlt">Lagrangian</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22493676-communication-simplified-coupled-cluster-lagrangian-polarizable-embedding','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22493676-communication-simplified-coupled-cluster-lagrangian-polarizable-embedding"><span>Communication: A simplified coupled-cluster <span class="hlt">Lagrangian</span> for polarizable embedding</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Krause, Katharina; Klopper, Wim, E-mail: klopper@kit.edu</p> <p></p> <p>A simplified coupled-cluster <span class="hlt">Lagrangian</span>, which is linear in the <span class="hlt">Lagrangian</span> multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the <span class="hlt">Lagrangian</span> multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the <span class="hlt">Lagrangian</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.753b2042L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.753b2042L"><span>Forced pitch motion of wind turbines</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Leble, V.; Barakos, G.</p> <p>2016-09-01</p> <p>The possibility of a wind turbine entering vortex ring state during pitching oscillations is explored in this paper. The aerodynamic performance of the rotor was computed using the Helicopter Multi-Block flow solver. This <span class="hlt">code</span> solves the Navier-Stokes equations in integral form using the arbitrary <span class="hlt">Lagrangian-Eulerian</span> formulation for time-dependent domains with moving boundaries. A 10-MW wind turbine was put to perform yawing and pitching oscillations suggesting the partial vortex ring state during pitching motion. The results also show the strong effect of the frequency and amplitude of oscillations on the wind turbine performance.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018LMaPh.108..699C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018LMaPh.108..699C"><span>A Chiang-type <span class="hlt">lagrangian</span> in CP^2</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cannas da Silva, Ana</p> <p>2018-03-01</p> <p>We analyse a monotone <span class="hlt">lagrangian</span> in CP^2 that is hamiltonian isotopic to the standard <span class="hlt">lagrangian</span> RP^2, yet exhibits a distinguishing behaviour under reduction by one of the toric circle actions, namely it intersects transversally the reduction level set and it projects one-to-one onto a great circle in CP^1. This <span class="hlt">lagrangian</span> thus provides an example of embedded composition fitting work of Wehrheim-Woodward and Weinstein.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22220578-eulerian-simulations-collisional-effects-electrostatic-plasma-waves','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22220578-eulerian-simulations-collisional-effects-electrostatic-plasma-waves"><span><span class="hlt">Eulerian</span> simulations of collisional effects on electrostatic plasma waves</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Pezzi, Oreste; Valentini, Francesco; Perrone, Denise</p> <p>2013-09-15</p> <p>The problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attack, both from the theoretical and the numerical point of view. In this paper, a <span class="hlt">Eulerian</span> time-splitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through one-dimensional operators of the Fokker-Planck type, both in linear and nonlinear forms. The accuracy of the numerical <span class="hlt">code</span> is discussed by comparing the numerical results to the analytical predictions obtained in some limit cases when tryingmore » to evaluate the effects of collisions in the phenomenon of wave plasma echo and collisional dissipation of Bernstein-Greene-Kruskal waves. Particular attention is devoted to the study of the nonlinear Dougherty collisional operator, recently used to describe the collisional dissipation of electron plasma waves in a pure electron plasma column [M. W. Anderson and T. M. O'Neil, Phys. Plasmas 14, 112110 (2007)]. Finally, for the study of collisional plasmas, a recipe to set the simulation parameters in order to prevent the filamentation problem can be provided, by exploiting the property of velocity diffusion operators to smooth out small velocity scales.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20020052438','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20020052438"><span><span class="hlt">Eulerian</span> Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>He, Guowei; Bushnell, Dennis M. (Technical Monitor)</p> <p>2002-01-01</p> <p>The <span class="hlt">Eulerian</span> mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An <span class="hlt">Eulerian</span> mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DPPUP2025T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DPPUP2025T"><span>Simulations of Laboratory Astrophysics Experiments using the CRASH <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Trantham, Matthew; Kuranz, Carolyn; Fein, Jeff; Wan, Willow; Young, Rachel; Keiter, Paul; Drake, R. Paul</p> <p>2015-11-01</p> <p>Computer simulations can assist in the design and analysis of laboratory astrophysics experiments. The Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan developed a <span class="hlt">code</span> that has been used to design and analyze high-energy-density experiments on OMEGA, NIF, and other large laser facilities. This <span class="hlt">Eulerian</span> <span class="hlt">code</span> uses block-adaptive mesh refinement (AMR) with implicit multigroup radiation transport, electron heat conduction and laser ray tracing. This poster will demonstrate some of the experiments the CRASH <span class="hlt">code</span> has helped design or analyze including: Kelvin-Helmholtz, Rayleigh-Taylor, magnetized flows, jets, and laser-produced plasmas. This work is funded by the following grants: DEFC52-08NA28616, DE-NA0001840, and DE-NA0002032.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016IzMat..80.1257T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016IzMat..80.1257T"><span>Special Bohr-Sommerfeld <span class="hlt">Lagrangian</span> submanifolds</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tyurin, N. A.</p> <p>2016-12-01</p> <p>We introduce a new notion in symplectic geometry, that of speciality for <span class="hlt">Lagrangian</span> submanifolds satisfying the Bohr- Sommerfeld condition. We show that it enables one to construct finite-dimensional moduli spaces of special Bohr- Sommerfeld <span class="hlt">Lagrangian</span> submanifolds with respect to any ample line bundle on an algebraic variety with a Hodge metric regarded as the symplectic form. This construction can be used to study mirror symmetry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940006462','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940006462"><span>Combustion chamber analysis <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Przekwas, A. J.; Lai, Y. G.; Krishnan, A.; Avva, R. K.; Giridharan, M. G.</p> <p>1993-01-01</p> <p>A three-dimensional, time dependent, Favre averaged, finite volume Navier-Stokes <span class="hlt">code</span> has been developed to model compressible and incompressible flows (with and without chemical reactions) in liquid rocket engines. The <span class="hlt">code</span> has a non-staggered formulation with generalized body-fitted-coordinates (BFC) capability. Higher order differencing methodologies such as MUSCL and Osher-Chakravarthy schemes are available. Turbulent flows can be modeled using any of the five turbulent models present in the <span class="hlt">code</span>. A two-phase, two-liquid, <span class="hlt">Lagrangian</span> spray model has been incorporated into the <span class="hlt">code</span>. Chemical equilibrium and finite rate reaction models are available to model chemically reacting flows. The discrete ordinate method is used to model effects of thermal radiation. The <span class="hlt">code</span> has been validated extensively against benchmark experimental data and has been applied to model flows in several propulsion system components of the SSME and the STME.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/16383566','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/16383566"><span>Monte Carlo charged-particle tracking and energy deposition on a <span class="hlt">Lagrangian</span> mesh.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Yuan, J; Moses, G A; McKenty, P W</p> <p>2005-10-01</p> <p>A Monte Carlo algorithm for alpha particle tracking and energy deposition on a cylindrical computational mesh in a <span class="hlt">Lagrangian</span> hydrodynamics <span class="hlt">code</span> used for inertial confinement fusion (ICF) simulations is presented. The straight line approximation is used to follow propagation of "Monte Carlo particles" which represent collections of alpha particles generated from thermonuclear deuterium-tritium (DT) reactions. Energy deposition in the plasma is modeled by the continuous slowing down approximation. The scheme addresses various aspects arising in the coupling of Monte Carlo tracking with <span class="hlt">Lagrangian</span> hydrodynamics; such as non-orthogonal severely distorted mesh cells, particle relocation on the moving mesh and particle relocation after rezoning. A comparison with the flux-limited multi-group diffusion transport method is presented for a polar direct drive target design for the National Ignition Facility. Simulations show the Monte Carlo transport method predicts about earlier ignition than predicted by the diffusion method, and generates higher hot spot temperature. Nearly linear speed-up is achieved for multi-processor parallel simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012PhFl...24h5101V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012PhFl...24h5101V"><span>A <span class="hlt">Lagrangian</span> subgrid-scale model with dynamic estimation of <span class="hlt">Lagrangian</span> time scale for large eddy simulation of complex flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Verma, Aman; Mahesh, Krishnan</p> <p>2012-08-01</p> <p>The dynamic <span class="hlt">Lagrangian</span> averaging approach for the dynamic Smagorinsky model for large eddy simulation is extended to an unstructured grid framework and applied to complex flows. The <span class="hlt">Lagrangian</span> time scale is dynamically computed from the solution and does not need any adjustable parameter. The time scale used in the standard <span class="hlt">Lagrangian</span> model contains an adjustable parameter θ. The dynamic time scale is computed based on a "surrogate-correlation" of the Germano-identity error (GIE). Also, a simple material derivative relation is used to approximate GIE at different events along a pathline instead of <span class="hlt">Lagrangian</span> tracking or multi-linear interpolation. Previously, the time scale for homogeneous flows was computed by averaging along directions of homogeneity. The present work proposes modifications for inhomogeneous flows. This development allows the <span class="hlt">Lagrangian</span> averaged dynamic model to be applied to inhomogeneous flows without any adjustable parameter. The proposed model is applied to LES of turbulent channel flow on unstructured zonal grids at various Reynolds numbers. Improvement is observed when compared to other averaging procedures for the dynamic Smagorinsky model, especially at coarse resolutions. The model is also applied to flow over a cylinder at two Reynolds numbers and good agreement with previous computations and experiments is obtained. Noticeable improvement is obtained using the proposed model over the standard <span class="hlt">Lagrangian</span> model. The improvement is attributed to a physically consistent <span class="hlt">Lagrangian</span> time scale. The model also shows good performance when applied to flow past a marine propeller in an off-design condition; it regularizes the eddy viscosity and adjusts locally to the dominant flow features.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1045418','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1045418"><span>A general higher-order remap algorithm for ALE calculations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Chiravalle, Vincent P</p> <p>2011-01-05</p> <p>A numerical technique for solving the equations of fluid dynamics with arbitrary mesh motion is presented. The three phases of the Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) methodology are outlined: the <span class="hlt">Lagrangian</span> phase, grid relaxation phase and remap phase. The <span class="hlt">Lagrangian</span> phase follows a well known approach from the HEMP <span class="hlt">code</span>; in addition the strain rate andflow divergence are calculated in a consistent manner according to Margolin. A donor cell method from the SALE <span class="hlt">code</span> forms the basis of the remap step, but unlike SALE a higher order correction based on monotone gradients is also added to the remap. Four test problemsmore » were explored to evaluate the fidelity of these numerical techniques, as implemented in a simple test <span class="hlt">code</span>, written in the C programming language, called Cercion. Novel cell-centered data structures are used in Cercion to reduce the complexity of the programming and maximize the efficiency of memory usage. The locations of the shock and contact discontinuity in the Riemann shock tube problem are well captured. Cercion demonstrates a high degree of symmetry when calculating the Sedov blast wave solution, with a peak density at the shock front that is similar to the value determined by the RAGE <span class="hlt">code</span>. For a flyer plate test problem both Cercion and FLAG give virtually the same velocity temporal profile at the target-vacuum interface. When calculating a cylindrical implosion of a steel shell, Cercion and FLAG agree well and the Cercion results are insensitive to the use of ALE.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018MNRAS.473.1603H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018MNRAS.473.1603H"><span>GANDALF - Graphical Astrophysics <span class="hlt">code</span> for N-body Dynamics And <span class="hlt">Lagrangian</span> Fluids</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hubber, D. A.; Rosotti, G. P.; Booth, R. A.</p> <p>2018-01-01</p> <p>GANDALF is a new hydrodynamics and N-body dynamics <span class="hlt">code</span> designed for investigating planet formation, star formation and star cluster problems. GANDALF is written in C++, parallelized with both OPENMP and MPI and contains a PYTHON library for analysis and visualization. The <span class="hlt">code</span> has been written with a fully object-oriented approach to easily allow user-defined implementations of physics modules or other algorithms. The <span class="hlt">code</span> currently contains implementations of smoothed particle hydrodynamics, meshless finite-volume and collisional N-body schemes, but can easily be adapted to include additional particle schemes. We present in this paper the details of its implementation, results from the test suite, serial and parallel performance results and discuss the planned future development. The <span class="hlt">code</span> is freely available as an open source project on the <span class="hlt">code</span>-hosting website github at https://github.com/gandalfcode/gandalf and is available under the GPLv2 license.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26613354','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26613354"><span>Dredging for dilution: A simulation based case study in a Tidal River.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Bilgili, Ata; Proehl, Jeffrey A; Swift, M Robinson</p> <p>2016-02-01</p> <p>A 2-D hydrodynamic finite element model with a <span class="hlt">Lagrangian</span> particle module is used to investigate the effects of dredging on the hydrodynamics and the horizontal dilution of pollutant particles originating from a wastewater treatment facility (WWTF) in tidal Oyster River in New Hampshire, USA. The model is driven by the semi-diurnal (M2) tidal component and includes the effect of flooding and drying of riverine mud flats. The particle tracking method consists of tidal advection plus a horizontal random walk model of sub-grid scale turbulent processes. Our approach is to perform continuous pollutant particle releases from the outfall, simulating three different scenarios: a base-case representing the present conditions and two different dredged channel/outfall location configurations. Hydrodynamics are investigated in an <span class="hlt">Eulerian</span> framework and <span class="hlt">Lagrangian</span> particle dilution improvement ratios are calculated for all cases. Results show that the simulated hydrodynamics are consistent with observed conditions. <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> residuals predict an outward path suggesting flushing of pollutants on longer (>M2) time scales. Simulated dilution maps show that, in addition to dredging, the relocation of the WWTF outfall into the dredged main channel is required for increased dilution performance. The methodology presented here can be applied to similar managerial problems in all similar systems worldwide with relatively little effort, with the combination of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> methods working together towards a better solution. The statistical significance brought into methodology, by using a large number of particles (16000 in this case), is to be emphasized, especially with the growing number of networked parallel computer clusters worldwide. This paper improves on the study presented in Bilgili et al., 2006b, by adding an <span class="hlt">Eulerian</span> analysis. Copyright © 2015 Elsevier Ltd. All rights reserved.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li class="active"><span>17</span></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_17 --> <div id="page_18" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li class="active"><span>18</span></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="341"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1364765','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1364765"><span>Drekar v.2.0</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Seefeldt, Ben; Sondak, David; Hensinger, David M.</p> <p></p> <p>Drekar is an application <span class="hlt">code</span> that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The <span class="hlt">code</span> will be released open source under a BSD license. The <span class="hlt">code</span> is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DFD.D7004C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DFD.D7004C"><span><span class="hlt">Eulerian</span> Simulation of Acoustic Waves Over Long Range in Realistic Environments</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chitta, Subhashini; Steinhoff, John</p> <p>2015-11-01</p> <p>In this paper, we describe a new method for computation of long-range acoustics. The approach is a hybrid of near and far-field methods, and is unique in its <span class="hlt">Eulerian</span> treatment of the far-field propagation. The near-field generated by any existing method to project an acoustic solution onto a spherical surface that surrounds a source. The acoustic field on this source surface is then extended to an arbitrarily large distance in an inhomogeneous far-field. This would normally require an <span class="hlt">Eulerian</span> solution of the wave equation. However, conventional <span class="hlt">Eulerian</span> methods have prohibitive grid requirements. This problem is overcome by using a new method, ``Wave Confinement'' (WC) that propagates wave-identifying phase fronts as nonlinear solitary waves that live on grid indefinitely. This involves modification of wave equation by the addition of a nonlinear term without changing the basic conservation properties of the equation. These solitary waves can then be used to ``carry'' the essential integrals of the acoustic wave. For example, arrival time, centroid position and other properties that are invariant as the wave passes a grid point. Because of this property the grid can be made as coarse as necessary, consistent with overall accuracy to resolve atmospheric/ground variations. This work is being funded by the U.S. Army under a Small Business Innovation Research (SBIR) program (contract number: # W911W6-12-C-0036). The authors would like to thank Dr. Frank Caradonna and Dr. Ben W. Sim for this support.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20070018036','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20070018036"><span>Simulating Space Capsule Water Landing with Explicit Finite Element Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wang, John T.; Lyle, Karen H.</p> <p>2007-01-01</p> <p>A study of using an explicit nonlinear dynamic finite element <span class="hlt">code</span> for simulating the water landing of a space capsule was performed. The finite element model contains <span class="hlt">Lagrangian</span> shell elements for the space capsule and <span class="hlt">Eulerian</span> solid elements for the water and air. An Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70012388','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70012388"><span>Littoral transport in the surf zone elucidated by an <span class="hlt">Eulerian</span> sediment tracer.</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Duane, D.B.; James, W.R.</p> <p>1980-01-01</p> <p>An <span class="hlt">Eulerian</span>, or time integration, sand tracer experiment was designed and carried out in the surf zone near Pt. Mugu, California on April 19, 1972. Data indicate that conditions of stationarity and finite boundaries required for proper application of <span class="hlt">Eulerian</span> tracer theory exist for short time periods in the surf zone. Grain counts suggest time required for tracer sand to attain equilibrium concentration is on the order of 30-60 minutes. Grain counts also indicate transport (discharge) was strongly dependent upon grain size, with the maximum rate occurring in the size 2.5-2.75 phi, decreasing to both finer and coarser sizes. The measured instantaneous transport was at the annual rate of 2.4 x 106 m3/yr.- Authors</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19850018599','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19850018599"><span>Liquid rocket combustor computer <span class="hlt">code</span> development</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liang, P. Y.</p> <p>1985-01-01</p> <p>The Advanced Rocket Injector/Combustor <span class="hlt">Code</span> (ARICC) that has been developed to model the complete chemical/fluid/thermal processes occurring inside rocket combustion chambers are highlighted. The <span class="hlt">code</span>, derived from the CONCHAS-SPRAY <span class="hlt">code</span> originally developed at Los Alamos National Laboratory incorporates powerful features such as the ability to model complex injector combustion chamber geometries, <span class="hlt">Lagrangian</span> tracking of droplets, full chemical equilibrium and kinetic reactions for multiple species, a fractional volume of fluid (VOF) description of liquid jet injection in addition to the gaseous phase fluid dynamics, and turbulent mass, energy, and momentum transport. Atomization and droplet dynamic models from earlier generation <span class="hlt">codes</span> are transplated into the present <span class="hlt">code</span>. Currently, ARICC is specialized for liquid oxygen/hydrogen propellants, although other fuel/oxidizer pairs can be easily substituted.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CPM...tmp....2F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CPM...tmp....2F"><span>Meshless <span class="hlt">Lagrangian</span> SPH method applied to isothermal lid-driven cavity flow at low-Re numbers</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fraga Filho, C. A. D.; Chacaltana, J. T. A.; Pinto, W. J. N.</p> <p>2018-01-01</p> <p>SPH is a recent particle method applied in the cavities study, without many results available in the literature. The lid-driven cavity flow is a classic problem of the fluid mechanics, extensively explored in the literature and presenting a considerable complexity. The aim of this paper is to present a solution from the <span class="hlt">Lagrangian</span> viewpoint for this problem. The discretization of the continuum domain is performed using the <span class="hlt">Lagrangian</span> particles. The physical laws of mass, momentum and energy conservation are presented by the Navier-Stokes equations. A serial numerical <span class="hlt">code</span>, written in Fortran programming language, has been used to perform the numerical simulations. The application of the SPH and comparison with the literature (mesh methods and a meshless collocation method) have been done. The positions of the primary vortex centre and the non-dimensional velocity profiles passing through the geometric centre of the cavity have been analysed. The numerical <span class="hlt">Lagrangian</span> results showed a good agreement when compared to the results found in the literature, specifically for { Re} < 100.00 . Suggestions for improvements in the SPH model presented are listed, in the search for better results for flows with higher Reynolds numbers.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JGRC..120.3624L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JGRC..120.3624L"><span>Seagrass metabolism across a productivity gradient using the eddy covariance, <span class="hlt">Eulerian</span> control volume, and biomass addition techniques</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Long, Matthew H.; Berg, Peter; Falter, James L.</p> <p>2015-05-01</p> <p>The net ecosystem metabolism of the seagrass Thalassia testudinum was studied across a nutrient and productivity gradient in Florida Bay, Florida, using the <span class="hlt">Eulerian</span> control volume, eddy covariance, and biomass addition techniques. In situ oxygen fluxes were determined by a triangular <span class="hlt">Eulerian</span> control volume with sides 250 m long and by eddy covariance instrumentation at its center. The biomass addition technique evaluated the aboveground seagrass productivity through the net biomass added. The spatial and temporal resolutions, accuracies, and applicability of each method were compared. The eddy covariance technique better resolved the short-term flux rates and the productivity gradient across the bay, which was consistent with the long-term measurements from the biomass addition technique. The net primary production rates from the biomass addition technique, which were expected to show greater autotrophy due to the exclusion of sediment metabolism and belowground production, were 71, 53, and 30 mmol carbon m-2 d-1 at 3 sites across the bay. The net ecosystem metabolism was 35, 25, and 11 mmol oxygen m-2 d-1 from the eddy covariance technique and 10, -103, and 14 mmol oxygen m-2 d-1 from the <span class="hlt">Eulerian</span> control volume across the same sites, respectively. The low-flow conditions in the shallow bays allowed for periodic stratification and long residence times within the <span class="hlt">Eulerian</span> control volume that likely reduced its precision. Overall, the eddy covariance technique had the highest temporal resolution while producing accurate long-term flux rates that surpassed the capabilities of the biomass addition and <span class="hlt">Eulerian</span> control volume techniques in these shallow coastal bays.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20080034887','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20080034887"><span>LSPRAY-III: A <span class="hlt">Lagrangian</span> Spray Module</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.</p> <p>2008-01-01</p> <p>LSPRAY-III is a <span class="hlt">Lagrangian</span> spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray formulation, its <span class="hlt">code</span> structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-III, we have advanced the state-of-the-art in spray computations in several important ways.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040050627','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040050627"><span>LSPRAY-II: A <span class="hlt">Lagrangian</span> Spray Module</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.</p> <p>2004-01-01</p> <p>LSPRAY-II is a <span class="hlt">Lagrangian</span> spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray formulation, its <span class="hlt">code</span> structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-II, we have advanced the state-of-the-art in spray computations in several important ways.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015ccrg.book..429I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015ccrg.book..429I"><span><span class="hlt">Code</span> Samples Used for Complexity and Control</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ivancevic, Vladimir G.; Reid, Darryn J.</p> <p>2015-11-01</p> <p>The following sections are included: * MathematicaⓇ <span class="hlt">Code</span> * Generic Chaotic Simulator * Vector Differential Operators * NLS Explorer * 2C++ <span class="hlt">Code</span> * C++ Lambda Functions for Real Calculus * Accelerometer Data Processor * Simple Predictor-Corrector Integrator * Solving the BVP with the Shooting Method * Linear Hyperbolic PDE Solver * Linear Elliptic PDE Solver * Method of Lines for a Set of the NLS Equations * C# <span class="hlt">Code</span> * Iterative Equation Solver * Simulated Annealing: A Function Minimum * Simple Nonlinear Dynamics * Nonlinear Pendulum Simulator * <span class="hlt">Lagrangian</span> Dynamics Simulator * Complex-Valued Crowd Attractor Dynamics * Freeform Fortran <span class="hlt">Code</span> * Lorenz Attractor Simulator * Complex Lorenz Attractor * Simple SGE Soliton * Complex Signal Presentation * Gaussian Wave Packet * Hermitian Matrices * Euclidean L2-Norm * Vector/Matrix Operations * Plain C-<span class="hlt">Code</span>: Levenberg-Marquardt Optimizer * Free Basic <span class="hlt">Code</span>: 2D Crowd Dynamics with 3000 Agents</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22809180','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22809180"><span><span class="hlt">Lagrangian</span> motion, coherent structures, and lines of persistent material strain.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Samelson, R M</p> <p>2013-01-01</p> <p><span class="hlt">Lagrangian</span> motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating <span class="hlt">Lagrangian</span> regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, <span class="hlt">Lagrangian</span> regime boundaries may often be indicated as material curves on which the <span class="hlt">Lagrangian</span>-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate <span class="hlt">Lagrangian</span> regime boundaries and lines of principal <span class="hlt">Lagrangian</span> strain (also called <span class="hlt">Lagrangian</span> coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/<span class="hlt">Lagrangian</span> strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003AGUFMNG12D..06G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003AGUFMNG12D..06G"><span>GeoFramework: A Modeling Framework for Solid Earth Geophysics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gurnis, M.; Aivazis, M.; Tromp, J.; Tan, E.; Thoutireddy, P.; Liu, Q.; Choi, E.; Dicaprio, C.; Chen, M.; Simons, M.; Quenette, S.; Appelbe, B.; Aagaard, B.; Williams, C.; Lavier, L.; Moresi, L.; Law, H.</p> <p>2003-12-01</p> <p>As data sets in geophysics become larger and of greater relevance to other earth science disciplines, and as earth science becomes more interdisciplinary in general, modeling tools are being driven in new directions. There is now a greater need to link modeling <span class="hlt">codes</span> to one another, link modeling <span class="hlt">codes</span> to multiple datasets, and to make modeling software available to non modeling specialists. Coupled with rapid progress in computer hardware (including the computational speed afforded by massively parallel computers), progress in numerical algorithms, and the introduction of software frameworks, these lofty goals of merging software in geophysics are now possible. The GeoFramework project, a collaboration between computer scientists and geoscientists, is a response to these needs and opportunities. GeoFramework is based on and extends Pyre, a Python-based modeling framework, recently developed to link solid (<span class="hlt">Lagrangian</span>) and fluid (<span class="hlt">Eulerian</span>) models, as well as mesh generators, visualization packages, and databases, with one another for engineering applications. The utility and generality of Pyre as a general purpose framework in science is now being recognized. Besides its use in engineering and geophysics, it is also being used in particle physics and astronomy. Geology and geophysics impose their own unique requirements on software frameworks which are not generally available in existing frameworks and so there is a need for research in this area. One of the special requirements is the way <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> <span class="hlt">codes</span> will need to be linked in time and space within a plate tectonics context. GeoFramework has grown beyond its initial goal of linking a limited number of exiting <span class="hlt">codes</span> together. The following <span class="hlt">codes</span> are now being reengineered within the context of Pyre: Tecton, 3-D FE Visco-elastic <span class="hlt">code</span> for lithospheric relaxation; CitComS, a <span class="hlt">code</span> for spherical mantle convection; SpecFEM3D, a SEM <span class="hlt">code</span> for global and regional seismic waves; eqsim, a FE <span class="hlt">code</span> for dynamic</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010PhTea..48..512H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010PhTea..48..512H"><span>Gravity, Time, and <span class="hlt">Lagrangians</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Huggins, Elisha</p> <p>2010-11-01</p> <p>Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the <span class="hlt">Lagrangian</span>. (Why would one subtract potential energy from kinetic energy?) In this paper we discuss a thought experiment that relates gravity and time. Then we use a Feynman thought experiment to explain the minus sign in the <span class="hlt">Lagrangian</span>. Our surprise was that these two topics are related.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22524964-reach-perturbative-methods-dark-matter-density-fields','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22524964-reach-perturbative-methods-dark-matter-density-fields"><span>On the reach of perturbative methods for dark matter density fields</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Baldauf, Tobias; Zaldarriaga, Matias; Schaan, Emmanuel, E-mail: baldauf@ias.edu, E-mail: eschaan@astro.princeton.edu, E-mail: matiasz@ias.edu</p> <p></p> <p>We study the mapping from <span class="hlt">Lagrangian</span> to <span class="hlt">Eulerian</span> space in the context of the Effective Field Theory (EFT) of Large Scale Structure. We compute <span class="hlt">Lagrangian</span> displacements with <span class="hlt">Lagrangian</span> Perturbation Theory (LPT) and perform the full non-perturbative transformation from displacement to density. When expanded up to a given order, this transformation reproduces the standard <span class="hlt">Eulerian</span> Perturbation Theory (SPT) at the same order. However, the full transformation from displacement to density also includes higher order terms. These terms explicitly resum long wavelength motions, thus making the resulting density field better correlated with the true non-linear density field. As a result, the regimemore » of validity of this approach is expected to extend that of the <span class="hlt">Eulerian</span> EFT, and match that of the IR-resummed <span class="hlt">Eulerian</span> EFT. This approach thus effectively enables a test of the IR-resummed EFT at the field level. We estimate the size of stochastic, non-perturbative contributions to the matter density power spectrum. We find that in our highest order calculation, at redshift z = 0 the power spectrum of the density field is reproduced with an accuracy of 1% (10%) up to k = 0.25 hMpc{sup −1} (k = 0.46 hMpc{sup −1}). We believe that the dominant source of the remaining error is the stochastic contribution. Unfortunately, on these scales the stochastic term does not yet scale as k{sup 4} as it does in the very low k regime. Thus, modeling this contribution might be challenging.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017ascl.soft12006A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017ascl.soft12006A"><span>Nyx: Adaptive mesh, massively-parallel, cosmological simulation <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Almgren, Ann; Beckner, Vince; Friesen, Brian; Lukic, Zarija; Zhang, Weiqun</p> <p>2017-12-01</p> <p>Nyx <span class="hlt">code</span> solves equations of compressible hydrodynamics on an adaptive grid hierarchy coupled with an N-body treatment of dark matter. The gas dynamics in Nyx use a finite volume methodology on an adaptive set of 3-D <span class="hlt">Eulerian</span> grids; dark matter is represented as discrete particles moving under the influence of gravity. Particles are evolved via a particle-mesh method, using Cloud-in-Cell deposition/interpolation scheme. Both baryonic and dark matter contribute to the gravitational field. In addition, Nyx includes physics for accurately modeling the intergalactic medium; in optically thin limits and assuming ionization equilibrium, the <span class="hlt">code</span> calculates heating and cooling processes of the primordial-composition gas in an ionizing ultraviolet background radiation field.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920023015&hterms=marriage&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dmarriage','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920023015&hterms=marriage&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dmarriage"><span>Modeling of SSME fuel preburner ASI</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liang, Pak-Yan</p> <p>1992-01-01</p> <p>The Augmented Spark Ignitor (ASI) is a LOX/H2/electrical spark system that functions as an ignition source and sustainer for stable combustion. It is used in the Space Shuttle Main Engine (SSME) preburner combustor, the SMME main combustion chamber, the J-1 and J-2 engines, as well as proposed designs of the Space Transportation Main Engine (STME) main combustor and gas generators. An undertaking to characterize the flow of the ASI is documented. The <span class="hlt">code</span> consists of a marriage of the Implicit-Continuous <span class="hlt">Eulerian</span>/Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Code</span> (ICE-ALE) Navier-Stokes solver with the Volume-of-Fluid (VOF) Methodology for tracking of two immiscible fluids with sharp discontinuities. Spray droplets are represented by discrete numerical parcels tracked in a <span class="hlt">Lagrangian</span> fashion. Numerous physical sub-models are also incorporated to describe the processes of atomization, droplet collision, droplet breakup, evaporation, and droplet and gas phase turbulence. An equilibrium chemistry model accounting for 8 active gaseous species is also used. Taking advantage of this symmetry plane, half of the actual ASI is modeled with a 3-D grid that geometrically resolves the LOX ports, the spark plug locations, and the hydrogen injection slots.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70013803','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70013803"><span>Two-dimensional <span class="hlt">Lagrangian</span> simulation of suspended sediment</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Schoellhamer, David H.</p> <p>1988-01-01</p> <p>A two-dimensional laterally averaged model for suspended sediment transport in steady gradually varied flow that is based on the <span class="hlt">Lagrangian</span> reference frame is presented. The layered <span class="hlt">Lagrangian</span> transport model (LLTM) for suspended sediment performs laterally averaged concentration. The elevations of nearly horizontal streamlines and the simulation time step are selected to optimize model stability and efficiency. The computational elements are parcels of water that are moved along the streamlines in the <span class="hlt">Lagrangian</span> sense and are mixed with neighboring parcels. Three applications show that the LLTM can accurately simulate theoretical and empirical nonequilibrium suspended sediment distributions and slug injections of suspended sediment in a laboratory flume.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1997PhFl....9..433P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1997PhFl....9..433P"><span><span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> view of the bursting period</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Podvin, Bérengère; Gibson, John; Berkooz, Gal; Lumley, John</p> <p>1997-02-01</p> <p>Low-dimensional models for the turbulent wall layer display an intermittent phenomenon with an ejection phase and a sweep phase that strongly resembles the bursting phenomenon observed in experimental flows. The probability distribution of inter-burst times has the observed shape [E. Stone and P. J. Holmes, Physica D 37, 20 (1989); SIAM J. Appl. Math. 50, 726 (1990); Phys. Lett. A 5, 29 (1991); P. J. Holmes and E. Stone, in Studies in Turbulence, edited by T. B. Gatski, S. Sarkar, and C. G. Speziale (Springer, Heidelberg, 1992)]. However, the time scales both for bursts and interburst durations are unrealistically long, a fact that was not appreciated until recently. We believe that the long time scales are due to the model's inclusion of only a single coherent structure, when in fact a succession of quasi-independent structures are being swept past the sensor in an experiment. A simple statistical model of this situation restores the magnitude of the observed bursting period, although there is a great deal of flexibility in the various parameters involved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1352360-verification-assessment-piston-boundary-conditions-lagrangian-simulation-compressible-flow-similarity-solutions','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1352360-verification-assessment-piston-boundary-conditions-lagrangian-simulation-compressible-flow-similarity-solutions"><span>Verification assessment of piston boundary conditions for <span class="hlt">Lagrangian</span> simulation of compressible flow similarity solutions</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Ramsey, Scott D.; Ivancic, Philip R.; Lilieholm, Jennifer F.</p> <p>2015-12-10</p> <p>This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the <span class="hlt">code</span> and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in <span class="hlt">Lagrangian</span> compressible flow simulations as rigid boundary-driven flow, even if no such “piston”more » is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in <span class="hlt">Lagrangian</span> compressible flow solvers. Finally, the consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common <span class="hlt">code</span> verification analysis metrics (e.g., shock strength/position errors and global convergence rates).« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1352360','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1352360"><span>Verification assessment of piston boundary conditions for <span class="hlt">Lagrangian</span> simulation of compressible flow similarity solutions</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Ramsey, Scott D.; Ivancic, Philip R.; Lilieholm, Jennifer F.</p> <p></p> <p>This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the <span class="hlt">code</span> and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in <span class="hlt">Lagrangian</span> compressible flow simulations as rigid boundary-driven flow, even if no such “piston”more » is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in <span class="hlt">Lagrangian</span> compressible flow solvers. Finally, the consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common <span class="hlt">code</span> verification analysis metrics (e.g., shock strength/position errors and global convergence rates).« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li class="active"><span>18</span></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_18 --> <div id="page_19" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li class="active"><span>19</span></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="361"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDG28009L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDG28009L"><span>Scale-by-scale contributions to <span class="hlt">Lagrangian</span> particle acceleration</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lalescu, Cristian C.; Wilczek, Michael</p> <p>2017-11-01</p> <p>Fluctuations on a wide range of scales in both space and time are characteristic of turbulence. <span class="hlt">Lagrangian</span> particles, advected by the flow, probe these fluctuations along their trajectories. In an effort to isolate the influence of the different scales on <span class="hlt">Lagrangian</span> statistics, we employ direct numerical simulations (DNS) combined with a filtering approach. Specifically, we study the acceleration statistics of tracers advected in filtered fields to characterize the smallest temporal scales of the flow. Emphasis is put on the acceleration variance as a function of filter scale, along with the scaling properties of the relevant terms of the Navier-Stokes equations. We furthermore discuss scaling ranges for higher-order moments of the tracer acceleration, as well as the influence of the choice of filter on the results. Starting from the <span class="hlt">Lagrangian</span> tracer acceleration as the short time limit of the <span class="hlt">Lagrangian</span> velocity increment, we also quantify the influence of filtering on <span class="hlt">Lagrangian</span> intermittency. Our work complements existing experimental results on intermittency and accelerations of finite-sized, neutrally-buoyant particles: for the passive tracers used in our DNS, feedback effects are neglected such that the spatial averaging effect is cleanly isolated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28505811','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28505811"><span>Chaotic <span class="hlt">Lagrangian</span> models for turbulent relative dispersion.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Lacorata, Guglielmo; Vulpiani, Angelo</p> <p>2017-04-01</p> <p>A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by <span class="hlt">Lagrangian</span> chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-<span class="hlt">Lagrangian</span> coordinates. <span class="hlt">Lagrangian</span> dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as <span class="hlt">Lagrangian</span> predictability studies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvE..95d3106L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvE..95d3106L"><span>Chaotic <span class="hlt">Lagrangian</span> models for turbulent relative dispersion</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lacorata, Guglielmo; Vulpiani, Angelo</p> <p>2017-04-01</p> <p>A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by <span class="hlt">Lagrangian</span> chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-<span class="hlt">Lagrangian</span> coordinates. <span class="hlt">Lagrangian</span> dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as <span class="hlt">Lagrangian</span> predictability studies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004APS..DFD.ND005T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004APS..DFD.ND005T"><span>Tests of dynamic <span class="hlt">Lagrangian</span> eddy viscosity models in Large Eddy Simulations of flow over three-dimensional bluff bodies</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tseng, Yu-Heng; Meneveau, Charles; Parlange, Marc B.</p> <p>2004-11-01</p> <p>Large Eddy Simulations (LES) of atmospheric boundary-layer air movement in urban environments are especially challenging due to complex ground topography. Typically in such applications, fairly coarse grids must be used where the subgrid-scale (SGS) model is expected to play a crucial role. A LES <span class="hlt">code</span> using pseudo-spectral discretization in horizontal planes and second-order differencing in the vertical is implemented in conjunction with the immersed boundary method to incorporate complex ground topography, with the classic equilibrium log-law boundary condition in the new-wall region, and with several versions of the eddy-viscosity model: (1) the constant-coefficient Smagorinsky model, (2) the dynamic, scale-invariant <span class="hlt">Lagrangian</span> model, and (3) the dynamic, scale-dependent <span class="hlt">Lagrangian</span> model. Other planar-averaged type dynamic models are not suitable because spatial averaging is not possible without directions of statistical homogeneity. These SGS models are tested in LES of flow around a square cylinder and of flow over surface-mounted cubes. Effects on the mean flow are documented and found not to be major. Dynamic <span class="hlt">Lagrangian</span> models give a physically more realistic SGS viscosity field, and in general, the scale-dependent <span class="hlt">Lagrangian</span> model produces larger Smagorinsky coefficient than the scale-invariant one, leading to reduced distributions of resolved rms velocities especially in the boundary layers near the bluff bodies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26240515','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26240515"><span>Markov Chain Monte Carlo from <span class="hlt">Lagrangian</span> Dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Lan, Shiwei; Stathopoulos, Vasileios; Shahbaba, Babak; Girolami, Mark</p> <p>2015-04-01</p> <p>Hamiltonian Monte Carlo (HMC) improves the computational e ciency of the Metropolis-Hastings algorithm by reducing its random walk behavior. Riemannian HMC (RHMC) further improves the performance of HMC by exploiting the geometric properties of the parameter space. However, the geometric integrator used for RHMC involves implicit equations that require fixed-point iterations. In some cases, the computational overhead for solving implicit equations undermines RHMC's benefits. In an attempt to circumvent this problem, we propose an explicit integrator that replaces the momentum variable in RHMC by velocity. We show that the resulting transformation is equivalent to transforming Riemannian Hamiltonian dynamics to <span class="hlt">Lagrangian</span> dynamics. Experimental results suggests that our method improves RHMC's overall computational e ciency in the cases considered. All computer programs and data sets are available online (http://www.ics.uci.edu/~babaks/Site/<span class="hlt">Codes</span>.html) in order to allow replication of the results reported in this paper.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29543033','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29543033"><span>Nonunitary <span class="hlt">Lagrangians</span> and Unitary Non-<span class="hlt">Lagrangian</span> Conformal Field Theories.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Buican, Matthew; Laczko, Zoltan</p> <p>2018-02-23</p> <p>In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N=2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us <span class="hlt">Lagrangians</span> for particular observables in certain subsectors of many "non-<span class="hlt">Lagrangian</span>" SCFTs by sacrificing unitarity while preserving the full N=2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvL.120h1601B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvL.120h1601B"><span>Nonunitary <span class="hlt">Lagrangians</span> and Unitary Non-<span class="hlt">Lagrangian</span> Conformal Field Theories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Buican, Matthew; Laczko, Zoltan</p> <p>2018-02-01</p> <p>In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories. On the other hand, in two dimensions, it is often possible to algebraically construct observables of interacting CFTs using free fields without the need to explicitly construct an underlying RG flow. In this Letter, we begin to extend this idea to higher dimensions by showing that one can compute certain observables of an infinite set of unitary strongly interacting four-dimensional N =2 superconformal field theories (SCFTs) by performing simple calculations involving sets of nonunitary free four-dimensional hypermultiplets. These free fields are distant cousins of the Majorana fermion underlying the two-dimensional Ising model and are not obviously connected to our interacting theories via an RG flow. Rather surprisingly, this construction gives us <span class="hlt">Lagrangians</span> for particular observables in certain subsectors of many "non-<span class="hlt">Lagrangian</span>" SCFTs by sacrificing unitarity while preserving the full N =2 superconformal algebra. As a by-product, we find relations between characters in unitary and nonunitary affine Kac-Moody algebras. We conclude by commenting on possible generalizations of our construction.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/18165256','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/18165256"><span>An overview of a <span class="hlt">Lagrangian</span> method for analysis of animal wake dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Peng, Jifeng; Dabiri, John O</p> <p>2008-01-01</p> <p>The fluid dynamic analysis of animal wakes is becoming increasingly popular in studies of animal swimming and flying, due in part to the development of quantitative flow visualization techniques such as digital particle imaging velocimetry (DPIV). In most studies, quasi-steady flow is assumed and the flow analysis is based on velocity and/or vorticity fields measured at a single time instant during the stroke cycle. The assumption of quasi-steady flow leads to neglect of unsteady (time-dependent) wake vortex added-mass effects, which can contribute significantly to the instantaneous locomotive forces. In this paper we review a <span class="hlt">Lagrangian</span> approach recently introduced to determine unsteady wake vortex structure by tracking the trajectories of individual fluid particles in the flow, rather than by analyzing the velocity/vorticity fields at fixed locations and single instants in time as in the <span class="hlt">Eulerian</span> perspective. Once the momentum of the wake vortex and its added mass are determined, the corresponding unsteady locomotive forces can be quantified. Unlike previous studies that estimated the time-averaged forces over the stroke cycle, this approach enables study of how instantaneous locomotive forces evolve over time. The utility of this method for analyses of DPIV velocity measurements is explored, with the goal of demonstrating its applicability to data that are typically available to investigators studying animal swimming and flying. The methods are equally applicable to computational fluid dynamics studies where velocity field calculations are available.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=124866&keyword=Lagrangian&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=124866&keyword=Lagrangian&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>3DFATMIC: THREE DIMENSIONAL SUBSURFACE FLOW, FATE AND TRANSPORT OF MICROBES AND CHEMICALS MODEL - USER'S MANUAL VERSION 1.0</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>This document is the user's manual of 3DFATMIC, a 3-Dimensional Subsurface Flow, Fate and Transport of Microbes and Chemicals Model using a <span class="hlt">Lagrangian-Eulerian</span> adapted zooming and peak capturing (LEZOOMPC) algorithm.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1163152','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1163152"><span>Geometric multigrid for an implicit-time immersed boundary method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Guy, Robert D.; Philip, Bobby; Griffith, Boyce E.</p> <p>2014-10-12</p> <p>The immersed boundary (IB) method is an approach to fluid-structure interaction that uses <span class="hlt">Lagrangian</span> variables to describe the deformations and resulting forces of the structure and <span class="hlt">Eulerian</span> variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for <span class="hlt">Eulerian</span> equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methodsmore » require significantly more complex solvers that effectively treat both <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> variables simultaneously. Moreover, several different approaches to solving the coupled <span class="hlt">Lagrangian-Eulerian</span> equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. Finally, these tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.A41L..02A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A41L..02A"><span>Using <span class="hlt">Lagrangian</span> Chemical Transport Modeling to Assess the Impact of Biomass Burning on Ozone and PM2.5</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Alvarado, M. J.; Lonsdale, C. R.; Brodowski, C. M.</p> <p>2017-12-01</p> <p>One of the challenges of using in situ measurements to study the air quality and climate impacts of biomass burning is correctly determining the contribution of biomass burning sources to the measured ambient concentrations. This is especially important for policy purposes, as the ozone (O3) and fine particulate matter (PM2.5) from natural wildfires should not be confused with that from controllable anthropogenic sources. We have developed a <span class="hlt">Lagrangian</span> chemical transport model called STILT-ASP that is able to quantify the impact of wildfire events on O3 and PM2.5 measurements made at surface monitoring sites, by mobile laboratories, or by aircraft. STILT-ASP is built by coupling the Stochastic Time Inverted <span class="hlt">Lagrangian</span> Transport (STILT) model with AER's Aerosol Simulation Program (ASP), which has been used in many studies of the gas and aerosol chemistry of biomass burning smoke. Here we present recent revisions made in STILT-ASP v2.0, including the use of more detailed chemical speciation of fire emissions and biogenic emissions calculated using the MEGAN model with meteorological inputs consistent with those used to drive STILT. We will present the results of an evaluation of the performance of STILT-ASP v2.0 using surface, mobile lab, and aircraft data from the 2013 Houston DISCOVER-AQ campaign. STILT-ASP v2.0 showed good average performance for O3 during the peak of the high O3 episodes on Sept. 25-26, 2013, with a mean bias of -4 ppbv. We will also demonstrate the use of STILT-ASP to evaluate the impact of biomass burning on O3 and PM2.5 in urban areas and to assess the impact of remote fires on the boundary conditions used in <span class="hlt">Eulerian</span> chemical transport models like CAMx.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19800006097','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19800006097"><span>GIM <span class="hlt">code</span> user's manual for the STAR-100 computer. [for generating numerical analogs of the conversion laws</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Spradley, L.; Pearson, M.</p> <p>1979-01-01</p> <p>The General Interpolants Method (GIM), a three dimensional, time dependent, hybrid procedure for generating numerical analogs of the conversion laws, is described. The Navier-Stokes equations written for an <span class="hlt">Eulerian</span> system are considered. The conversion of the GIM <span class="hlt">code</span> to the STAR-100 computer, and the implementation of 'GIM-ON-STAR' is discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015ascl.soft09007T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015ascl.soft09007T"><span>pycola: N-body COLA method <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tassev, Svetlin; Eisenstein, Daniel J.; Wandelt, Benjamin D.; Zaldarriagag, Matias</p> <p>2015-09-01</p> <p>pycola is a multithreaded Python/Cython N-body <span class="hlt">code</span>, implementing the Comoving <span class="hlt">Lagrangian</span> Acceleration (COLA) method in the temporal and spatial domains, which trades accuracy at small-scales to gain computational speed without sacrificing accuracy at large scales. This is especially useful for cheaply generating large ensembles of accurate mock halo catalogs required to study galaxy clustering and weak lensing. The COLA method achieves its speed by calculating the large-scale dynamics exactly using LPT while letting the N-body <span class="hlt">code</span> solve for the small scales, without requiring it to capture exactly the internal dynamics of halos.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016ascl.soft05003V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ascl.soft05003V"><span>Shadowfax: Moving mesh hydrodynamical integration <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vandenbroucke, Bert</p> <p>2016-05-01</p> <p>Shadowfax simulates galaxy evolution. Written in object-oriented modular C++, it evolves a mixture of gas, subject to the laws of hydrodynamics and gravity, and any collisionless fluid only subject to gravity, such as cold dark matter or stars. For the hydrodynamical integration, it makes use of a (co-) moving <span class="hlt">Lagrangian</span> mesh. The <span class="hlt">code</span> has a 2D and 3D version, contains utility programs to generate initial conditions and visualize simulation snapshots, and its input/output is compatible with a number of other simulation <span class="hlt">codes</span>, e.g. Gadget2 (ascl:0003.001) and GIZMO (ascl:1410.003).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017IJGMM..1450171E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017IJGMM..1450171E"><span>Scalar curvature of <span class="hlt">Lagrangian</span> Riemannian submersions and their harmonicity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Eken Meri˙ç, Şemsi; Kiliç, Erol; Sağiroğlu, Yasemi˙n</p> <p></p> <p>In this paper, we consider a <span class="hlt">Lagrangian</span> Riemannian submersion from a Hermitian manifold to a Riemannian manifold and establish some basic inequalities to obtain relationships between the intrinsic and extrinsic invariants for such a submersion. Indeed, using these inequalities, we provide necessary and sufficient conditions for which a <span class="hlt">Lagrangian</span> Riemannian submersion π has totally geodesic or totally umbilical fibers. Moreover, we study the harmonicity of <span class="hlt">Lagrangian</span> Riemannian submersions and obtain a characterization for such submersions to be harmonic.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MNRAS.458.1517F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MNRAS.458.1517F"><span><span class="hlt">Lagrangian</span> methods of cosmic web classification</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.</p> <p>2016-05-01</p> <p>The cosmic web defines the large-scale distribution of matter we see in the Universe today. Classifying the cosmic web into voids, sheets, filaments and nodes allows one to explore structure formation and the role environmental factors have on halo and galaxy properties. While existing studies of cosmic web classification concentrate on grid-based methods, this work explores a <span class="hlt">Lagrangian</span> approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The <span class="hlt">Lagrangian</span> approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the <span class="hlt">Lagrangian</span> nature admits a straightforward inclusion of the Hubble flow negating the necessity of a visually defined threshold value which is commonly employed by grid-based classification methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20150021547&hterms=rotary+engine&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Drotary%2Bengine','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20150021547&hterms=rotary+engine&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Drotary%2Bengine"><span>Three-Dimensional Analysis and Modeling of a Wankel Engine</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.; Willis, E. A.</p> <p>1991-01-01</p> <p>A new computer <span class="hlt">code</span>, AGNI-3D, has been developed for the modeling of combustion, spray, and flow properties in a stratified-charge rotary engine (SCRE). The mathematical and numerical details of the new <span class="hlt">code</span> are described by the first author in a separate NASA publication. The solution procedure is based on an <span class="hlt">Eulerian-Lagrangian</span> approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas-mixture with variable properties are solved in generalized, <span class="hlt">Eulerian</span> coordinates on a moving grid by making use of an implicit finite-volume, Steger-Warming flux vector splitting scheme. The liquid-phase equations are solved in <span class="hlt">Lagrangian</span> coordinates. The engine configuration studied was similar to existing rotary engine flow-visualization and hot-firing test rigs. The results of limited test cases indicate a good degree of qualitative agreement between the predicted and measured pressures. It is conjectured that the impulsive nature of the torque generated by the observed pressure nonuniformity may be one of the mechanisms responsible for the excessive wear of the timing gears observed during the early stages of the rotary combustion engine (RCE) development. It was identified that the turbulence intensities near top-dead-center were dominated by the compression process and only slightly influenced by the intake and exhaust processes. Slow mixing resulting from small turbulence intensities within the rotor pocket and also from a lack of formation of any significant recirculation regions within the rotor pocket were identified as the major factors leading to incomplete combustion. Detailed flowfield results during exhaust and intake, fuel injection, fuel vaporization, combustion, mixing and expansion processes are also presented. The numerical procedure is very efficient as it takes 7 to 10 CPU hours on a CRAY Y-MP for one entire engine cycle when the computations are performed over a 31 x16 x 20 grid.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920023063&hterms=chemistry+equilibrium&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dchemistry%2Bequilibrium','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920023063&hterms=chemistry+equilibrium&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dchemistry%2Bequilibrium"><span>A two-phase restricted equilibrium model for combustion of metalized solid propellants</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Sabnis, J. S.; Dejong, F. J.; Gibeling, H. J.</p> <p>1992-01-01</p> <p>An <span class="hlt">Eulerian-Lagrangian</span> two-phase approach was adopted to model the multi-phase reacting internal flow in a solid rocket with a metalized propellant. An <span class="hlt">Eulerian</span> description was used to analyze the motion of the continuous phase which includes the gas as well as the small (micron-sized) particulates, while a <span class="hlt">Lagrangian</span> description is used for the analysis of the discrete phase which consists of the larger particulates in the motor chamber. The particulates consist of Al and Al2O3 such that the particulate composition is 100 percent Al at injection from the propellant surface with Al2O3 fraction increasing due to combustion along the particle trajectory. An empirical model is used to compute the combustion rate for agglomerates while the continuous phase chemistry is treated using chemical equilibrium. The computer <span class="hlt">code</span> was used to simulate the reacting flow in a solid rocket motor with an AP/HTPB/Al propellant. The computed results show the existence of an extended combustion zone in the chamber rather than a thin reaction region. The presence of the extended combustion zone results in the chamber flow field and chemical being far from isothermal (as would be predicted by a surface combustion assumption). The temperature in the chamber increases from about 2600 K at the propellant surface to about 3350 K in the core. Similarly the chemical composition and the density of the propellant gas also show spatially non-uniform distribution in the chamber. The analysis developed under the present effort provides a more sophisticated tool for solid rocket internal flow predictions than is presently available, and can be useful in studying apparent anomalies and improving the simple correlations currently in use. The <span class="hlt">code</span> can be used in the analysis of combustion efficiency, thermal load in the internal insulation, plume radiation, etc.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1986PhFl...29.3573A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1986PhFl...29.3573A"><span>Vaporization of irradiated droplets</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Armstrong, R. L.; O'Rourke, P. J.; Zardecki, A.</p> <p>1986-11-01</p> <p>The vaporization of a spherically symmetric liquid droplet subject to a high-intensity laser flux is investigated on the basis of a hydrodynamic description of the system composed of the vapor and ambient gas. In the limit of the convective vaporization, the boundary conditions at the fluid-gas interface are formulated by using the notion of a Knudsen layer in which translational equilibrium is established. This leads to approximate jump conditions at the interface. For homogeneous energy deposition, the hydrodynamic equations are solved numerically with the aid of the CON1D computer <span class="hlt">code</span> (``CON1D: A computer program for calculating spherically symmetric droplet combustion,'' Los Alamos National Laboratory Report No. LA-10269-MS, December, 1984), based on the implict continuous-fluid <span class="hlt">Eulerian</span> (ICE) [J. Comput. Phys. 8, 197 (1971)] and arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) [J. Comput. Phys. 14, 1227 (1974)] numerical mehtods. The solutions exhibit the existence of two shock waves propagating in opposite directions with respect to the contact discontinuity surface that separates the ambient gas and vapor.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/875605','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/875605"><span>Methods for simulation-based analysis of fluid-structure interaction.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Barone, Matthew Franklin; Payne, Jeffrey L.</p> <p>2005-10-01</p> <p>Methods for analysis of fluid-structure interaction using high fidelity simulations are critically reviewed. First, a literature review of modern numerical techniques for simulation of aeroelastic phenomena is presented. The review focuses on methods contained within the arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) framework for coupling computational fluid dynamics <span class="hlt">codes</span> to computational structural mechanics <span class="hlt">codes</span>. The review treats mesh movement algorithms, the role of the geometric conservation law, time advancement schemes, wetted surface interface strategies, and some representative applications. The complexity and computational expense of coupled Navier-Stokes/structural dynamics simulations points to the need for reduced order modeling to facilitate parametric analysis. The proper orthogonalmore » decomposition (POD)/Galerkin projection approach for building a reduced order model (ROM) is presented, along with ideas for extension of the methodology to allow construction of ROMs based on data generated from ALE simulations.« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li class="active"><span>19</span></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_19 --> <div id="page_20" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li class="active"><span>20</span></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="381"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20110016098','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20110016098"><span>Assessment of Turbulence-Chemistry Interaction Models in the National Combustion <span class="hlt">Code</span> (NCC) - Part I</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wey, Thomas Changju; Liu, Nan-suey</p> <p>2011-01-01</p> <p>This paper describes the implementations of the linear-eddy model (LEM) and an <span class="hlt">Eulerian</span> FDF/PDF model in the National Combustion <span class="hlt">Code</span> (NCC) for the simulation of turbulent combustion. The impacts of these two models, along with the so called laminar chemistry model, are then illustrated via the preliminary results from two combustion systems: a nine-element gas fueled combustor and a single-element liquid fueled combustor.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CQGra..35a5007A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CQGra..35a5007A"><span>Field theory of the <span class="hlt">Eulerian</span> perfect fluid</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ariki, Taketo; Morales, Pablo A.</p> <p>2018-01-01</p> <p>The <span class="hlt">Eulerian</span> perfect-fluid theory is reformulated from its action principle in a pure field-theoretic manner. Conservation of the convective current is no longer imposed by Lin’s constraints, but rather adopted as the central idea of the theory. Our formulation, for the first time, successfully reduces redundant degrees of freedom promoting one half of the Clebsch variables to true dynamical fields. Interactions on these fields allow for the exchange of the convective current of quantities such as mass and charge, which are uniformly understood as the breaking of the underlying symmetry of the force-free fluid. The Clebsch fields play the essential role of exchanging angular momentum with the force field producing vorticity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JCoPh.272....1V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JCoPh.272....1V"><span>An improved bounded semi-<span class="hlt">Lagrangian</span> scheme for the turbulent transport of passive scalars</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Verma, Siddhartha; Xuan, Y.; Blanquart, G.</p> <p>2014-09-01</p> <p>An improved bounded semi-<span class="hlt">Lagrangian</span> scalar transport scheme based on cubic Hermite polynomial reconstruction is proposed in this paper. Boundedness of the scalar being transported is ensured by applying derivative limiting techniques. Single sub-cell extrema are allowed to exist as they are often physical, and help minimize numerical dissipation. This treatment is distinct from enforcing strict monotonicity as done by D.L. Williamson and P.J. Rasch [5], and allows better preservation of small scale structures in turbulent simulations. The proposed bounding algorithm, although a seemingly subtle difference from strict monotonicity enforcement, is shown to result in significant performance gain in laminar cases, and in three-dimensional turbulent mixing layers. The scheme satisfies several important properties, including boundedness, low numerical diffusion, and high accuracy. Performance gain in the turbulent case is assessed by comparing scalar energy and dissipation spectra produced by several bounded and unbounded schemes. The results indicate that the proposed scheme is capable of furnishing extremely accurate results, with less severe resolution requirements than all the other bounded schemes tested. Additional simulations in homogeneous isotropic turbulence, with scalar timestep size unconstrained by the CFL number, show good agreement with spectral scheme results available in the literature. Detailed analytical examination of gain and phase error characteristics of the original cubic Hermite polynomial is also included, and points to dissipation and dispersion characteristics comparable to, or better than, those of a fifth order upwind <span class="hlt">Eulerian</span> scheme.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DPPJP8081T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DPPJP8081T"><span>Simulations of Laboratory Astrophysics Experiments using the CRASH <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Trantham, Matthew; Kuranz, Carolyn; Manuel, Mario; Keiter, Paul; Drake, R. P.</p> <p>2014-10-01</p> <p>Computer simulations can assist in the design and analysis of laboratory astrophysics experiments. The Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan developed a <span class="hlt">code</span> that has been used to design and analyze high-energy-density experiments on OMEGA, NIF, and other large laser facilities. This <span class="hlt">Eulerian</span> <span class="hlt">code</span> uses block-adaptive mesh refinement (AMR) with implicit multigroup radiation transport, electron heat conduction and laser ray tracing. This poster/talk will demonstrate some of the experiments the CRASH <span class="hlt">code</span> has helped design or analyze including: Kelvin-Helmholtz, Rayleigh-Taylor, imploding bubbles, and interacting jet experiments. This work is funded by the Predictive Sciences Academic Alliances Program in NNSA-ASC via Grant DEFC52-08NA28616, by the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, Grant Number DE-NA0001840, and by the National Laser User Facility Program, Grant Number DE-NA0000850.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhLB..772..694C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhLB..772..694C"><span>Extended hamiltonian formalism and Lorentz-violating <span class="hlt">lagrangians</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Colladay, Don</p> <p>2017-09-01</p> <p>A new perspective on the classical mechanical formulation of particle trajectories in Lorentz-violating theories is presented. Using the extended hamiltonian formalism, a Legendre Transformation between the associated covariant <span class="hlt">lagrangian</span> and hamiltonian varieties is constructed. This approach enables calculation of trajectories using Hamilton's equations in momentum space and the Euler-Lagrange equations in velocity space away from certain singular points that arise in the theory. Singular points are naturally de-singularized by requiring the trajectories to be smooth functions of both velocity and momentum variables. In addition, it is possible to identify specific sheets of the dispersion relations that correspond to specific solutions for the <span class="hlt">lagrangian</span>. Examples corresponding to bipartite Finsler functions are computed in detail. A direct connection between the <span class="hlt">lagrangians</span> and the field-theoretic solutions to the Dirac equation is also established for a special case.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25903879','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25903879"><span>Thermostating extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Martínez, Enrique; Cawkwell, Marc J; Voter, Arthur F; Niklasson, Anders M N</p> <p>2015-04-21</p> <p>Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended <span class="hlt">Lagrangian</span> Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached at each time step. The thermostated extended <span class="hlt">Lagrangian</span> framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DPPUP8090B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DPPUP8090B"><span>Validation of a Laser-Ray Package in an <span class="hlt">Eulerian</span> <span class="hlt">Code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bradley, Paul; Hall, Mike; McKenty, Patrick; Collins, Tim; Keller, David</p> <p>2014-10-01</p> <p>A laser-ray absorption package was recently installed in the RAGE <span class="hlt">code</span> by the Laboratory for Laser Energetics (LLE). In this presentation, we describe our use of this package to implode Omega 60 beam symmetric direct drive capsules. The capsules have outer diameters of about 860 microns, CH plastic shell thicknesses between 8 and 32 microns, DD or DT gas fills between 5 and 20 atmospheres, and a 1 ns square pulse of 23 to 27 kJ. These capsule implosions were previously modeled with a calibrated energy source in the outer layer of the capsule, where we matched bang time and burn ion temperature well, but the simulated yields were two to three times higher than the data. We will run simulations with laser ray energy deposition to the experiments and the results to the yield and spectroscopic data. Work performed by Los Alamos National Laboratory under Contract DE-AC52-06NA25396 for the National Nuclear Security Administration of the U.S. Department of Energy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25725498','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25725498"><span>L-GRAAL: <span class="hlt">Lagrangian</span> graphlet-based network aligner.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Malod-Dognin, Noël; Pržulj, Nataša</p> <p>2015-07-01</p> <p>Discovering and understanding patterns in networks of protein-protein interactions (PPIs) is a central problem in systems biology. Alignments between these networks aid functional understanding as they uncover important information, such as evolutionary conserved pathways, protein complexes and functional orthologs. A few methods have been proposed for global PPI network alignments, but because of NP-completeness of underlying sub-graph isomorphism problem, producing topologically and biologically accurate alignments remains a challenge. We introduce a novel global network alignment tool, <span class="hlt">Lagrangian</span> GRAphlet-based ALigner (L-GRAAL), which directly optimizes both the protein and the interaction functional conservations, using a novel alignment search heuristic based on integer programming and <span class="hlt">Lagrangian</span> relaxation. We compare L-GRAAL with the state-of-the-art network aligners on the largest available PPI networks from BioGRID and observe that L-GRAAL uncovers the largest common sub-graphs between the networks, as measured by edge-correctness and symmetric sub-structures scores, which allow transferring more functional information across networks. We assess the biological quality of the protein mappings using the semantic similarity of their Gene Ontology annotations and observe that L-GRAAL best uncovers functionally conserved proteins. Furthermore, we introduce for the first time a measure of the semantic similarity of the mapped interactions and show that L-GRAAL also uncovers best functionally conserved interactions. In addition, we illustrate on the PPI networks of baker's yeast and human the ability of L-GRAAL to predict new PPIs. Finally, L-GRAAL's results are the first to show that topological information is more important than sequence information for uncovering functionally conserved interactions. L-GRAAL is <span class="hlt">coded</span> in C++. Software is available at: http://bio-nets.doc.ic.ac.uk/L-GRAAL/. n.malod-dognin@imperial.ac.uk Supplementary data are available at</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/634079','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/634079"><span>Benchmarking the SPHINX and CTH shock physics <span class="hlt">codes</span> for three problems in ballistics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Wilson, L.T.; Hertel, E.; Schwalbe, L.</p> <p>1998-02-01</p> <p>The CTH <span class="hlt">Eulerian</span> hydrocode, and the SPHINX smooth particle hydrodynamics (SPH) <span class="hlt">code</span> were used to model a shock tube, two long rod penetrations into semi-infinite steel targets, and a long rod penetration into a spaced plate array. The results were then compared to experimental data. Both SPHINX and CTH modeled the one-dimensional shock tube problem well. Both <span class="hlt">codes</span> did a reasonable job in modeling the outcome of the axisymmetric rod impact problem. Neither <span class="hlt">code</span> correctly reproduced the depth of penetration in both experiments. In the 3-D problem, both <span class="hlt">codes</span> reasonably replicated the penetration of the rod through the first plate.more » After this, however, the predictions of both <span class="hlt">codes</span> began to diverge from the results seen in the experiment. In terms of computer resources, the run times are problem dependent, and are discussed in the text.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011JHEP...07..061G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011JHEP...07..061G"><span>Parent formulation at the <span class="hlt">Lagrangian</span> level</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Grigoriev, Maxim</p> <p>2011-07-01</p> <p>The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of <span class="hlt">Lagrangian</span> systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a <span class="hlt">Lagrangian</span> version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV-BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang-Mills theory, and gravity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1422959','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1422959"><span>Thermostating extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Martínez, Enrique; Cawkwell, Marc J.; Voter, Arthur F.</p> <p></p> <p>Here, Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended <span class="hlt">Lagrangian</span> Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached atmore » each time step. Lastly, the thermostated extended <span class="hlt">Lagrangian</span> framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1422959-thermostating-extended-lagrangian-born-oppenheimer-molecular-dynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1422959-thermostating-extended-lagrangian-born-oppenheimer-molecular-dynamics"><span>Thermostating extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Martínez, Enrique; Cawkwell, Marc J.; Voter, Arthur F.; ...</p> <p>2015-04-21</p> <p>Here, Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended <span class="hlt">Lagrangian</span> Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached atmore » each time step. Lastly, the thermostated extended <span class="hlt">Lagrangian</span> framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1001413','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1001413"><span>Quantifying Discretization Effects on Brain Trauma Simulations</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2016-01-01</p> <p>arbitrarily formed meshes can propagate error when resolving interactions among the skull , cerebrospinal fluid, and brain. We compared <span class="hlt">Lagrangian</span>, pure...embedded methods from top to bottom. ......3 Fig. 2 Loading node-set for <span class="hlt">Eulerian</span> rotational problem. The dark shaded area around the skull is the area to...and top inner edges of the skull . The example shown is a <span class="hlt">Lagrangian</span> rotational model. The red and green materials represent the brain and skull</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930035782&hterms=passive+transport&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dpassive%2Btransport','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930035782&hterms=passive+transport&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dpassive%2Btransport"><span>Enhancement of diffusive transport in oscillatory flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Knobloch, E.; Merryfield, W. J.</p> <p>1992-01-01</p> <p>The theory of transport of passive scalars in oscillatory flows is reexamined. The differences between transport in standing and traveling waves are emphasized. Both <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> diffusivities are calculated, and the conditions for their applicability are discussed. Numerical simulations are conducted to understand the expulsion of gradients from time-dependent eddies and the resulting transport. The results indicate that it is the <span class="hlt">Eulerian</span> diffusivity that is of primary relevance for describing enhanced transport on spatial scales larger than that of the eddies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhDT.......102P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhDT.......102P"><span>Implementing a Loosely Coupled Fluid Structure Interaction Finite Element Model in PHASTA</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pope, David</p> <p></p> <p>Fluid Structure Interaction problems are an important multi-physics phenomenon in the design of aerospace vehicles and other engineering applications. A variety of computational fluid dynamics solvers capable of resolving the fluid dynamics exist. PHASTA is one such computational fluid dynamics solver. Enhancing the capability of PHASTA to resolve Fluid-Structure Interaction first requires implementing a structural dynamics solver. The implementation also requires a correction of the mesh used to solve the fluid equations to account for the deformation of the structure. This results in mesh motion and causes the need for an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> modification to the fluid dynamics equations currently implemented in PHASTA. With the implementation of both structural dynamics physics, mesh correction, and the Arbitrary <span class="hlt">Lagrangian-Eulerian</span> modification of the fluid dynamics equations, PHASTA is made capable of solving Fluid-Structure Interaction problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015GMDD....8.8895C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015GMDD....8.8895C"><span>ASHEE: a compressible, Equilibrium-<span class="hlt">Eulerian</span> model for volcanic ash plumes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cerminara, M.; Esposti Ongaro, T.; Berselli, L. C.</p> <p>2015-10-01</p> <p>A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase <span class="hlt">Eulerian</span> transport equations (Neri et al., 2003) for a mixture of gases and solid dispersed particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model (Ferry and Balachandar, 2001), valid for low concentration regimes (particle volume fraction less than 10-3) and particles Stokes number (St, i.e., the ratio between their relaxation time and flow characteristic time) not exceeding about 0.2. The new model, which is called ASHEE (ASH Equilibrium <span class="hlt">Eulerian</span>), is significantly faster than the N-phase <span class="hlt">Eulerian</span> model while retaining the capability to describe gas-particle non-equilibrium effects. Direct numerical simulation accurately reproduce the dynamics of isotropic, compressible turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration and clustering of particles by turbulence, thus verifying the model reliability and suitability for the numerical simulation of high-Reynolds number and high-temperature regimes in presence of a dispersed phase. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous flow properties. In particular, the self-similar Gaussian radial profile and the development of large-scale coherent structures are reproduced, including the rate of turbulent mixing and entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. For very fine particles (St → 0, when non-equilibrium effects are negligible) the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.339..210S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.339..210S"><span>Simulation of reactive polydisperse sprays strongly coupled to unsteady flows in solid rocket motors: Efficient strategy using <span class="hlt">Eulerian</span> Multi-Fluid methods</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sibra, A.; Dupays, J.; Murrone, A.; Laurent, F.; Massot, M.</p> <p>2017-06-01</p> <p>In this paper, we tackle the issue of the accurate simulation of evaporating and reactive polydisperse sprays strongly coupled to unsteady gaseous flows. In solid propulsion, aluminum particles are included in the propellant to improve the global performances but the distributed combustion of these droplets in the chamber is suspected to be a driving mechanism of hydrodynamic and acoustic instabilities. The faithful prediction of two-phase interactions is a determining step for future solid rocket motor optimization. When looking at saving computational ressources as required for industrial applications, performing reliable simulations of two-phase flow instabilities appears as a challenge for both modeling and scientific computing. The size polydispersity, which conditions the droplet dynamics, is a key parameter that has to be accounted for. For moderately dense sprays, a kinetic approach based on a statistical point of view is particularly appropriate. The spray is described by a number density function and its evolution follows a Williams-Boltzmann transport equation. To solve it, we use <span class="hlt">Eulerian</span> Multi-Fluid methods, based on a continuous discretization of the size phase space into sections, which offer an accurate treatment of the polydispersion. The objective of this paper is threefold: first to derive a new Two Size Moment Multi-Fluid model that is able to tackle evaporating polydisperse sprays at low cost while accurately describing the main driving mechanisms, second to develop a dedicated evaporation scheme to treat simultaneously mass, moment and energy exchanges with the gas and between the sections. Finally, to design a time splitting operator strategy respecting both reactive two-phase flow physics and cost/accuracy ratio required for industrial computations. Using a research <span class="hlt">code</span>, we provide 0D validations of the new scheme before assessing the splitting technique's ability on a reference two-phase flow acoustic case. Implemented in the industrial</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008ACPD....818727S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008ACPD....818727S"><span>Implications of <span class="hlt">Lagrangian</span> transport for coupled chemistry-climate simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.</p> <p>2008-10-01</p> <p>For the first time a purely <span class="hlt">Lagrangian</span> transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the <span class="hlt">Lagrangian</span> scheme ATTILA for the transport of water vapour, cloud water and chemical trace species in the ECHAM4.L39(DLR)/CHEM (E39C) CCM. The advantage of the <span class="hlt">Lagrangian</span> approach is that it is numerically non-diffusive and therefore maintains steeper and more realistic gradients than the operational semi-<span class="hlt">Lagrangian</span> transport scheme. In case of radiatively active species changes in the simulated distributions feed back to model dynamics which in turn affect the modelled transport. The implications of the <span class="hlt">Lagrangian</span> transport scheme for stratospheric model dynamics and tracer distributions in the upgraded model version E39C-ATTILA (E39C-A) are evaluated by comparison with observations and results of the E39C model with the operational semi-<span class="hlt">Lagrangian</span> advection scheme. We find that several deficiencies in stratospheric dynamics in E39C seem to originate from a pronounced modelled wet bias and an associated cold bias in the extra-tropical lowermost stratosphere. The reduction of the simulated moisture and temperature bias in E39C-A leads to a significant advancement of stratospheric dynamics in terms of the mean state as well as annual and interannual variability. As a consequence of the favourable numerical characteristics of the <span class="hlt">Lagrangian</span> transport scheme and the improved model dynamics, E39C-A generally shows more realistic stratospheric tracer distributions: Compared to E39C high stratospheric chlorine (Cly) concentrations extend further downward and agree now well with analyses derived from observations. Therefore E39C-A realistically covers the altitude of maximum ozone depletion in the stratosphere. The location of the ozonopause, i.e. the transition from low tropospheric to high stratospheric ozone values, is also clearly improved in E39C-A. Furthermore, the simulated temporal evolution of stratospheric Cly in the past is</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JGP...128..140K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JGP...128..140K"><span>Hamiltonian stability for weighted measure and generalized <span class="hlt">Lagrangian</span> mean curvature flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kajigaya, Toru; Kunikawa, Keita</p> <p>2018-06-01</p> <p>In this paper, we generalize several results for the Hamiltonian stability and the mean curvature flow of <span class="hlt">Lagrangian</span> submanifolds in a Kähler-Einstein manifold to more general Kähler manifolds including a Fano manifold equipped with a Kähler form ω ∈ 2 πc1(M) by using the method proposed by Behrndt (2011). Namely, we first consider a weighted measure on a <span class="hlt">Lagrangian</span> submanifold L in a Kähler manifold M and investigate the variational problem of L for the weighted volume functional. We call a stationary point of the weighted volume functional f-minimal, and define the notion of Hamiltonian f-stability as a local minimizer under Hamiltonian deformations. We show such examples naturally appear in a toric Fano manifold. Moreover, we consider the generalized <span class="hlt">Lagrangian</span> mean curvature flow in a Fano manifold which is introduced by Behrndt and Smoczyk-Wang. We generalize the result of H. Li, and show that if the initial <span class="hlt">Lagrangian</span> submanifold is a small Hamiltonian deformation of an f-minimal and Hamiltonian f-stable <span class="hlt">Lagrangian</span> submanifold, then the generalized MCF converges exponentially fast to an f-minimal <span class="hlt">Lagrangian</span> submanifold.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27327139','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27327139"><span><span class="hlt">Lagrangian</span> descriptors in dissipative systems.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Junginger, Andrej; Hernandez, Rigoberto</p> <p>2016-11-09</p> <p>The reaction dynamics of time-dependent systems can be resolved through a recrossing-free dividing surface associated with the transition state trajectory-that is, the unique trajectory which is bound to the barrier region for all time in response to a given time-dependent potential. A general procedure based on the minimization of <span class="hlt">Lagrangian</span> descriptors has recently been developed by Craven and Hernandez [Phys. Rev. Lett., 2015, 115, 148301] to construct this particular trajectory without requiring perturbative expansions relative to the naive transition state point at the top of the barrier. The extension of the method to account for dissipation in the equations of motion requires additional considerations established in this paper because the calculation of the <span class="hlt">Lagrangian</span> descriptor involves the integration of trajectories in forward and backward time. The two contributions are in general very different because the friction term can act as a source (in backward time) or sink (in forward time) of energy, leading to the possibility that information about the phase space structure may be lost due to the dominance of only one of the terms. To compensate for this effect, we introduce a weighting scheme within the <span class="hlt">Lagrangian</span> descriptor and demonstrate that for thermal Langevin dynamics it preserves the essential phase space structures, while they are lost in the nonweighted case.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li class="active"><span>20</span></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_20 --> <div id="page_21" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li class="active"><span>21</span></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="401"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19740019118','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19740019118"><span>A macroscopic plasma <span class="hlt">Lagrangian</span> and its application to wave interactions and resonances</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Peng, Y. K. M.</p> <p>1974-01-01</p> <p>The derivation of a macroscopic plasma <span class="hlt">Lagrangian</span> is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the <span class="hlt">Lagrangian</span> is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a <span class="hlt">Lagrangian</span> are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The <span class="hlt">Lagrangians</span> for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma <span class="hlt">Lagrangian</span> is shown to differ from the velocity-integrated low <span class="hlt">Lagrangian</span> by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JChPh.147e4103N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JChPh.147e4103N"><span>Next generation extended <span class="hlt">Lagrangian</span> first principles molecular dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Niklasson, Anders M. N.</p> <p>2017-08-01</p> <p>Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended <span class="hlt">Lagrangian</span> framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28789552','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28789552"><span>Next generation extended <span class="hlt">Lagrangian</span> first principles molecular dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Niklasson, Anders M N</p> <p>2017-08-07</p> <p>Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for general Hohenberg-Kohn density-functional theory and compared with the extended <span class="hlt">Lagrangian</span> framework of first principles molecular dynamics by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)]. It is shown how extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics overcomes several shortcomings of regular, direct Born-Oppenheimer molecular dynamics, while improving or maintaining important features of Car-Parrinello simulations. The accuracy of the electronic degrees of freedom in extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics, with respect to the exact Born-Oppenheimer solution, is of second-order in the size of the integration time step and of fourth order in the potential energy surface. Improved stability over recent formulations of extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics is achieved by generalizing the theory to finite temperature ensembles, using fractional occupation numbers in the calculation of the inner-product kernel of the extended harmonic oscillator that appears as a preconditioner in the electronic equations of motion. Material systems that normally exhibit slow self-consistent field convergence can be simulated using integration time steps of the same order as in direct Born-Oppenheimer molecular dynamics, but without the requirement of an iterative, non-linear electronic ground-state optimization prior to the force evaluations and without a systematic drift in the total energy. In combination with proposed low-rank and on the fly updates of the kernel, this formulation provides an efficient and general framework for quantum-based Born-Oppenheimer molecular dynamics simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=30913&Lab=ORD&keyword=finite+AND+element&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=30913&Lab=ORD&keyword=finite+AND+element&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>AN OPTIMAL ADAPTIVE LOCAL GRID REFINEMENT APPROACH TO MODELING CONTAMINANT TRANSPORT</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>A <span class="hlt">Lagrangian-Eulerian</span> method with an optimal adaptive local grid refinement is used to model contaminant transport equations. pplication of this approach to two bench-mark problems indicates that it completely resolves difficulties of peak clipping, numerical diffusion, and spuri...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19830044831&hterms=averaged+lagrangian&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Daveraged%2Blagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19830044831&hterms=averaged+lagrangian&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Daveraged%2Blagrangian"><span>Microscopic <span class="hlt">Lagrangian</span> description of warm plasmas. IV - Macroscopic approximation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kim, H.; Crawford, F. W.</p> <p>1983-01-01</p> <p>The averaged-<span class="hlt">Lagrangian</span> method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic <span class="hlt">Lagrangian</span> treated by Kim and Crawford (1977) and by Galloway and Crawford (1977) is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfven wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic <span class="hlt">Lagrangian</span> density.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvF...2e4602S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvF...2e4602S"><span><span class="hlt">Lagrangian</span> acceleration statistics in a turbulent channel flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Stelzenmuller, Nickolas; Polanco, Juan Ignacio; Vignal, Laure; Vinkovic, Ivana; Mordant, Nicolas</p> <p>2017-05-01</p> <p><span class="hlt">Lagrangian</span> acceleration statistics in a fully developed turbulent channel flow at Reτ=1440 are investigated, based on tracer particle tracking in experiments and direct numerical simulations. The evolution with wall distance of the <span class="hlt">Lagrangian</span> velocity and acceleration time scales is analyzed. Dependency between acceleration components in the near-wall region is described using cross-correlations and joint probability density functions. The strong streamwise coherent vortices typical of wall-bounded turbulent flows are shown to have a significant impact on the dynamics. This results in a strong anisotropy at small scales in the near-wall region that remains present in most of the channel. Such statistical properties may be used as constraints in building advanced <span class="hlt">Lagrangian</span> stochastic models to predict the dispersion and mixing of chemical components for combustion or environmental studies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940012969','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940012969"><span>Computational analysis of Variable Thrust Engine (VTE) performance</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Giridharan, M. G.; Krishnan, A.; Przekwas, A. J.</p> <p>1993-01-01</p> <p>The Variable Thrust Engine (VTE) of the Orbital Maneuvering Vehicle (OMV) uses a hypergolic propellant combination of Monomethyl Hydrazine (MMH) and Nitrogen Tetroxide (NTO) as fuel and oxidizer, respectively. The performance of the VTE depends on a number of complex interacting phenomena such as atomization, spray dynamics, vaporization, turbulent mixing, convective/radiative heat transfer, and hypergolic combustion. This study involved the development of a comprehensive numerical methodology to facilitate detailed analysis of the VTE. An existing Computational Fluid Dynamics (CFD) <span class="hlt">code</span> was extensively modified to include the following models: a two-liquid, two-phase <span class="hlt">Eulerian-Lagrangian</span> spray model; a chemical equilibrium model; and a discrete ordinate radiation heat transfer model. The modified <span class="hlt">code</span> was used to conduct a series of simulations to assess the effects of various physical phenomena and boundary conditions on the VTE performance. The details of the models and the results of the simulations are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014IJCFD..28..420M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014IJCFD..28..420M"><span>Material point method of modelling and simulation of reacting flow of oxygen</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mason, Matthew; Chen, Kuan; Hu, Patrick G.</p> <p>2014-07-01</p> <p>Aerospace vehicles are continually being designed to sustain flight at higher speeds and higher altitudes than previously attainable. At hypersonic speeds, gases within a flow begin to chemically react and the fluid's physical properties are modified. It is desirable to model these effects within the Material Point Method (MPM). The MPM is a combined <span class="hlt">Eulerian-Lagrangian</span> particle-based solver that calculates the physical properties of individual particles and uses a background grid for information storage and exchange. This study introduces chemically reacting flow modelling within the MPM numerical algorithm and illustrates a simple application using the AeroElastic Material Point Method (AEMPM) <span class="hlt">code</span>. The governing equations of reacting flows are introduced and their direct application within an MPM <span class="hlt">code</span> is discussed. A flow of 100% oxygen is illustrated and the results are compared with independently developed computational non-equilibrium algorithms. Observed trends agree well with results from an independently developed source.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010PhRvA..81b2112K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010PhRvA..81b2112K"><span>Functional integral for non-<span class="hlt">Lagrangian</span> systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kochan, Denis</p> <p>2010-02-01</p> <p>A functional integral formulation of quantum mechanics for non-<span class="hlt">Lagrangian</span> systems is presented. The approach, which we call “stringy quantization,” is based solely on classical equations of motion and is free of any ambiguity arising from <span class="hlt">Lagrangian</span> and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general A-power friction force -κq˙A. Results for A=1 are compared with those obtained in the approaches by Caldirola-Kanai, Bateman, and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95b5017K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95b5017K"><span>Effective <span class="hlt">Lagrangian</span> in de Sitter spacetime</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kitamoto, Hiroyuki; Kitazawa, Yoshihisa</p> <p>2017-01-01</p> <p>Scale invariant fluctuations of metric are a universal feature of quantum gravity in de Sitter spacetime. We construct an effective <span class="hlt">Lagrangian</span> which summarizes their implications on local physics by integrating superhorizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective <span class="hlt">Lagrangian</span> as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009IJMPA..24.5319K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009IJMPA..24.5319K"><span>Quantization of Non-<span class="hlt">Lagrangian</span> Systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kochan, Denis</p> <p></p> <p>A novel method for quantization of non-<span class="hlt">Lagrangian</span> (open) systems is proposed. It is argued that the essential object, which provides both classical and quantum evolution, is a certain canonical two-form defined in extended velocity space. In this setting classical dynamics is recovered from the stringy-type variational principle, which employs umbilical surfaces instead of histories of the system. Quantization is then accomplished in accordance with the introduced variational principle. The path integral for the transition probability amplitude (propagator) is rearranged to a surface functional integral. In the standard case of closed (<span class="hlt">Lagrangian</span>) systems the presented method reduces to the standard Feynman's approach. The inverse problem of the calculus of variation, the problem of quantization ambiguity and the quantum mechanics in the presence of friction are analyzed in detail.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhyA..471..540S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhyA..471..540S"><span>The S-<span class="hlt">Lagrangian</span> and a theory of homeostasis in living systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sandler, U.; Tsitolovsky, L.</p> <p>2017-04-01</p> <p>A major paradox of living things is their ability to actively counteract degradation in a continuously changing environment or being injured through homeostatic protection. In this study, we propose a dynamic theory of homeostasis based on a generalized <span class="hlt">Lagrangian</span> approach (S-<span class="hlt">Lagrangian</span>), which can be equally applied to physical and nonphysical systems. Following discoverer of homeostasis Cannon (1935), we assume that homeostasis results from tendency of the organisms to decrease of the stress and avoid of death. We show that the universality of homeostasis is a consequence of analytical properties of the S-<span class="hlt">Lagrangian</span>, while peculiarities of the biochemical and physiological mechanisms of homeostasis determine phenomenological parameters of the S-<span class="hlt">Lagrangian</span>. Additionally, we reveal that plausible assumptions about S-<span class="hlt">Lagrangian</span> features lead to good agreement between theoretical descriptions and observed homeostatic behavior. Here, we have focused on homeostasis of living systems, however, the proposed theory is also capable of being extended to social systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012MeSol..47..137K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012MeSol..47..137K"><span>Forms of null <span class="hlt">Lagrangians</span> in field theories of continuum mechanics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kovalev, V. A.; Radaev, Yu. N.</p> <p>2012-02-01</p> <p>The divergence representation of a null <span class="hlt">Lagrangian</span> that is regular in a star-shaped domain is used to obtain its general expression containing field gradients of order ≤ 1 in the case of spacetime of arbitrary dimension. It is shown that for a static three-component field in the three-dimensional space, a null <span class="hlt">Lagrangian</span> can contain up to 15 independent elements in total. The general form of a null <span class="hlt">Lagrangian</span> in the four-dimensional Minkowski spacetime is obtained (the number of physical field variables is assumed arbitrary). A complete theory of the null <span class="hlt">Lagrangian</span> for the n-dimensional spacetime manifold (including the four-dimensional Minkowski spacetime as a special case) is given. Null <span class="hlt">Lagrangians</span> are then used as a basis for solving an important variational problem of an integrating factor. This problem involves searching for factors that depend on the spacetime variables, field variables, and their gradients and, for a given system of partial differential equations, ensure the equality between the scalar product of a vector multiplier by the system vector and some divergence expression for arbitrary field variables and, hence, allow one to formulate a divergence conservation law on solutions to the system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016ApJS..225....4B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ApJS..225....4B"><span>TEA: A <span class="hlt">Code</span> Calculating Thermochemical Equilibrium Abundances</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver</p> <p>2016-07-01</p> <p>We present an open-source Thermochemical Equilibrium Abundances (TEA) <span class="hlt">code</span> that calculates the abundances of gaseous molecular species. The <span class="hlt">code</span> is based on the methodology of White et al. and Eriksson. It applies Gibbs free-energy minimization using an iterative, <span class="hlt">Lagrangian</span> optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature-pressure pairs. We tested the <span class="hlt">code</span> against the method of Burrows & Sharp, the free thermochemical equilibrium <span class="hlt">code</span> Chemical Equilibrium with Applications (CEA), and the example given by Burrows & Sharp. Using their thermodynamic data, TEA reproduces their final abundances, but with higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a <span class="hlt">code</span> document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhLB..779..485L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhLB..779..485L"><span>A unifying framework for ghost-free Lorentz-invariant <span class="hlt">Lagrangian</span> field theories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Li, Wenliang</p> <p>2018-04-01</p> <p>We propose a framework for Lorentz-invariant <span class="hlt">Lagrangian</span> field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general <span class="hlt">Lagrangians</span> are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established <span class="hlt">Lagrangian</span> theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for <span class="hlt">Lagrangian</span> field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/17151883','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/17151883"><span>Structured population dynamics: continuous size and discontinuous stage structures.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Buffoni, Giuseppe; Pasquali, Sara</p> <p>2007-04-01</p> <p>A nonlinear stochastic model for the dynamics of a population with either a continuous size structure or a discontinuous stage structure is formulated in the <span class="hlt">Eulerian</span> formalism. It takes into account dispersion effects due to stochastic variability of the development process of the individuals. The discrete equations of the numerical approximation are derived, and an analysis of the existence and stability of the equilibrium states is performed. An application to a copepod population is illustrated; numerical results of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> models are compared.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvD..97f5019R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvD..97f5019R"><span>Leading-order classical <span class="hlt">Lagrangians</span> for the nonminimal standard-model extension</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Reis, J. A. A. S.; Schreck, M.</p> <p>2018-03-01</p> <p>In this paper, we derive the general leading-order classical <span class="hlt">Lagrangian</span> covering all fermion operators of the nonminimal standard-model extension (SME). Such a <span class="hlt">Lagrangian</span> is considered to be the point-particle analog of the effective field theory description of Lorentz violation that is provided by the SME. At leading order in Lorentz violation, the <span class="hlt">Lagrangian</span> obtained satisfies the set of five nonlinear equations that govern the map from the field theory to the classical description. This result can be of use for phenomenological studies of classical bodies in gravitational fields.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19810057814&hterms=averaged+lagrangian&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Daveraged%2Blagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19810057814&hterms=averaged+lagrangian&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Daveraged%2Blagrangian"><span><span class="hlt">Lagrangian</span> methods in nonlinear plasma wave interaction</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Crawford, F. W.</p> <p>1980-01-01</p> <p>Analysis of nonlinear plasma wave interactions is usually very complicated, and simplifying mathematical approaches are highly desirable. The application of averaged-<span class="hlt">Lagrangian</span> methods offers a considerable reduction in effort, with improved insight into synchronism and conservation (Manley-Rowe) relations. This chapter indicates how suitable <span class="hlt">Lagrangian</span> densities have been defined, expanded, and manipulated to describe nonlinear wave-wave and wave-particle interactions in the microscopic, macroscopic and cold plasma models. Recently, further simplifications have been introduced by the use of techniques derived from Lie algebra. These and likely future developments are reviewed briefly.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CSR....47..145F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CSR....47..145F"><span>Using <span class="hlt">Lagrangian</span> Coherent Structures to understand coastal water quality</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fiorentino, L. A.; Olascoaga, M. J.; Reniers, A.; Feng, Z.; Beron-Vera, F. J.; MacMahan, J. H.</p> <p>2012-09-01</p> <p>The accumulation of pollutants near the shoreline can result in low quality coastal water with negative effects on human health. To understand the role of mixing by tidal flows in coastal water quality we study the nearshore <span class="hlt">Lagrangian</span> circulation. Specifically, we reveal <span class="hlt">Lagrangian</span> Coherent Structures (LCSs), i.e., distinguished material curves which shape global mixing patterns and thus act as skeletons of the <span class="hlt">Lagrangian</span> circulation. This is done using the recently developed geodesic theory of transport barriers. Particular focus is placed on Hobie Beach, a recreational subtropical marine beach located in Virginia Key, Miami, Florida. According to studies of water quality, Hobie Beach is characterized by high microbial levels. Possible sources of pollution in Hobie Beach include human bather shedding, dog fecal matter, runoff, and sand efflux at high tides. Consistent with the patterns formed by satellite-tracked drifter trajectories, the LCSs extracted from simulated currents reveal a <span class="hlt">Lagrangian</span> circulation favoring the retention near the shoreline of pollutants released along the shoreline, which can help explain the low quality water registered at Hobie Beach.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018NuPhB.928..107M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018NuPhB.928..107M"><span>Integration over families of <span class="hlt">Lagrangian</span> submanifolds in BV formalism</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mikhailov, Andrei</p> <p>2018-03-01</p> <p>Gauge fixing is interpreted in BV formalism as a choice of <span class="hlt">Lagrangian</span> submanifold in an odd symplectic manifold (the BV phase space). A natural construction defines an integration procedure on families of <span class="hlt">Lagrangian</span> submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted in this way. We discuss the role of gauge symmetries in this construction. We derive the conditions which should be imposed on gauge symmetries for the consistency of our integration procedure. We explain how these conditions behave under the deformations of the worldsheet theory. In particular, we show that integrated vertex operator is actually an inhomogeneous differential form on the space of <span class="hlt">Lagrangian</span> submanifolds.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li class="active"><span>21</span></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_21 --> <div id="page_22" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li class="active"><span>22</span></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="421"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.348..493T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.348..493T"><span>An updated <span class="hlt">Lagrangian</span> particle hydrodynamics (ULPH) for Newtonian fluids</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tu, Qingsong; Li, Shaofan</p> <p>2017-11-01</p> <p>In this work, we have developed an updated <span class="hlt">Lagrangian</span> particle hydrodynamics (ULPH) for Newtonian fluid. Unlike the smoothed particle hydrodynamics, the non-local particle hydrodynamics formulation proposed here is consistent and convergence. Unlike the state-based peridynamics, the discrete particle dynamics proposed here has no internal material bond between particles, and it is not formulated with respect to initial or a fixed referential configuration. In specific, we have shown that (1) the non-local update <span class="hlt">Lagrangian</span> particle hydrodynamics formulation converges to the conventional local fluid mechanics formulation; (2) the non-local updated <span class="hlt">Lagrangian</span> particle hydrodynamics can capture arbitrary flow discontinuities without any changes in the formulation, and (3) the proposed non-local particle hydrodynamics is computationally efficient and robust.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=magnetic+AND+particles&id=EJ832524','ERIC'); return false;" href="https://eric.ed.gov/?q=magnetic+AND+particles&id=EJ832524"><span>Symmetries in <span class="hlt">Lagrangian</span> Dynamics</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Ferrario, Carlo; Passerini, Arianna</p> <p>2007-01-01</p> <p>In the framework of Noether's theorem, a distinction between <span class="hlt">Lagrangian</span> and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1910943P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1910943P"><span>Transport upscaling from pore- to Darcy-scale: Incorporating pore-scale Berea sandstone <span class="hlt">Lagrangian</span> velocity statistics into a Darcy-scale transport CTRW model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Puyguiraud, Alexandre; Dentz, Marco; Gouze, Philippe</p> <p>2017-04-01</p> <p>For the past several years a lot of attention has been given to pore-scale flow in order to understand and model transport, mixing and reaction in porous media. Nevertheless we believe that an accurate study of spatial and temporal evolution of velocities could bring important additional information for the upscaling from pore to higher scales. To gather these pieces of information, we perform Stokes flow simulations on pore-scale digitized images of a Berea sandstone core. First, micro-tomography (XRMT) imaging and segmentation processes allow us to obtain 3D black and white images of the sample [1]. Then we used an OpenFoam solver to perform the Stokes flow simulations mentioned above, which gives us the velocities at the interfaces of a cubic mesh. Subsequently, we use a particle streamline reconstruction technique which uses the <span class="hlt">Eulerian</span> velocity field previously obtained. This technique, based on a modified Pollock algorithm [2], enables us to make particle tracking simulations on the digitized sample. In order to build a stochastic pore-scale transport model, we analyze the <span class="hlt">Lagrangian</span> velocity series in two different ways. First we investigate the velocity evolution by sampling isochronically (t-<span class="hlt">Lagrangian</span>), and by studying its statistical properties in terms of one- and two-points statistics. Intermittent patterns can be observed. These are due to the persistance of low velocities over a characteristic space length. Other results are investigated, such as correlation functions and velocity PDFs, which permit us to study more deeply this persistence in the velocities and to compute the correlation times. However, with the second approach, doing these same analysis in space by computing the velocities equidistantly, enables us to remove the intermittency shown in the temporal evolution and to model these velocity series as a Markov process. This renders the stochastic particle dynamics into a CTRW [3]. [1] Gjetvaj, F., A. Russian, P. Gouze, and M. Dentz (2015</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19880068211&hterms=fuel+rockets+use&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dfuel%2Brockets%2Buse','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19880068211&hterms=fuel+rockets+use&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dfuel%2Brockets%2Buse"><span>Predicting the velocity and azimuth of fragments generated by the range destruction or random failure of rocket casings and tankage</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Eck, Marshall; Mukunda, Meera</p> <p>1988-01-01</p> <p>A calculational method is described which provides a powerful tool for predicting solid rocket motor (SRM) casing and liquid rocket tankage fragmentation response. The approach properly partitions the available impulse to each major system-mass component. It uses the Pisces <span class="hlt">code</span> developed by Physics International to couple the forces generated by an <span class="hlt">Eulerian</span>-modeled gas flow field to a <span class="hlt">Lagrangian</span>-modeled fuel and casing system. The details of the predictive analytical modeling process and the development of normalized relations for momentum partition as a function of SRM burn time and initial geometry are discussed. Methods for applying similar modeling techniques to liquid-tankage-overpressure failures are also discussed. Good agreement between predictions and observations are obtained for five specific events.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001AGUFMNG42A0407P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001AGUFMNG42A0407P"><span>Predictability of the <span class="hlt">Lagrangian</span> Motion in the Upper Ocean</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Piterbarg, L. I.; Griffa, A.; Griffa, A.; Mariano, A. J.; Ozgokmen, T. M.; Ryan, E. H.</p> <p>2001-12-01</p> <p>The complex non-linear dynamics of the upper ocean leads to chaotic behavior of drifter trajectories in the ocean. Our study is focused on estimating the predictability limit for the position of an individual <span class="hlt">Lagrangian</span> particle or a particle cluster based on the knowledge of mean currents and observations of nearby particles (predictors). The <span class="hlt">Lagrangian</span> prediction problem, besides being a fundamental scientific problem, is also of great importance for practical applications such as search and rescue operations and for modeling the spread of fish larvae. A stochastic multi-particle model for the <span class="hlt">Lagrangian</span> motion has been rigorously formulated and is a generalization of the well known "random flight" model for a single particle. Our model is mathematically consistent and includes a few easily interpreted parameters, such as the <span class="hlt">Lagrangian</span> velocity decorrelation time scale, the turbulent velocity variance, and the velocity decorrelation radius, that can be estimated from data. The top Lyapunov exponent for an isotropic version of the model is explicitly expressed as a function of these parameters enabling us to approximate the predictability limit to first order. <span class="hlt">Lagrangian</span> prediction errors for two new prediction algorithms are evaluated against simple algorithms and each other and are used to test the predictability limits of the stochastic model for isotropic turbulence. The first algorithm is based on a Kalman filter and uses the developed stochastic model. Its implementation for drifter clusters in both the Tropical Pacific and Adriatic Sea, showed good prediction skill over a period of 1-2 weeks. The prediction error is primarily a function of the data density, defined as the number of predictors within a velocity decorrelation spatial scale from the particle to be predicted. The second algorithm is model independent and is based on spatial regression considerations. Preliminary results, based on simulated, as well as, real data, indicate that it performs</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1913672M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1913672M"><span>Three dimensional <span class="hlt">Lagrangian</span> structures in the Antarctic Polar Vortex.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mancho, Ana M.; Garcia-Garrido, Victor J.; Curbelo, Jezabel; Niang, Coumba; Mechoso, Carlos R.; Wiggins, Stephen</p> <p>2017-04-01</p> <p>Dynamical systems theory has supported the description of transport processes in fluid dynamics. For understanding trajectory patterns in chaotic advection the geometrical approach by Poincaré seeks for spatial structures that separate regions corresponding to qualitatively different types of trajectories. These structures have been referred to as <span class="hlt">Lagrangian</span> Coherent Structures (LCS), which typically in geophysical flows are well described under the approach of incompressible 2D flows. Different tools have been used to visualize LCS. In this presentation we use <span class="hlt">Lagrangian</span> Descriptors [1,2,3,4] (function M) for visualizing 3D <span class="hlt">Lagrangian</span> structures in the atmosphere, in particular in the Antarctic Polar Vortex. The function M is computed in a fully 3D incompressible flow obtained from data provided by the European Centre for Medium-Range Weather Forecast and it is represented in 2D surfaces. We discuss the findings during the final warming that took place in the spring of 1979 [5]. This research is supported by MINECO grant MTM2014-56392-R. Support is acknowledged also from CSIC grant COOPB20265, U.S. NSF grant AGS-1245069 and ONR grant No. N00014- 01-1-0769. C. Niang acknowledges Fundacion Mujeres por Africa and ICMAT Severo Ochoa project SEV-2011-0087 for financial support. [1] C. Mendoza, A. M. Mancho. The hidden geometry of ocean flows. Physical Review Letters 105 (2010), 3, 038501-1-038501-4. [2] A. M. Mancho, S. Wiggins, J. Curbelo, C. Mendoza. <span class="hlt">Lagrangian</span> Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation. 18 (2013) 3530-3557. [3] C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A. M. Mancho. <span class="hlt">Lagrangian</span> descriptors for two dimensional, area preserving autonomous and nonautonomous maps. Communications in Nonlinear Science and Numerical Simulations, 27 (2015) (1-3), 40-51. [4] C. Lopesino, F. Balibrea-Iniesta, V. J. García-Garrido, S. Wiggins, and A</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1257092','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1257092"><span>Predictions for the drive capabilities of the RancheroS Flux Compression Generator into various load inductances using the <span class="hlt">Eulerian</span> AMR <span class="hlt">Code</span> Roxane</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Watt, Robert Gregory</p> <p></p> <p>The Ranchero Magnetic Flux Compression Generator (FCG) has been used to create current pulses in the 10-­100 MA range for driving both “static” low inductance (0.5 nH) loads1 for generator demonstration purposes and high inductance (10-­20 nH) imploding liner loads2 for ultimate use in physics experiments at very high energy density. Simulations of the standard Ranchero generator have recently shown that it had a design issue that could lead to flux trapping in the generator, and a non-­ robust predictability in its use in high energy density experiments. A re-­examination of the design concept for the standard Ranchero generator, promptedmore » by the possible appearance of an aneurism at the output glide plane, has led to a new generation of Ranchero generators designated the RancheroS (for swooped). This generator has removed the problematic output glide plane and replaced it with a region of constantly increasing diameter in the output end of the FCG cavity in which the armature is driven outward under the influence of an additional HE load not present in the original Ranchero. The resultant RancheroS generator, to be tested in LA43S-­L13, probably in early FY17, has a significantly increased initial inductance and may be able to drive a somewhat higher load inductance than the standard Ranchero. This report will use the <span class="hlt">Eulerian</span> AMR <span class="hlt">code</span> Roxane to study the ability of the new design to drive static loads, with a goal of providing a database corresponding to the load inductances for which the generator might be used and the anticipated peak currents such loads might produce in physics experiments. Such a database, combined with a simple analytic model of an ideal generator, where d(LI)/dt = 0, and supplemented by earlier estimates of losses in actual use of the standard Ranchero, scaled to estimate the increase in losses due to the longer current carrying perimeter in the RancheroS, can then be used to bound the expectations for the current drive one</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013APS..DPPCP8041T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013APS..DPPCP8041T"><span>Modeling Laboratory Astrophysics Experiments using the CRASH <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Trantham, Matthew; Drake, R. P.; Grosskopf, Michael; Bauerle, Matthew; Kruanz, Carolyn; Keiter, Paul; Malamud, Guy; Crash Team</p> <p>2013-10-01</p> <p>The understanding of high energy density systems can be advanced by laboratory astrophysics experiments. Computer simulations can assist in the design and analysis of these experiments. The Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan developed a <span class="hlt">code</span> that has been used to design and analyze high-energy-density experiments on OMEGA, NIF, and other large laser facilities. This <span class="hlt">Eulerian</span> <span class="hlt">code</span> uses block-adaptive mesh refinement (AMR) with implicit multigroup radiation transport and electron heat conduction. This poster/talk will demonstrate some of the experiments the CRASH <span class="hlt">code</span> has helped design or analyze including: Radiative shocks experiments, Kelvin-Helmholtz experiments, Rayleigh-Taylor experiments, plasma sheet, and interacting jets experiments. This work is funded by the Predictive Sciences Academic Alliances Program in NNSA-ASC via grant DEFC52- 08NA28616, by the NNSA-DS and SC-OFES Joint Program in High-Energy-Density Laboratory Plasmas, grant number DE-FG52-09NA29548, and by the National Laser User Facility Program, grant number DE-NA0000850.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25962472','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25962472"><span>Implementation of extended <span class="hlt">Lagrangian</span> dynamics in GROMACS for polarizable simulations using the classical Drude oscillator model.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Lemkul, Justin A; Roux, Benoît; van der Spoel, David; MacKerell, Alexander D</p> <p>2015-07-15</p> <p>Explicit treatment of electronic polarization in empirical force fields used for molecular dynamics simulations represents an important advancement in simulation methodology. A straightforward means of treating electronic polarization in these simulations is the inclusion of Drude oscillators, which are auxiliary, charge-carrying particles bonded to the cores of atoms in the system. The additional degrees of freedom make these simulations more computationally expensive relative to simulations using traditional fixed-charge (additive) force fields. Thus, efficient tools are needed for conducting these simulations. Here, we present the implementation of highly scalable algorithms in the GROMACS simulation package that allow for the simulation of polarizable systems using extended <span class="hlt">Lagrangian</span> dynamics with a dual Nosé-Hoover thermostat as well as simulations using a full self-consistent field treatment of polarization. The performance of systems of varying size is evaluated, showing that the present <span class="hlt">code</span> parallelizes efficiently and is the fastest implementation of the extended <span class="hlt">Lagrangian</span> methods currently available for simulations using the Drude polarizable force field. © 2015 Wiley Periodicals, Inc.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhyD..372...31B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhyD..372...31B"><span>Generalized <span class="hlt">Lagrangian</span> coherent structures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Balasuriya, Sanjeeva; Ouellette, Nicholas T.; Rypina, Irina I.</p> <p>2018-06-01</p> <p>The notion of a <span class="hlt">Lagrangian</span> Coherent Structure (LCS) is by now well established as a way to capture transient coherent transport dynamics in unsteady and aperiodic fluid flows that are known over finite time. We show that the concept of an LCS can be generalized to capture coherence in other quantities of interest that are transported by, but not fully locked to, the fluid. Such quantities include those with dynamic, biological, chemical, or thermodynamic relevance, such as temperature, pollutant concentration, vorticity, kinetic energy, plankton density, and so on. We provide a conceptual framework for identifying the Generalized <span class="hlt">Lagrangian</span> Coherent Structures (GLCSs) associated with such evolving quantities. We show how LCSs can be seen as a special case within this framework, and provide an overarching discussion of various methods for identifying LCSs. The utility of this more general viewpoint is highlighted through a variety of examples. We also show that although LCSs approximate GLCSs in certain limiting situations under restrictive assumptions on how the velocity field affects the additional quantities of interest, LCSs are not in general sufficient to describe their coherent transport.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017ExFl...58...33V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017ExFl...58...33V"><span>Comparative assessment of pressure field reconstructions from particle image velocimetry measurements and <span class="hlt">Lagrangian</span> particle tracking</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>van Gent, P. L.; Michaelis, D.; van Oudheusden, B. W.; Weiss, P.-É.; de Kat, R.; Laskari, A.; Jeon, Y. J.; David, L.; Schanz, D.; Huhn, F.; Gesemann, S.; Novara, M.; McPhaden, C.; Neeteson, N. J.; Rival, D. E.; Schneiders, J. F. G.; Schrijer, F. F. J.</p> <p>2017-04-01</p> <p>A test case for pressure field reconstruction from particle image velocimetry (PIV) and <span class="hlt">Lagrangian</span> particle tracking (LPT) has been developed by constructing a simulated experiment from a zonal detached eddy simulation for an axisymmetric base flow at Mach 0.7. The test case comprises sequences of four subsequent particle images (representing multi-pulse data) as well as continuous time-resolved data which can realistically only be obtained for low-speed flows. Particle images were processed using tomographic PIV processing as well as the LPT algorithm `Shake-The-Box' (STB). Multiple pressure field reconstruction techniques have subsequently been applied to the PIV results (<span class="hlt">Eulerian</span> approach, iterative least-square pseudo-tracking, Taylor's hypothesis approach, and instantaneous Vortex-in-Cell) and LPT results (FlowFit, Vortex-in-Cell-plus, Voronoi-based pressure evaluation, and iterative least-square pseudo-tracking). All methods were able to reconstruct the main features of the instantaneous pressure fields, including methods that reconstruct pressure from a single PIV velocity snapshot. Highly accurate reconstructed pressure fields could be obtained using LPT approaches in combination with more advanced techniques. In general, the use of longer series of time-resolved input data, when available, allows more accurate pressure field reconstruction. Noise in the input data typically reduces the accuracy of the reconstructed pressure fields, but none of the techniques proved to be critically sensitive to the amount of noise added in the present test case.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27575211','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27575211"><span>Influence of compressibility on the <span class="hlt">Lagrangian</span> statistics of vorticity-strain-rate interactions.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Danish, Mohammad; Sinha, Sawan Suman; Srinivasan, Balaji</p> <p>2016-07-01</p> <p>The objective of this study is to investigate the influence of compressibility on <span class="hlt">Lagrangian</span> statistics of vorticity and strain-rate interactions. The <span class="hlt">Lagrangian</span> statistics are extracted from "almost" time-continuous data sets of direct numerical simulations of compressible decaying isotropic turbulence by employing a cubic spline-based <span class="hlt">Lagrangian</span> particle tracker. We study the influence of compressibility on <span class="hlt">Lagrangian</span> statistics of alignment in terms of compressibility parameters-turbulent Mach number, normalized dilatation-rate, and flow topology. In comparison to incompressible turbulence, we observe that the presence of compressibility in a flow field weakens the alignment tendency of vorticity toward the largest strain-rate eigenvector. Based on the <span class="hlt">Lagrangian</span> statistics of alignment conditioned on dilatation and topology, we find that the weakened tendency of alignment observed in compressible turbulence is because of a special group of fluid particles that have an initially negligible dilatation-rate and are associated with stable-focus-stretching topology.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1184028-generalized-extended-lagrangian-born-oppenheimer-molecular-dynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1184028-generalized-extended-lagrangian-born-oppenheimer-molecular-dynamics"><span>Generalized extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Niklasson, Anders M. N.; Cawkwell, Marc J.</p> <p>2014-10-29</p> <p>Extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics based on Kohn-Sham density functional theory is generalized in the limit of vanishing self-consistent field optimization prior to the force evaluations. The equations of motion are derived directly from the extended <span class="hlt">Lagrangian</span> under the condition of an adiabatic separation between the nuclear and the electronic degrees of freedom. We show how this separation is automatically fulfilled and system independent. The generalized equations of motion require only one diagonalization per time step and are applicable to a broader range of materials with improved accuracy and stability compared to previous formulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930039947&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930039947&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing"><span><span class="hlt">Lagrangian</span> solution of supersonic real gas flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Loh, Ching-Yuen; Liou, Meng-Sing</p> <p>1993-01-01</p> <p>The present extention of a <span class="hlt">Lagrangian</span> approach of the Riemann solution procedure, which was originally proposed for perfect gases, to real gases, is nontrivial and requires the development of an exact real-gas Riemann solver for the <span class="hlt">Lagrangian</span> form of the conservation laws. Calculations including complex wave interactions of various types were conducted to test the accuracy and robustness of the approach. Attention is given to the case of 2D oblique waves' capture, where a slip line is clearly in evidence; the real gas effect is demonstrated in the case of a generic engine nozzle.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1248278','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1248278"><span>Developing a Learning Algorithm-Generated Empirical Relaxer</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Mitchell, Wayne; Kallman, Josh; Toreja, Allen</p> <p>2016-03-30</p> <p>One of the main difficulties when running Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) simulations is determining how much to relax the mesh during the <span class="hlt">Eulerian</span> step. This determination is currently made by the user on a simulation-by-simulation basis. We present a Learning Algorithm-Generated Empirical Relaxer (LAGER) which uses a regressive random forest algorithm to automate this decision process. We also demonstrate that LAGER successfully relaxes a variety of test problems, maintains simulation accuracy, and has the potential to significantly decrease both the person-hours and computational hours needed to run a successful ALE simulation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26274277','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26274277"><span>Intermittent <span class="hlt">Lagrangian</span> velocities and accelerations in three-dimensional porous medium flow.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Holzner, M; Morales, V L; Willmann, M; Dentz, M</p> <p>2015-07-01</p> <p>Intermittency of <span class="hlt">Lagrangian</span> velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on <span class="hlt">Lagrangian</span> velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential <span class="hlt">Lagrangian</span> velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed <span class="hlt">Lagrangian</span> flow and transport behaviors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013APS..MAR.V1290M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013APS..MAR.V1290M"><span><span class="hlt">Lagrangian</span> Approach to Study Catalytic Fluidized Bed Reactors</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Madi, Hossein; Hossein Madi Team; Marcelo Kaufman Rechulski Collaboration; Christian Ludwig Collaboration; Tilman Schildhauer Collaboration</p> <p>2013-03-01</p> <p><span class="hlt">Lagrangian</span> approach of fluidized bed reactors is a method, which simulates the movement of catalyst particles (caused by the fluidization) by changing the gas composition around them. Application of such an investigation is in the analysis of the state of catalysts and surface reactions under quasi-operando conditions. The hydrodynamics of catalyst particles within a fluidized bed reactor was studied to improve a <span class="hlt">Lagrangian</span> approach. A fluidized bed methanation employed in the production of Synthetic Natural Gas from wood was chosen as the case study. The <span class="hlt">Lagrangian</span> perspective was modified and improved to include different particle circulation patterns, which were investigated through this study. Experiments were designed to evaluate the concepts of the model. The results indicate that the setup is able to perform the designed experiments and a good agreement between the simulation and the experimental results were observed. It has been shown that fluidized bed reactors, as opposed to fixed beds, can be used to avoid the deactivation of the methanation catalyst due to carbon deposits. Carbon deposition on the catalysts tested with the <span class="hlt">Lagrangian</span> approach was investigated by temperature programmed oxidation (TPO) analysis of ex-situ catalyst samples. This investigation was done to identify the effects of particles velocity and their circulation patterns on the amount and type of deposited carbon on the catalyst surface. Ecole Polytechnique Federale de Lausanne(EPFL), Paul Scherrer Institute (PSI)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21517594','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21517594"><span><span class="hlt">Lagrangian</span> statistics and flow topology in forced two-dimensional turbulence.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kadoch, B; Del-Castillo-Negrete, D; Bos, W J T; Schneider, K</p> <p>2011-03-01</p> <p>A study of the relationship between <span class="hlt">Lagrangian</span> statistics and flow topology in fluid turbulence is presented. The topology is characterized using the Weiss criterion, which provides a conceptually simple tool to partition the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background). The flow corresponds to forced two-dimensional Navier-Stokes turbulence in doubly periodic and circular bounded domains, the latter with no-slip boundary conditions. In the double periodic domain, the probability density function (pdf) of the Weiss field exhibits a negative skewness consistent with the fact that in periodic domains the flow is dominated by coherent vortex structures. On the other hand, in the circular domain, the elliptic and hyperbolic regions seem to be statistically similar. We follow a <span class="hlt">Lagrangian</span> approach and obtain the statistics by tracking large ensembles of passively advected tracers. The pdfs of residence time in the topologically different regions are computed introducing the <span class="hlt">Lagrangian</span> Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf has exponential decaying tails. The conditional pdfs (with respect to the flow topology) of the <span class="hlt">Lagrangian</span> velocity exhibit Gaussian-like behavior in the periodic and in the bounded domains. In contrast to the freely decaying turbulence case, the conditional pdfs of the <span class="hlt">Lagrangian</span> acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the <span class="hlt">Lagrangian</span> curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order -2.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JGP....60..857V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JGP....60..857V"><span>The <span class="hlt">Lagrangian</span>-Hamiltonian formalism for higher order field theories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vitagliano, Luca</p> <p>2010-06-01</p> <p>We generalize the <span class="hlt">Lagrangian</span>-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order <span class="hlt">Lagrangian</span> field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011JPhA...44L5203P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011JPhA...44L5203P"><span><span class="hlt">Lagrangian</span>-Hamiltonian unified formalism for autonomous higher order dynamical systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso</p> <p>2011-09-01</p> <p>The <span class="hlt">Lagrangian</span>-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the <span class="hlt">Lagrangian</span> and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the <span class="hlt">Lagrangian</span>-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li class="active"><span>22</span></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_22 --> <div id="page_23" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li class="active"><span>23</span></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="441"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1088058','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1088058"><span>Penetration of rod projectiles in semi-infinite targets : a validation test for <span class="hlt">Eulerian</span> X-FEM in ALEGRA.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Park, Byoung Yoon; Leavy, Richard Brian; Niederhaus, John Henry J.</p> <p>2013-03-01</p> <p>The finite-element shock hydrodynamics <span class="hlt">code</span> ALEGRA has recently been upgraded to include an X-FEM implementation in 2D for simulating impact, sliding, and release between materials in the <span class="hlt">Eulerian</span> frame. For validation testing purposes, the problem of long-rod penetration in semi-infinite targets is considered in this report, at velocities of 500 to 3000 m/s. We describe testing simulations done using ALEGRA with and without the X-FEM capability, in order to verify its adequacy by showing X-FEM recovers the good results found with the standard ALEGRA formulation. The X-FEM results for depth of penetration differ from previously measured experimental data by lessmore » than 2%, and from the standard formulation results by less than 1%. They converge monotonically under mesh refinement at first order. Sensitivities to domain size and rear boundary condition are investigated and shown to be small. Aside from some simulation stability issues, X-FEM is found to produce good results for this classical impact and penetration problem.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22489841-lagrangian-hamiltonian-constraints-guiding-center-hamiltonian-theories','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22489841-lagrangian-hamiltonian-constraints-guiding-center-hamiltonian-theories"><span><span class="hlt">Lagrangian</span> and Hamiltonian constraints for guiding-center Hamiltonian theories</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Tronko, Natalia; Brizard, Alain J.</p> <p></p> <p>A consistent guiding-center Hamiltonian theory is derived by Lie-transform perturbation method, with terms up to second order in magnetic-field nonuniformity. Consistency is demonstrated by showing that the guiding-center transformation presented here satisfies separate Jacobian and <span class="hlt">Lagrangian</span> constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space <span class="hlt">Lagrangian</span> is identified through a calculation of the guiding-center polarization. It is shown that this new polarization term also yields a simpler expression of the guiding-center toroidal canonical momentum, which satisfies an exact conservation law in axisymmetric magnetic geometries. Finally, an application of the guiding-center <span class="hlt">Lagrangian</span> constraint onmore » the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26328583','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26328583"><span>Dissipative inertial transport patterns near coherent <span class="hlt">Lagrangian</span> eddies in the ocean.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan</p> <p>2015-08-01</p> <p>Recent developments in dynamical systems theory have revealed long-lived and coherent <span class="hlt">Lagrangian</span> (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent <span class="hlt">Lagrangian</span> eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size finiteness of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent <span class="hlt">Lagrangian</span> eddies attract (repel) negatively (positively) buoyant finite-size particles, while cyclonic coherent <span class="hlt">Lagrangian</span> eddies attract (repel) positively (negatively) buoyant finite-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=150744&keyword=510&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=150744&keyword=510&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>PREFACE SPECIAL ISSUE ON MODEL EVALUATION: EVALUATION OF URBAN AND REGIONAL <span class="hlt">EULERIAN</span> AIR QUALITY MODELS</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>The "Preface to the Special Edition on Model Evaluation: Evaluation of Urban and Regional <span class="hlt">Eulerian</span> Air Quality Models" is a brief introduction to the papers included in a special issue of Atmospheric Environment. The Preface provides a background for the papers, which have thei...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1919023P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1919023P"><span><span class="hlt">Lagrangian</span> Observations and Modeling of Marine Larvae</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Paris, Claire B.; Irisson, Jean-Olivier</p> <p>2017-04-01</p> <p>Just within the past two decades, studies on the early-life history stages of marine organisms have led to new paradigms in population dynamics. Unlike passive plant seeds that are transported by the wind or by animals, marine larvae have motor and sensory capabilities. As a result, marine larvae have a tremendous capacity to actively influence their dispersal. This is continuously revealed as we develop new techniques to observe larvae in their natural environment and begin to understand their ability to detect cues throughout ontogeny, process the information, and use it to ride ocean currents and navigate their way back home, or to a place like home. We present innovative in situ and numerical modeling approaches developed to understand the underlying mechanisms of larval transport in the ocean. We describe a novel concept of a <span class="hlt">Lagrangian</span> platform, the Drifting In Situ Chamber (DISC), designed to observe and quantify complex larval behaviors and their interactions with the pelagic environment. We give a brief history of larval ecology research with the DISC, showing that swimming is directional in most species, guided by cues as diverse as the position of the sun or the underwater soundscape, and even that (unlike humans!) larvae orient better and swim faster when moving as a group. The observed <span class="hlt">Lagrangian</span> behavior of individual larvae are directly implemented in the Connectivity Modeling System (CMS), an open source <span class="hlt">Lagrangian</span> tracking application. Simulations help demonstrate the impact that larval behavior has compared to passive <span class="hlt">Lagrangian</span> trajectories. These methodologies are already the base of exciting findings and are promising tools for documenting and simulating the behavior of other small pelagic organisms, forecasting their migration in a changing ocean.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5774699','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5774699"><span>A generic framework for individual-based modelling and physical-biological interaction</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p></p> <p>2018-01-01</p> <p>The increased availability of high-resolution ocean data globally has enabled more detailed analyses of physical-biological interactions and their consequences to the ecosystem. We present IBMlib, which is a versatile, portable and computationally effective framework for conducting <span class="hlt">Lagrangian</span> simulations in the marine environment. The purpose of the framework is to handle complex individual-level biological models of organisms, combined with realistic 3D oceanographic model of physics and biogeochemistry describing the environment of the organisms without assumptions about spatial or temporal scales. The open-source framework features a minimal robust interface to facilitate the coupling between individual-level biological models and oceanographic models, and we provide application examples including forward/backward simulations, habitat connectivity calculations, assessing ocean conditions, comparison of physical circulation models, model ensemble runs and recently posterior <span class="hlt">Eulerian</span> simulations using the IBMlib framework. We present the <span class="hlt">code</span> design ideas behind the longevity of the <span class="hlt">code</span>, our implementation experiences, as well as <span class="hlt">code</span> performance benchmarking. The framework may contribute substantially to progresses in representing, understanding, predicting and eventually managing marine ecosystems. PMID:29351280</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1424084-toroidal-regularization-guiding-center-lagrangian','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1424084-toroidal-regularization-guiding-center-lagrangian"><span>Toroidal regularization of the guiding center <span class="hlt">Lagrangian</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Burby, J. W.; Ellison, C. L.</p> <p>2017-11-22</p> <p>In the <span class="hlt">Lagrangian</span> theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the <span class="hlt">Lagrangian</span> guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center <span class="hlt">Lagrangian</span> by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1424084-toroidal-regularization-guiding-center-lagrangian','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1424084-toroidal-regularization-guiding-center-lagrangian"><span>Toroidal regularization of the guiding center <span class="hlt">Lagrangian</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Burby, J. W.; Ellison, C. L.</p> <p></p> <p>In the <span class="hlt">Lagrangian</span> theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the <span class="hlt">Lagrangian</span> guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center <span class="hlt">Lagrangian</span> by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20100039430','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20100039430"><span>Ignition-and-Growth Modeling of NASA Standard Detonator and a Linear Shaped Charge</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Oguz, Sirri</p> <p>2010-01-01</p> <p>The main objective of this study is to quantitatively investigate the ignition and shock sensitivity of NASA Standard Detonator (NSD) and the shock wave propagation of a linear shaped charge (LSC) after being shocked by NSD flyer plate. This combined explosive train was modeled as a coupled Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) model with LS-DYNA hydro <span class="hlt">code</span>. An ignition-and-growth (I&G) reactive model based on unreacted and reacted Jones-Wilkins-Lee (JWL) equations of state was used to simulate the shock initiation. Various NSD-to-LSC stand-off distances were analyzed to calculate the shock initiation (or failure to initiate) and detonation wave propagation along the shaped charge. Simulation results were verified by experimental data which included VISAR tests for NSD flyer plate velocity measurement and an aluminum target severance test for LSC performance verification. Parameters used for the analysis were obtained from various published data or by using CHEETAH thermo-chemical <span class="hlt">code</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1296691','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1296691"><span>Analysis of xRAGE and flag high explosive burn models with PBX 9404 cylinder tests</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Harrier, Danielle; Andersen, Kyle Richard</p> <p></p> <p>High explosives are energetic materials that release their chemical energy in a short interval of time. They are able to generate extreme heat and pressure by a shock driven chemical decomposition reaction, which makes them valuable tools that must be understood. This study investigated the accuracy and performance of two Los Alamos National Laboratory hydrodynamic <span class="hlt">codes</span>, which are used to determine the behavior of explosives within a variety of systems: xRAGE which utilizes an <span class="hlt">Eulerian</span> mesh, and FLAG with utilizes a <span class="hlt">Lagrangian</span> mesh. Various programmed and reactive burn models within both <span class="hlt">codes</span> were tested using a copper cylinder expansion test.more » The test was based on a recent experimental setup which contained the plastic bonded explosive PBX 9404. Detonation velocity versus time curves for this explosive were obtained using Photon Doppler Velocimetry (PDV). The modeled results from each of the burn models tested were then compared to one another and to the experimental results. This study validate« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/92060','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/92060"><span>Murt user`s guide: A hybrid <span class="hlt">Lagrangian-Eulerian</span> finite element model of multiple-pore-region solute transport through subsurface media</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Gwo, J.P.; Jardine, P.M.; Yeh, G.T.</p> <p></p> <p>Matrix diffusion, a diffusive mass transfer process,in the structured soils and geologic units at ORNL, is believe to be an important subsurface mass transfer mechanism; it may affect off-site movement of radioactive wastes and remediation of waste disposal sites by locally exchanging wastes between soil/rock matrix and macropores/fractures. Advective mass transfer also contributes to waste movement but is largely neglected by researchers. This report presents the first documented 2-D multiregion solute transport <span class="hlt">code</span> (MURT) that incorporates not only diffusive but also advective mass transfer and can be applied to heterogeneous porous media under transient flow conditions. In this report, theoreticalmore » background is reviewed and the derivation of multiregion solute transport equations is presented. Similar to MURF (Gwo et al. 1994), a multiregion subsurface flow <span class="hlt">code</span>, multiplepore domains as suggested by previous investigators (eg, Wilson and Luxmoore 1988) can be implemented in MURT. Transient or steady-state flow fields of the pore domains can be either calculated by MURF or by modelers. The mass transfer process is briefly discussed through a three-pore-region multiregion solute transport mechanism. Mass transfer equations that describe mass flux across pore region interfaces are also presented and parameters needed to calculate mass transfer coefficients detailed. Three applications of MURT (tracer injection problem, sensitivity analysis of advective and diffusive mass transfer, hillslope ponding infiltration and secondary source problem) were simulated and results discussed. Program structure of MURT and functions of MURT subroutiness are discussed so that users can adapt the <span class="hlt">code</span>; guides for input data preparation are provided in appendices.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=75840&keyword=API&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=75840&keyword=API&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>DESCRIPTION OF ATMOSPHERIC TRANSPORT PROCESSES IN <span class="hlt">EULERIAN</span> AIR QUALITY MODELS</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>Key differences among many types of air quality models are the way atmospheric advection and turbulent diffusion processes are treated. Gaussian models use analytical solutions of the advection-diffusion equations. <span class="hlt">Lagrangian</span> models use a hypothetical air parcel concept effecti...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27415358','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27415358"><span>Spectral-clustering approach to <span class="hlt">Lagrangian</span> vortex detection.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George</p> <p>2016-06-01</p> <p>One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of <span class="hlt">Lagrangian</span> trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent <span class="hlt">Lagrangian</span> vortices in several two- and three-dimensional flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA495081','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA495081"><span>Heterogeneous Teams of Autonomous Vehicles: Advanced Sensing & Control</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2009-03-01</p> <p>Final Technical 3. DATES COVERED (From To) 7/1/05-12/31708 4. TITLE AND SUBTITLE Heterogeneous Teams of Autonomous Vehicles Advanced Sensing...assimilating data from underwater and surface autonomous vehicles in addition to the usual sources of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> systems into a small scale</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22661056-tea-code-calculating-thermochemical-equilibrium-abundances','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22661056-tea-code-calculating-thermochemical-equilibrium-abundances"><span>TEA: A <span class="hlt">CODE</span> CALCULATING THERMOCHEMICAL EQUILIBRIUM ABUNDANCES</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver, E-mail: jasmina@physics.ucf.edu</p> <p>2016-07-01</p> <p>We present an open-source Thermochemical Equilibrium Abundances (TEA) <span class="hlt">code</span> that calculates the abundances of gaseous molecular species. The <span class="hlt">code</span> is based on the methodology of White et al. and Eriksson. It applies Gibbs free-energy minimization using an iterative, <span class="hlt">Lagrangian</span> optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature–pressure pairs. We tested the <span class="hlt">code</span> against the method of Burrows and Sharp, the free thermochemical equilibrium <span class="hlt">code</span> Chemical Equilibrium with Applications (CEA), and the example given by Burrows and Sharp. Using their thermodynamic data, TEA reproduces their final abundances, but withmore » higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a <span class="hlt">code</span> document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...10..106B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...10..106B"><span><span class="hlt">Lagrangians</span> for generalized Argyres-Douglas theories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Benvenuti, Sergio; Giacomelli, Simone</p> <p>2017-10-01</p> <p>We continue the study of <span class="hlt">Lagrangian</span> descriptions of N=2 Argyres-Douglas theories. We use our recent interpretation in terms of sequential confinement to guess the <span class="hlt">Lagrangians</span> of all the Argyres-Douglas models with Abelian three dimensional mirror. We find classes of four dimensional N=1 quivers that flow in the infrared to generalized Argyres-Douglas theories, such as the ( A k , A kN + N -1) models. We study in detail how the N=1 chiral rings map to the Coulomb and Higgs Branches of the N=2 CFT's. The three dimensional mirror RG flows are shown to land on the N=4 complete graph quivers. We also compactify to three dimensions the gauge theory dual to ( A 1, D 4), and find the expected Abelianization duality with N=4 SQED with 3 flavors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/16860933','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/16860933"><span>Performance estimation of a Venturi scrubber using a computational model for capturing dust particles with liquid spray.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Pak, S I; Chang, K S</p> <p>2006-12-01</p> <p>A Venturi scrubber has dispersed three-phase flow of gas, dust, and liquid. Atomization of a liquid jet and interaction between the phases has a large effect on the performance of Venturi scrubbers. In this study, a computational model for the interactive three-phase flow in a Venturi scrubber has been developed to estimate pressure drop and collection efficiency. The <span class="hlt">Eulerian-Lagrangian</span> method is used to solve the model numerically. Gas flow is solved using the <span class="hlt">Eulerian</span> approach by using the Navier-Stokes equations, and the motion of dust and liquid droplets, described by the Basset-Boussinesq-Oseen (B-B-O) equation, is solved using the <span class="hlt">Lagrangian</span> approach. This model includes interaction between gas and droplets, atomization of a liquid jet, droplet deformation, breakup and collision of droplets, and capture of dust by droplets. A circular Pease-Anthony Venturi scrubber was simulated numerically with this new model. The numerical results were compared with earlier experimental data for pressure drop and collection efficiency, and gave good agreements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26861803','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26861803"><span>Computing the stresses and deformations of the human eye components due to a high explosive detonation using fluid-structure interaction model.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Karimi, Alireza; Razaghi, Reza; Navidbakhsh, Mahdi; Sera, Toshihiro; Kudo, Susumu</p> <p>2016-05-01</p> <p>In spite the fact that a very small human body surface area is comprised by the eye, its wounds due to detonation have recently been dramatically amplified. Although many efforts have been devoted to measure injury of the globe, there is still a lack of knowledge on the injury mechanism due to Primary Blast Wave (PBW). The goal of this study was to determine the stresses and deformations of the human eye components, including the cornea, aqueous, iris, ciliary body, lens, vitreous, retina, sclera, optic nerve, and muscles, attributed to PBW induced by trinitrotoluene (TNT) explosion via a <span class="hlt">Lagrangian-Eulerian</span> computational coupling model. Magnetic Resonance Imaging (MRI) was employed to establish a Finite Element (FE) model of the human eye according to a normal human eye. The solid components of the eye were modelled as <span class="hlt">Lagrangian</span> mesh, while an explosive TNT, air domain, and aqueous were modelled using Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) mesh. Nonlinear dynamic FE simulations were accomplished using the explicit FE <span class="hlt">code</span>, namely LS-DYNA. In order to simulate the blast wave generation, propagation, and interaction with the eye, the ALE formulation with Jones-Wilkins-Lee (JWL) equation defining the explosive material were employed. The results revealed a peak stress of 135.70kPa brought about by detonation upsurge on the cornea at the distance of 25cm. The highest von Mises stresses were observed on the sclera (267.3kPa), whereas the lowest one was seen on the vitreous body (0.002kPa). The results also showed a relatively high resultant displacement for the macula as well as a high variation for the radius of curvature for the cornea and lens, which can result in both macular holes, optic nerve damage and, consequently, vision loss. These results may have implications not only for understanding the value of stresses and strains in the human eye components but also giving an outlook about the process of PBW triggers damage to the eye. Copyright © 2016 Elsevier Ltd</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040086560','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040086560"><span><span class="hlt">Lagrangian</span> Assimilation of Satellite Data for Climate Studies in the Arctic</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lindsay, Ronald W.; Zhang, Jin-Lun; Stern, Harry</p> <p>2004-01-01</p> <p>Under this grant we have developed and tested a new <span class="hlt">Lagrangian</span> model of sea ice. A <span class="hlt">Lagrangian</span> model keeps track of material parcels as they drift in the model domain. Besides providing a natural framework for the assimilation of <span class="hlt">Lagrangian</span> data, it has other advantages: 1) a model that follows material elements is well suited for a medium such as sea ice in which an element retains its identity for a long period of time; 2) model cells can be added or dropped as needed, allowing the spatial resolution to be increased in areas of high variability or dense observations; 3) ice from particular regions, such as the marginal seas, can be marked and traced for a long time; and 4) slip lines in the ice motion are accommodated more naturally because there is no internal grid. Our work makes use of these strengths of the <span class="hlt">Lagrangian</span> formulation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017WRR....5310411D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017WRR....5310411D"><span>Elimination of the Reaction Rate "Scale Effect": Application of the <span class="hlt">Lagrangian</span> Reactive Particle-Tracking Method to Simulate Mixing-Limited, Field-Scale Biodegradation at the Schoolcraft (MI, USA) Site</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ding, Dong; Benson, David A.; Fernández-Garcia, Daniel; Henri, Christopher V.; Hyndman, David W.; Phanikumar, Mantha S.; Bolster, Diogo</p> <p>2017-12-01</p> <p>Measured (or empirically fitted) reaction rates at groundwater remediation sites are typically much lower than those found in the same material at the batch or laboratory scale. The reduced rates are commonly attributed to poorer mixing at the larger scales. A variety of methods have been proposed to account for this scaling effect in reactive transport. In this study, we use the <span class="hlt">Lagrangian</span> particle-tracking and reaction (PTR) method to simulate a field bioremediation experiment at the Schoolcraft, MI site. A denitrifying bacterium, Pseudomonas Stutzeri strain KC (KC), was injected to the aquifer, along with sufficient substrate, to degrade the contaminant, carbon tetrachloride (CT), under anaerobic conditions. The PTR method simulates chemical reactions through probabilistic rules of particle collisions, interactions, and transformations to address the scale effect (lower apparent reaction rates for each level of upscaling, from batch to column to field scale). In contrast to a prior <span class="hlt">Eulerian</span> reaction model, the PTR method is able to match the field-scale experiment using the rate coefficients obtained from batch experiments.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li class="active"><span>23</span></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_23 --> <div id="page_24" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li class="active"><span>24</span></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="461"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=thought+AND+experiments&pg=2&id=EJ912884','ERIC'); return false;" href="https://eric.ed.gov/?q=thought+AND+experiments&pg=2&id=EJ912884"><span>Gravity, Time, and <span class="hlt">Lagrangians</span></span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Huggins, Elisha</p> <p>2010-01-01</p> <p>Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the <span class="hlt">Lagrangian</span>. (Why would one…</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017NPGeo..24..379C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017NPGeo..24..379C"><span>Insights into the three-dimensional <span class="hlt">Lagrangian</span> geometry of the Antarctic polar vortex</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Curbelo, Jezabel; José García-Garrido, Víctor; Mechoso, Carlos Roberto; Mancho, Ana Maria; Wiggins, Stephen; Niang, Coumba</p> <p>2017-07-01</p> <p>In this paper we study the three-dimensional (3-D) <span class="hlt">Lagrangian</span> structures in the stratospheric polar vortex (SPV) above Antarctica. We analyse and visualize these structures using <span class="hlt">Lagrangian</span> descriptor function M. The procedure for calculation with reanalysis data is explained. Benchmarks are computed and analysed that allow us to compare 2-D and 3-D aspects of <span class="hlt">Lagrangian</span> transport. Dynamical systems concepts appropriate to 3-D, such as normally hyperbolic invariant curves, are discussed and applied. In order to illustrate our approach we select an interval of time in which the SPV is relatively undisturbed (August 1979) and an interval of rapid SPV changes (October 1979). Our results provide new insights into the <span class="hlt">Lagrangian</span> structure of the vertical extension of the stratospheric polar vortex and its evolution. Our results also show complex <span class="hlt">Lagrangian</span> patterns indicative of strong mixing processes in the upper troposphere and lower stratosphere. Finally, during the transition to summer in the late spring, we illustrate the vertical structure of two counterrotating vortices, one the polar and the other an emerging one, and the invariant separatrix that divides them.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CorRe..34..339K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CorRe..34..339K"><span>Environmental and ecological controls of coral community metabolism on Palmyra Atoll</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Koweek, David; Dunbar, Robert B.; Rogers, Justin S.; Williams, Gareth J.; Price, Nichole; Mucciarone, David; Teneva, Lida</p> <p>2015-03-01</p> <p>Accurate predictions of how coral reefs may respond to global climate change hinge on understanding the natural variability to which these ecosystems are exposed and to which they contribute. We present high-resolution estimates of net community calcification (NCC) and net community production (NCP) from Palmyra Atoll, an uninhabited, near-pristine coral reef ecosystem in the central Pacific. In August-October 2012, we employed a combination of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> frameworks to establish high spatial (~2.5 km2) and temporal (hourly) resolution coral community metabolic estimates. <span class="hlt">Lagrangian</span> drifts, all conducted during daylight hours, resulted in NCC estimates of -51 to 116 mmol C m-2 h-1, although most NCC estimates were in the range of 0-40 mmol C m-2 h-1. <span class="hlt">Lagrangian</span> drift NCP estimates ranged from -7 to 67 mmol C m-2 h-1. In the <span class="hlt">Eulerian</span> setup, we present carbonate system parameters (dissolved inorganic carbon, total alkalinity, pH, and pCO2) at sub-hourly resolution through several day-night cycles and provide hourly NCC and NCP rate estimates. We compared diel cycles of all four carbonate system parameters to the offshore surface water (0-50 m depth) and show large departures from offshore surface water chemistry. Hourly <span class="hlt">Eulerian</span> estimates of NCC aggregated over the entire study ranged from 14 to 53 mmol C m-2 h-1, showed substantial variability during daylight hours, and exhibited a diel cycle with elevated NCC in the afternoons and depressed, but positive, NCC at night. The <span class="hlt">Eulerian</span> NCP range was very high (-55 to 177 mmol C m-2 h-1) and exhibited strong variability during daylight hours. Principal components analysis revealed that NCC and NCP were most closely aligned with diel cycle forcing, whereas the NCC/NCP ratio was most closely aligned with reef community composition. Our analysis demonstrates that ecological community composition is the primary determinant of coral reef biogeochemistry on a near-pristine reef and that reef biogeochemistry is</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70025921','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70025921"><span>A finite-volume ELLAM for three-dimensional solute-transport modeling</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Russell, T.F.; Heberton, C.I.; Konikow, Leonard F.; Hornberger, G.Z.</p> <p>2003-01-01</p> <p>A three-dimensional finite-volume ELLAM method has been developed, tested, and successfully implemented as part of the U.S. Geological Survey (USGS) MODFLOW-2000 ground water modeling package. It is included as a solver option for the Ground Water Transport process. The FVELLAM uses space-time finite volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of <span class="hlt">Eulerian-Lagrangian</span> characteristic methods. The USGS FVELLAM <span class="hlt">code</span> simulates solute transport in flowing ground water for a single dissolved solute constituent and represents the processes of advective transport, hydrodynamic dispersion, mixing from fluid sources, retardation, and decay. Implicit time discretization of the dispersive and source/sink terms is combined with a <span class="hlt">Lagrangian</span> treatment of advection, in which forward tracking moves mass to the new time level, distributing mass among destination cells using approximate indicator functions. This allows the use of large transport time increments (large Courant numbers) with accurate results, even for advection-dominated systems (large Peclet numbers). Four test cases, including comparisons with analytical solutions and benchmarking against other numerical <span class="hlt">codes</span>, are presented that indicate that the FVELLAM can usually yield excellent results, even if relatively few transport time steps are used, although the quality of the results is problem-dependent.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22107674-stochastic-lagrangian-dynamics-charged-flows-regions-ionosphere','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22107674-stochastic-lagrangian-dynamics-charged-flows-regions-ionosphere"><span>Stochastic <span class="hlt">Lagrangian</span> dynamics for charged flows in the E-F regions of ionosphere</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Tang Wenbo; Mahalov, Alex</p> <p>2013-03-15</p> <p>We develop a three-dimensional numerical model for the E-F region ionosphere and study the <span class="hlt">Lagrangian</span> dynamics for plasma flows in this region. Our interest rests on the charge-neutral interactions and the statistics associated with stochastic <span class="hlt">Lagrangian</span> motion. In particular, we examine the organizing mixing patterns for plasma flows due to polarized gravity wave excitations in the neutral field, using <span class="hlt">Lagrangian</span> coherent structures (LCS). LCS objectively depict the flow topology-the extracted attractors indicate generation of ionospheric density gradients, due to accumulation of plasma. Using <span class="hlt">Lagrangian</span> measures such as the finite-time Lyapunov exponents, we locate the <span class="hlt">Lagrangian</span> skeletons for mixing in plasma,more » hence where charged fronts are expected to appear. With polarized neutral wind, we find that the corresponding plasma velocity is also polarized. Moreover, the polarized velocity alone, coupled with stochastic <span class="hlt">Lagrangian</span> motion, may give rise to polarized density fronts in plasma. Statistics of these trajectories indicate high level of non-Gaussianity. This includes clear signatures of variance, skewness, and kurtosis of displacements taking polarized structures aligned with the gravity waves, and being anisotropic.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4351671','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4351671"><span>Techniques to derive geometries for image-based <span class="hlt">Eulerian</span> computations</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Dillard, Seth; Buchholz, James; Vigmostad, Sarah; Kim, Hyunggun; Udaykumar, H.S.</p> <p>2014-01-01</p> <p>Purpose The performance of three frequently used level set-based segmentation methods is examined for the purpose of defining features and boundary conditions for image-based <span class="hlt">Eulerian</span> fluid and solid mechanics models. The focus of the evaluation is to identify an approach that produces the best geometric representation from a computational fluid/solid modeling point of view. In particular, extraction of geometries from a wide variety of imaging modalities and noise intensities, to supply to an immersed boundary approach, is targeted. Design/methodology/approach Two- and three-dimensional images, acquired from optical, X-ray CT, and ultrasound imaging modalities, are segmented with active contours, k-means, and adaptive clustering methods. Segmentation contours are converted to level sets and smoothed as necessary for use in fluid/solid simulations. Results produced by the three approaches are compared visually and with contrast ratio, signal-to-noise ratio, and contrast-to-noise ratio measures. Findings While the active contours method possesses built-in smoothing and regularization and produces continuous contours, the clustering methods (k-means and adaptive clustering) produce discrete (pixelated) contours that require smoothing using speckle-reducing anisotropic diffusion (SRAD). Thus, for images with high contrast and low to moderate noise, active contours are generally preferable. However, adaptive clustering is found to be far superior to the other two methods for images possessing high levels of noise and global intensity variations, due to its more sophisticated use of local pixel/voxel intensity statistics. Originality/value It is often difficult to know a priori which segmentation will perform best for a given image type, particularly when geometric modeling is the ultimate goal. This work offers insight to the algorithm selection process, as well as outlining a practical framework for generating useful geometric surfaces in an <span class="hlt">Eulerian</span> setting. PMID</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.355..492B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.355..492B"><span>Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE scheme</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Burton, D. E.; Morgan, N. R.; Charest, M. R. J.; Kenamond, M. A.; Fung, J.</p> <p>2018-02-01</p> <p>From the very origins of numerical hydrodynamics in the <span class="hlt">Lagrangian</span> work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, <span class="hlt">Lagrangian</span> schemes have evolved into Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methods [39] that combine the best properties of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense that it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. In particular, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. The paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24176703','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24176703"><span>Evaluation of wastewater contaminant transport in surface waters using verified <span class="hlt">Lagrangian</span> sampling.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Antweiler, Ronald C; Writer, Jeffrey H; Murphy, Sheila F</p> <p>2014-02-01</p> <p>Contaminants released from wastewater treatment plants can persist in surface waters for substantial distances. Much research has gone into evaluating the fate and transport of these contaminants, but this work has often assumed constant flow from wastewater treatment plants. However, effluent discharge commonly varies widely over a 24-hour period, and this variation controls contaminant loading and can profoundly influence interpretations of environmental data. We show that methodologies relying on the normalization of downstream data to conservative elements can give spurious results, and should not be used unless it can be verified that the same parcel of water was sampled. <span class="hlt">Lagrangian</span> sampling, which in theory samples the same water parcel as it moves downstream (the <span class="hlt">Lagrangian</span> parcel), links hydrologic and chemical transformation processes so that the in-stream fate of wastewater contaminants can be quantitatively evaluated. However, precise <span class="hlt">Lagrangian</span> sampling is difficult, and small deviations - such as missing the <span class="hlt">Lagrangian</span> parcel by less than 1h - can cause large differences in measured concentrations of all dissolved compounds at downstream sites, leading to erroneous conclusions regarding in-stream processes controlling the fate and transport of wastewater contaminants. Therefore, we have developed a method termed "verified <span class="hlt">Lagrangian</span>" sampling, which can be used to determine if the <span class="hlt">Lagrangian</span> parcel was actually sampled, and if it was not, a means for correcting the data to reflect the concentrations which would have been obtained had the <span class="hlt">Lagrangian</span> parcel been sampled. To apply the method, it is necessary to have concentration data for a number of conservative constituents from the upstream, effluent, and downstream sites, along with upstream and effluent concentrations that are constant over the short-term (typically 2-4h). These corrections can subsequently be applied to all data, including non-conservative constituents. Finally, we show how data</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EGUGA..15.9576D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..15.9576D"><span>Deformation of two-phase aggregates using standard numerical methods</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.</p> <p>2013-04-01</p> <p>Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a <span class="hlt">Lagrangian</span> marker-in-cell technique to represent the deforming fluid. Thanks to it <span class="hlt">Eulerian</span> nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the <span class="hlt">Lagrangian</span> finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to <span class="hlt">Lagrangian</span> finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the <span class="hlt">Eulerian</span> mesh.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28618545','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28618545"><span>Mean-<span class="hlt">Lagrangian</span> formalism and covariance of fluid turbulence.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ariki, Taketo</p> <p>2017-05-01</p> <p>Mean-field-based <span class="hlt">Lagrangian</span> framework is developed for the fluid turbulence theory, which enables physically objective discussions, especially, of the history effect. Mean flow serves as a purely geometrical object of Lie group theory, providing useful operations to measure the objective rate and history integration of the general tensor field. The proposed framework is applied, on the one hand, to one-point closure model, yielding an objective expression of the turbulence viscoelastic effect. Application to two-point closure, on the other hand, is also discussed, where natural extension of known <span class="hlt">Lagrangian</span> correlation is discovered on the basis of an extended covariance group.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014GMDD....7.7619C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014GMDD....7.7619C"><span>Development and evaluation of the Screening Trajectory Ozone Prediction System (STOPS, version 1.0)</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Czader, B. H.; Percell, P.; Byun, D.; Choi, Y.</p> <p>2014-11-01</p> <p>A hybrid <span class="hlt">Lagrangian-Eulerian</span> modeling tool has been developed using the <span class="hlt">Eulerian</span> framework of the Community Multiscale Air Quality (CMAQ) model. It is a moving nest that utilizes saved original CMAQ simulation results to provide boundary conditions, initial conditions, as well as emissions and meteorological parameters necessary for a simulation. Given that these file are available, this tool can run independently from the CMAQ whole domain simulation and it is designed to simulate source - receptor relationship upon changes in emissions. In this tool, the original CMAQ's horizontal domain is reduced to a small sub-domain that follows a trajectory defined by the mean mixed-layer wind. It has the same vertical structure and physical and chemical interactions as CMAQ except advection calculation. The advantage of this tool compared to other <span class="hlt">Lagrangian</span> models is its capability of utilizing realistic boundary conditions that change with space and time as well as detailed chemistry treatment. The correctness of the algorithms and the overall performance was evaluated against CMAQ simulation results. Its performance depends on the atmospheric conditions occurring during the simulation period with the comparisons being most similar to CMAQ results under uniform wind conditions. The mean bias varies between -0.03 and -0.78 and the slope is between 0.99 and 1.01 for different analyzed cases. For complicated meteorological condition, such as wind circulation, the simulated mixing ratios deviate from CMAQ values as a result of <span class="hlt">Lagrangian</span> approach of using mean wind for its movement, but are still close, with the mean varying between 0.07 and -4.29 and slope varying between 0.95 and 1.063 for different analyzed cases. For historical reasons this hybrid <span class="hlt">Lagrangian</span> - <span class="hlt">Eulerian</span> tool is named the Screening Trajectory Ozone Prediction System (STOPS) but its use is not limited to ozone prediction as similarly to CMAQ it can simulate concentrations of many species, including</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015GMD.....8.1383C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015GMD.....8.1383C"><span>Development and evaluation of the Screening Trajectory Ozone Prediction System (STOPS, version 1.0)</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Czader, B. H.; Percell, P.; Byun, D.; Kim, S.; Choi, Y.</p> <p>2015-05-01</p> <p>A hybrid <span class="hlt">Lagrangian-Eulerian</span> based modeling tool has been developed using the <span class="hlt">Eulerian</span> framework of the Community Multiscale Air Quality (CMAQ) model. It is a moving nest that utilizes saved original CMAQ simulation results to provide boundary conditions, initial conditions, as well as emissions and meteorological parameters necessary for a simulation. Given that these files are available, this tool can run independently of the CMAQ whole domain simulation, and it is designed to simulate source-receptor relationships upon changes in emissions. In this tool, the original CMAQ's horizontal domain is reduced to a small sub-domain that follows a trajectory defined by the mean mixed-layer wind. It has the same vertical structure and physical and chemical interactions as CMAQ except advection calculation. The advantage of this tool compared to other <span class="hlt">Lagrangian</span> models is its capability of utilizing realistic boundary conditions that change with space and time as well as detailed chemistry treatment. The correctness of the algorithms and the overall performance was evaluated against CMAQ simulation results. Its performance depends on the atmospheric conditions occurring during the simulation period, with the comparisons being most similar to CMAQ results under uniform wind conditions. The mean bias for surface ozone mixing ratios varies between -0.03 and -0.78 ppbV and the slope is between 0.99 and 1.01 for different analyzed cases. For complicated meteorological conditions, such as wind circulation, the simulated mixing ratios deviate from CMAQ values as a result of the <span class="hlt">Lagrangian</span> approach of using mean wind for its movement, but are still close, with the mean bias for ozone varying between 0.07 and -4.29 ppbV and the slope varying between 0.95 and 1.06 for different analyzed cases. For historical reasons, this hybrid <span class="hlt">Lagrangian-Eulerian</span> based tool is named the Screening Trajectory Ozone Prediction System (STOPS), but its use is not limited to ozone prediction as</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1328855','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1328855"><span>Action principle for Coulomb collisions in plasmas</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Hirvijoki, Eero</p> <p></p> <p>In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural <span class="hlt">Lagrangian</span> exists for the Landau-Fokker-Planck equation, an <span class="hlt">Eulerian</span> variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order <span class="hlt">Lagrangians</span> and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1328855-action-principle-coulomb-collisions-plasmas','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1328855-action-principle-coulomb-collisions-plasmas"><span>Action principle for Coulomb collisions in plasmas</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Hirvijoki, Eero</p> <p>2016-09-14</p> <p>In this study, an action principle for Coulomb collisions in plasmas is proposed. Although no natural <span class="hlt">Lagrangian</span> exists for the Landau-Fokker-Planck equation, an <span class="hlt">Eulerian</span> variational formulation is found considering the system of partial differential equations that couple the distribution function and the Rosenbluth-MacDonald-Judd potentials. Conservation laws are derived after generalizing the energy-momentum stress tensor for second order <span class="hlt">Lagrangians</span> and, in the case of a test-particle population in a given plasma background, the action principle is shown to correspond to the Langevin equation for individual particles.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70014953','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70014953"><span>High-resolution two dimensional advective transport</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Smith, P.E.; Larock, B.E.</p> <p>1989-01-01</p> <p>The paper describes a two-dimensional high-resolution scheme for advective transport that is based on a <span class="hlt">Eulerian-Lagrangian</span> method with a flux limiter. The scheme is applied to the problem of pure-advection of a rotated Gaussian hill and shown to preserve the monotonicity property of the governing conservation law.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29045443','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29045443"><span>A <span class="hlt">Lagrangian</span> meshfree method applied to linear and nonlinear elasticity.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Walker, Wade A</p> <p>2017-01-01</p> <p>The repeated replacement method (RRM) is a <span class="hlt">Lagrangian</span> meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in <span class="hlt">code</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5646830','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5646830"><span>A <span class="hlt">Lagrangian</span> meshfree method applied to linear and nonlinear elasticity</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p></p> <p>2017-01-01</p> <p>The repeated replacement method (RRM) is a <span class="hlt">Lagrangian</span> meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in <span class="hlt">code</span>. PMID:29045443</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.3368D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.3368D"><span>The stochastic dynamics of intermittent porescale particle motion</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dentz, Marco; Morales, Veronica; Puyguiraud, Alexandre; Gouze, Philippe; Willmann, Matthias; Holzner, Markus</p> <p>2017-04-01</p> <p>Numerical and experimental data for porescale particle dynamics show intermittent patterns in <span class="hlt">Lagrangian</span> velocities and accelerations, which manifest in long time intervals of low and short durations of high velocities [1, 2]. This phenomenon is due to the spatial persistence of particle velocities on characteristic heterogeneity length scales. In order to systematically quantify these behaviors and extract the stochastic dynamics of particle motion, we focus on the analysis of <span class="hlt">Lagrangian</span> velocities sampled equidistantly along trajectories [3]. This method removes the intermittency observed under isochrone sampling. The space-<span class="hlt">Lagrangian</span> velocity series can be quantified by a Markov process that is continuous in distance along streamline. It is fully parameterized in terms of the flux-weighted <span class="hlt">Eulerian</span> velocity PDF and the characteristic pore-length. The resulting stochastic particle motion describes a continuous time random walk (CTRW). This approach allows for the process based interpretation of experimental and numerical porescale velocity, acceleration and displacement data. It provides a framework for the characterization and upscaling of particle transport and dispersion from the pore to the Darcy-scale based on the medium geometry and <span class="hlt">Eulerian</span> flow attributes. [1] P. De Anna, T. Le Borgne, M. Dentz, A.M. Tartakovsky, D. Bolster, and P. Davy, "Flow intermittency, dispersion, and correlated continuous time random walks in porous media," Phys. Rev. Lett. 110, 184502 (2013). [2] M. Holzner, V. L. Morales, M. Willmann, and M. Dentz, "Intermittent <span class="hlt">Lagrangian</span> velocities and accelerations in three- dimensional porous medium flow," Phys. Rev. E 92, 013015 (2015). [3] M. Dentz, P. K. Kang, A. Comolli, T. Le Borgne, and D. R. Lester, "Continuous time random walks for the evolution of <span class="hlt">Lagrangian</span> velocities," Phys. Rev. Fluids (2016).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24235888','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24235888"><span>Incomplete augmented <span class="hlt">Lagrangian</span> preconditioner for steady incompressible Navier-Stokes equations.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun</p> <p>2013-01-01</p> <p>An incomplete augmented <span class="hlt">Lagrangian</span> preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented <span class="hlt">Lagrangian</span>-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3819930','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3819930"><span>Incomplete Augmented <span class="hlt">Lagrangian</span> Preconditioner for Steady Incompressible Navier-Stokes Equations</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun</p> <p>2013-01-01</p> <p>An incomplete augmented <span class="hlt">Lagrangian</span> preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented <span class="hlt">Lagrangian</span>-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li class="active"><span>24</span></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_24 --> <div id="page_25" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li class="active"><span>25</span></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="481"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006JFM...551...19C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006JFM...551...19C"><span>A model relating <span class="hlt">Eulerian</span> spatial and temporal velocity correlations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cholemari, Murali R.; Arakeri, Jaywant H.</p> <p>2006-03-01</p> <p>In this paper we propose a model to relate <span class="hlt">Eulerian</span> spatial and temporal velocity autocorrelations in homogeneous, isotropic and stationary turbulence. We model the decorrelation as the eddies of various scales becoming decorrelated. This enables us to connect the spatial and temporal separations required for a certain decorrelation through the ‘eddy scale’. Given either the spatial or the temporal velocity correlation, we obtain the ‘eddy scale’ and the rate at which the decorrelation proceeds. This leads to a spatial separation from the temporal correlation and a temporal separation from the spatial correlation, at any given value of the correlation relating the two correlations. We test the model using experimental data from a stationary axisymmetric turbulent flow with homogeneity along the axis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1980IJTP...19..405C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1980IJTP...19..405C"><span>Lorentz Invariance of Gravitational <span class="hlt">Lagrangians</span> in the Space of Reference Frames</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cognola, G.</p> <p>1980-06-01</p> <p>The recently proposed theories of gravitation in the space of reference frames S are based on a <span class="hlt">Lagrangian</span> invariant with respect to the homogeneous Lorentz group. However, in theories of this kind, the Lorentz invariance is not a necessary consequence of some physical principles, as in the theories formulated in space-time, but rather a purely esthetic request. In the present paper, we give a systematic method for the construction of gravitational theories in the space S, without assuming a priori the Lorentz invariance of the <span class="hlt">Lagrangian</span>. The Einstein-Cartan equations of gravitation are obtained requiring only that the <span class="hlt">Lagrangian</span> is invariant under proper rotations and has particular transformation properties under space reflections and space-time dilatations</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26778728','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26778728"><span>Deconstructing field-induced ketene isomerization through <span class="hlt">Lagrangian</span> descriptors.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Craven, Galen T; Hernandez, Rigoberto</p> <p>2016-02-07</p> <p>The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of <span class="hlt">Lagrangian</span> descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter-Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using <span class="hlt">Lagrangian</span> descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from <span class="hlt">Lagrangian</span> descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014DSRI...90...27P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014DSRI...90...27P"><span>Identifying <span class="hlt">Lagrangian</span> fronts with favourable fishery conditions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.</p> <p>2014-08-01</p> <p><span class="hlt">Lagrangian</span> fronts (LFs) in the ocean are defined as boundaries between surface waters with strongly different <span class="hlt">Lagrangian</span> properties. They can be accurately detected in a given velocity field by computing synoptic maps for displacements of synthetic tracers and other <span class="hlt">Lagrangian</span> indicators. We use Pacific saury catch and location data for a number of commercial fishery seasons in the region of the northwest Pacific with one of the richest fishery in the world. It is shown statistically that the saury fishing grounds with maximal catches are not randomly distributed over the region but located mainly along the sharp LFs where productive cold waters of the Oyashio Current, warmer waters of the southern branch of the Soya Current, and waters of warm-core Kuroshio rings converge. Computation of those fronts in altimetric geostrophic velocity fields both in the years with the First and Second Oyashio Intrusions shows that in spite of different oceanographic conditions LF locations may serve as good indicators of potential fishing grounds. Possible biophysical reasons for saury aggregation near sharp LFs are discussed. We propose a mechanism for effective export of nutrient rich waters based on stretching of material lines in the vicinity of hyperbolic objects in the ocean. The developed method, based on identifying LFs in any velocity fields, is quite general and may be applied to find potential fishing grounds for the other pelagic fish.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900004103','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900004103"><span>Simulation of spacecraft attitude dynamics using TREETOPS and model-specific computer <span class="hlt">Codes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Cochran, John E.; No, T. S.; Fitz-Coy, Norman G.</p> <p>1989-01-01</p> <p>The simulation of spacecraft attitude dynamics and control using the generic, multi-body <span class="hlt">code</span> called TREETOPS and other <span class="hlt">codes</span> written especially to simulate particular systems is discussed. Differences in the methods used to derive equations of motion--Kane's method for TREETOPS and the <span class="hlt">Lagrangian</span> and Newton-Euler methods, respectively, for the other two <span class="hlt">codes</span>--are considered. Simulation results from the TREETOPS <span class="hlt">code</span> are compared with those from the other two <span class="hlt">codes</span> for two example systems. One system is a chain of rigid bodies; the other consists of two rigid bodies attached to a flexible base body. Since the computer <span class="hlt">codes</span> were developed independently, consistent results serve as a verification of the correctness of all the programs. Differences in the results are discussed. Results for the two-rigid-body, one-flexible-body system are useful also as information on multi-body, flexible, pointing payload dynamics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2000MPLA...15...55H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2000MPLA...15...55H"><span>Symmetries of SU(2) Skyrmion in Hamiltonian and <span class="hlt">Lagrangian</span> Approaches</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hong, Soon-Tae; Kim, Yong-Wan; Park, Young-Jai</p> <p></p> <p>We apply the Batalin-Fradkin-Tyutin (BFT) method to the SU(2) Skyrmion to study the full symmetry structure of the model at the first-class Hamiltonian level. On the other hand, we also analyze the symmetry structure of the action having the WZ term, which corresponds to this Hamiltonian, in the framework of the <span class="hlt">Lagrangian</span> approach. Furthermore, following the BFV formalism we derive the BRST invariant gauge fixed <span class="hlt">Lagrangian</span> from the above extended action.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014MNRAS.437.3442H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014MNRAS.437.3442H"><span>The Zel'dovich approximation: key to understanding cosmic web complexity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hidding, Johan; Shandarin, Sergei F.; van de Weygaert, Rien</p> <p>2014-02-01</p> <p>We describe how the dynamics of cosmic structure formation defines the intricate geometric structure of the spine of the cosmic web. The Zel'dovich approximation is used to model the backbone of the cosmic web in terms of its singularity structure. The description by Arnold et al. in terms of catastrophe theory forms the basis of our analysis. This two-dimensional analysis involves a profound assessment of the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> projections of the gravitationally evolving four-dimensional phase-space manifold. It involves the identification of the complete family of singularity classes, and the corresponding caustics that we see emerging as structure in <span class="hlt">Eulerian</span> space evolves. In particular, as it is instrumental in outlining the spatial network of the cosmic web, we investigate the nature of spatial connections between these singularities. The major finding of our study is that all singularities are located on a set of lines in <span class="hlt">Lagrangian</span> space. All dynamical processes related to the caustics are concentrated near these lines. We demonstrate and discuss extensively how all 2D singularities are to be found on these lines. When mapping this spatial pattern of lines to <span class="hlt">Eulerian</span> space, we find a growing connectedness between initially disjoint lines, resulting in a percolating network. In other words, the lines form the blueprint for the global geometric evolution of the cosmic web.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1263394-bias-effective-field-theory-large-scale-structures','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1263394-bias-effective-field-theory-large-scale-structures"><span>Bias in the effective field theory of large scale structures</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Senatore, Leonardo</p> <p>2015-11-05</p> <p>We study how to describe collapsed objects, such as galaxies, in the context of the Effective Field Theory of Large Scale Structures. The overdensity of galaxies at a given location and time is determined by the initial tidal tensor, velocity gradients and spatial derivatives of the regions of dark matter that, during the evolution of the universe, ended up at that given location. Similarly to what was recently done for dark matter, we show how this <span class="hlt">Lagrangian</span> space description can be recovered by upgrading simpler <span class="hlt">Eulerian</span> calculations. We describe the <span class="hlt">Eulerian</span> theory. We show that it is perturbatively local inmore » space, but non-local in time, and we explain the observational consequences of this fact. We give an argument for why to a certain degree of accuracy the theory can be considered as quasi time-local and explain what the operator structure is in this case. Furthermore, we describe renormalization of the bias coefficients so that, after this and after upgrading the <span class="hlt">Eulerian</span> calculation to a <span class="hlt">Lagrangian</span> one, the perturbative series for galaxies correlation functions results in a manifestly convergent expansion in powers of k/k NL and k/k M, where k is the wavenumber of interest, k NL is the wavenumber associated to the non-linear scale, and k M is the comoving wavenumber enclosing the mass of a galaxy.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.9794Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.9794Z"><span>Observed and Modeled Pathways of the Iceland Scotland Overflow Water in the eastern North Atlantic</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zou, Sijia; Lozier, Susan; Zenk, Walter; Bower, Amy; Johns, William</p> <p>2017-04-01</p> <p>The Iceland Scotland Overflow Water (ISOW), one of the major components of the lower limb of the Atlantic Meridional Overturning Circulation (AMOC), is formed in the Nordic Seas and enters the eastern North Atlantic subpolar gyre via the Iceland-Scotland sill. After entraining the ambient waters, the relatively homogeneous ISOW spreads southward into the North Atlantic. An understanding of the distribution and variability of the spreading pathways of the ISOW is fundamental to our understanding of AMOC structure and variability. Three major ISOW pathways have been identified in the eastern North Atlantic by previous studies: 1) across the Reykjanes Ridge via deep gaps, 2) through the Charlie Gibbs Fracture Zone, and 3) southward along the eastern flank of the Mid Atlantic Ridge (MAR). However, most of these studies were conducted using an <span class="hlt">Eulerian</span> frame with limited observations, especially for the third pathway along the eastern flank of the MAR. In this work, we give a comprehensive description of ISOW pathways in the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> frames, quantify the relative importance of each pathway and examine the temporal variability of these pathways. Our study distinguishes itself from past studies by using both <span class="hlt">Eulerian</span> (current meter data) and <span class="hlt">Lagrangian</span> (eddy-resolving RAFOS float data) observations in combination with modeling output (1/12° FLAME) to describe ISOW spreading pathways and their variability.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CPM.....4..321N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CPM.....4..321N"><span>Seakeeping with the semi-<span class="hlt">Lagrangian</span> particle finite element method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio</p> <p>2017-07-01</p> <p>The application of the semi-<span class="hlt">Lagrangian</span> particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the <span class="hlt">Lagrangian</span> advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28041621','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28041621"><span>A new method to calibrate <span class="hlt">Lagrangian</span> model with ASAR images for oil slick trajectory.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Tian, Siyu; Huang, Xiaoxia; Li, Hongga</p> <p>2017-03-15</p> <p>Since <span class="hlt">Lagrangian</span> model coefficients vary with different conditions, it is necessary to calibrate the model to obtain optimal coefficient combination for special oil spill accident. This paper focuses on proposing a new method to calibrate <span class="hlt">Lagrangian</span> model with time series of Envisat ASAR images. Oil slicks extracted from time series images form a detected trajectory of special oil slick. <span class="hlt">Lagrangian</span> model is calibrated by minimizing the difference between simulated trajectory and detected trajectory. mean center position distance difference (MCPD) and rotation difference (RD) of Oil slicks' or particles' standard deviational ellipses (SDEs) are calculated as two evaluations. The two parameters are taken to evaluate the performance of <span class="hlt">Lagrangian</span> transport model with different coefficient combinations. This method is applied to Penglai 19-3 oil spill accident. The simulation result with calibrated model agrees well with related satellite observations. It is suggested the new method is effective to calibrate <span class="hlt">Lagrangian</span> model. Copyright © 2016 Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AIPC.1947c0005S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AIPC.1947c0005S"><span>Simulating X-ray bursts with a radiation hydrodynamics <span class="hlt">code</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Seong, Gwangeon; Kwak, Kyujin</p> <p>2018-04-01</p> <p>Previous simulations of X-ray bursts (XRBs), for example, those performed by MESA (Modules for Experiments in Stellar Astrophysics) could not address the dynamical effects of strong radiation, which are important to explain the photospheric radius expansion (PRE) phenomena seen in many XRBs. In order to study the effects of strong radiation, we propose to use SNEC (the SuperNova Explosion <span class="hlt">Code</span>), a 1D <span class="hlt">Lagrangian</span> open source <span class="hlt">code</span> that is designed to solve hydrodynamics and equilibrium-diffusion radiation transport together. Because SNEC is able to control modules of radiation-hydrodynamics for properly mapped inputs, radiation-dominant pressure occurring in PRE XRBs can be handled. Here we present simulation models for PRE XRBs by applying SNEC together with MESA.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29316401','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29316401"><span>Extended <span class="hlt">Lagrangian</span> Excited State Molecular Dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Bjorgaard, J A; Sheppard, D; Tretiak, S; Niklasson, A M N</p> <p>2018-02-13</p> <p>An extended <span class="hlt">Lagrangian</span> framework for excited state molecular dynamics (XL-ESMD) using time-dependent self-consistent field theory is proposed. The formulation is a generalization of the extended <span class="hlt">Lagrangian</span> formulations for ground state Born-Oppenheimer molecular dynamics [Phys. Rev. Lett. 2008 100, 123004]. The theory is implemented, demonstrated, and evaluated using a time-dependent semiempirical model, though it should be generally applicable to ab initio theory. The simulations show enhanced energy stability and a significantly reduced computational cost associated with the iterative solutions of both the ground state and the electronically excited states. Relaxed convergence criteria can therefore be used both for the self-consistent ground state optimization and for the iterative subspace diagonalization of the random phase approximation matrix used to calculate the excited state transitions. The XL-ESMD approach is expected to enable numerically efficient excited state molecular dynamics for such methods as time-dependent Hartree-Fock (TD-HF), Configuration Interactions Singles (CIS), and time-dependent density functional theory (TD-DFT).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhRvD..97h4048D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvD..97h4048D"><span><span class="hlt">Lagrangian</span> formulation of the general relativistic Poynting-Robertson effect</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>De Falco, Vittorio; Battista, Emmanuele; Falanga, Maurizio</p> <p>2018-04-01</p> <p>We propose the <span class="hlt">Lagrangian</span> formulation for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux of photons traveling along the null geodesics of the background spacetime, including the general relativistic Poynting-Robertson effect. The innovative part of this work is to prove the existence of the potential linked to the dissipative action caused by the Poynting-Robertson effect in general relativity through the help of an integrating factor, depending on the energy of the system. Generally, such kinds of inverse problems involving dissipative effects might not admit a <span class="hlt">Lagrangian</span> formulation; especially, in general relativity, there are no examples of such attempts in the literature so far. We reduce this general relativistic <span class="hlt">Lagrangian</span> formulation to the classic case in the weak-field limit. This approach facilitates further studies in improving the treatment of the radiation field, and it contains, for example, some implications for a deeper comprehension of the gravitational waves.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDD33003C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDD33003C"><span><span class="hlt">Lagrangian</span> transport in a class of three-dimensional buoyancy-driven flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Contreras, Sebastian; Speetjens, Michel; Clercx, Herman</p> <p>2017-11-01</p> <p>The study concerns the <span class="hlt">Lagrangian</span> dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as archetypal configuration for natural-convection flows in which gravity is perpendicular to the global temperature gradient. Limited insight into the <span class="hlt">Lagrangian</span> properties of this class of flows motivates this study. The 3D <span class="hlt">Lagrangian</span> dynamics are investigated in terms of the generic structure of the <span class="hlt">Lagrangian</span> flow topology that is described in terms of the Grashof number (Gr) and the Prandtl number (Pr). Gr is the principal control parameter for the flow topology: vanishing Gr yields a state of closed streamlines (integrable state); increasing Gr causes the formation of toroidal coherent structures embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ``smaller'' Gr. A buoyancy-induced bifurcation of the flow topology occurs for ``larger'' Gr and underlies the emergence of ``secondary rolls'' and secondary tori for ``larger'' Pr. Stagnation points and corresponding manifold interactions are key to the dynamics. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22089709-implementation-sink-particles-athena-code','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22089709-implementation-sink-particles-athena-code"><span>IMPLEMENTATION OF SINK PARTICLES IN THE ATHENA <span class="hlt">CODE</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Gong Hao; Ostriker, Eve C., E-mail: hgong@astro.umd.edu, E-mail: eco@astro.princeton.edu</p> <p>2013-01-15</p> <p>We describe the implementation and tests of sink particle algorithms in the <span class="hlt">Eulerian</span> grid-based <span class="hlt">code</span> Athena. The introduction of sink particles enables the long-term evolution of systems in which localized collapse occurs, and it is impractical (or unnecessary) to resolve the accretion shocks at the centers of collapsing regions. We discuss the similarities and differences of our methods compared to other implementations of sink particles. Our criteria for sink creation are motivated by the properties of the Larson-Penston collapse solution. We use standard particle-mesh methods to compute particle and gas gravity together. Accretion of mass and momenta onto sinks ismore » computed using fluxes returned by the Riemann solver. A series of tests based on previous analytic and numerical collapse solutions is used to validate our method and implementation. We demonstrate use of our <span class="hlt">code</span> for applications with a simulation of planar converging supersonic turbulent flow, in which multiple cores form and collapse to create sinks; these sinks continue to interact and accrete from their surroundings over several Myr.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014CPM.....1..103G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CPM.....1..103G"><span>Evaluating the performance of the particle finite element method in parallel architectures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gimenez, Juan M.; Nigro, Norberto M.; Idelsohn, Sergio R.</p> <p>2014-05-01</p> <p>This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an <span class="hlt">Eulerian</span> mesh and <span class="hlt">Lagrangian</span> particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical <span class="hlt">Eulerian</span> alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve <span class="hlt">Eulerian</span> stages of PFEM-2. However, <span class="hlt">Lagrangian</span> stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant-Friedrichs-Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical <span class="hlt">Eulerian</span> strategies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.360...57K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.360...57K"><span>A hybrid gyrokinetic ion and isothermal electron fluid <span class="hlt">code</span> for astrophysical plasma</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kawazura, Y.; Barnes, M.</p> <p>2018-05-01</p> <p>This paper describes a new <span class="hlt">code</span> for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) Schekochihin et al. (2009) [9]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron-ion mass ratio expansion. The <span class="hlt">code</span> is developed by incorporating the ITEF approximation into AstroGK, an <span class="hlt">Eulerian</span> δf gyrokinetics <span class="hlt">code</span> specialized to a slab geometry Numata et al. (2010) [41]. The new <span class="hlt">code</span> treats the linear terms in the ITEF equations implicitly while the nonlinear terms are treated explicitly. We show linear and nonlinear benchmark tests to prove the validity and applicability of the simulation <span class="hlt">code</span>. Since the fast electron timescale is eliminated by the mass ratio expansion, the Courant-Friedrichs-Lewy condition is much less restrictive than in full gyrokinetic <span class="hlt">codes</span>; the present hybrid <span class="hlt">code</span> runs ∼ 2√{mi /me } ∼ 100 times faster than AstroGK with a single ion species and kinetic electrons where mi /me is the ion-electron mass ratio. The improvement of the computational time makes it feasible to execute ion scale gyrokinetic simulations with a high velocity space resolution and to run multiple simulations to determine the dependence of turbulent dynamics on parameters such as electron-ion temperature ratio and plasma beta.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70174360','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70174360"><span>On inter-tidal transport equation</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cheng, Ralph T.; Feng, Shizuo; Pangen, Xi</p> <p>1989-01-01</p> <p>The transports of solutes, sediments, nutrients, and other tracers are fundamental to the interactive physical, chemical, and biological processes in estuaries. The characteristic time scales for most estuarine biological and chemical processes are on the order of several tidal cycles or longer. To address the long-term transport mechanism meaningfully, the formulation of an inter-tidal conservation equation is the main subject of this paper. The commonly used inter-tidal conservation equation takes the form of a convection-dispersion equation in which the convection is represented by the <span class="hlt">Eulerian</span> residual current, and the dispersion terms are due to the introduction of a Fickian hypothesis, unfortunately, the physical significance of this equation is not clear, and the introduction of a Fickian hypothesis is at best an ad hoc approximation. Some recent research results on the <span class="hlt">Lagrangian</span> residual current suggest that the long-term transport problem is more closely related to the <span class="hlt">Lagrangian</span> residual current than to the <span class="hlt">Eulerian</span> residual current. With the aid of additional insight of residual current, the inter-tidal transport equation has been reformulated in this paper using a small perturbation method for a weakly nonlinear tidal system. When tidal flows can be represented by an M2 system, the new intertidal transport equation also takes the form of a convective-dispersion equation without the introduction of a Fickian hypothesis. The convective velocity turns out to be the first order <span class="hlt">Lagrangian</span> residual current (the sum of the <span class="hlt">Eulerian</span> residual current and the Stokes’ drift), and the correlation terms take the form of convection with the Stokes’ drift as the convective velocity. The remaining dispersion terms are perturbations of lower order solution to higher order solutions due to shear effect and turbulent mixing.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JGRC..119.8029L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JGRC..119.8029L"><span><span class="hlt">Lagrangian</span> predictability characteristics of an Ocean Model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lacorata, Guglielmo; Palatella, Luigi; Santoleri, Rosalia</p> <p>2014-11-01</p> <p>The Mediterranean Forecasting System (MFS) Ocean Model, provided by INGV, has been chosen as case study to analyze <span class="hlt">Lagrangian</span> trajectory predictability by means of a dynamical systems approach. To this regard, numerical trajectories are tested against a large amount of Mediterranean drifter data, used as sample of the actual tracer dynamics across the sea. The separation rate of a trajectory pair is measured by computing the Finite-Scale Lyapunov Exponent (FSLE) of first and second kind. An additional kinematic <span class="hlt">Lagrangian</span> model (KLM), suitably treated to avoid "sweeping"-related problems, has been nested into the MFS in order to recover, in a statistical sense, the velocity field contributions to pair particle dispersion, at mesoscale level, smoothed out by finite resolution effects. Some of the results emerging from this work are: (a) drifter pair dispersion displays Richardson's turbulent diffusion inside the [10-100] km range, while numerical simulations of MFS alone (i.e., without subgrid model) indicate exponential separation; (b) adding the subgrid model, model pair dispersion gets very close to observed data, indicating that KLM is effective in filling the energy "mesoscale gap" present in MFS velocity fields; (c) there exists a threshold size beyond which pair dispersion becomes weakly sensitive to the difference between model and "real" dynamics; (d) the whole methodology here presented can be used to quantify model errors and validate numerical current fields, as far as forecasts of <span class="hlt">Lagrangian</span> dispersion are concerned.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li class="active"><span>25</span></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_25 --> <div class="footer-extlink text-muted" style="margin-bottom:1rem; text-align:center;">Some links on this page may take you to non-federal websites. 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