Sample records for lagrangian numerical scheme

  1. 3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"

    NASA Technical Reports Server (NTRS)

    Douglass, A.

    2005-01-01

    The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), 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.

  2. Eulerian-Lagrangian numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods

    USGS Publications Warehouse

    Cox, T.J.; Runkel, R.L.

    2008-01-01

    Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, Eulerian 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 Lagrangian control volumes across a fixed (Eulerian) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative Eulerian numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the Lagrangian scheme performs better than the Eulerian 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 Eulerian 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 Eulerian scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.

  3. A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

    DOE PAGES

    Ku, S.; Hager, R.; Chang, C. S.; ...

    2016-04-01

    In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less

  4. A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

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

    Ku, S.; Hager, R.; Chang, C. S.

    In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. In conclusion, the numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less

  5. A new hybrid-Lagrangian numerical scheme for gyrokinetic simulation of tokamak edge plasma

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

    Ku, S., E-mail: sku@pppl.gov; Hager, R.; Chang, C.S.

    In order to enable kinetic simulation of non-thermal edge plasmas at a reduced computational cost, a new hybrid-Lagrangian δf scheme has been developed that utilizes the phase space grid in addition to the usual marker particles, taking advantage of the computational strengths from both sides. The new scheme splits the particle distribution function of a kinetic equation into two parts. Marker particles contain the fast space-time varying, δf, part of the distribution function and the coarse-grained phase-space grid contains the slow space-time varying part. The coarse-grained phase-space grid reduces the memory-requirement and the computing cost, while the marker particles providemore » scalable computing ability for the fine-grained physics. Weights of the marker particles are determined by a direct weight evolution equation instead of the differential form weight evolution equations that the conventional delta-f schemes use. The particle weight can be slowly transferred to the phase space grid, thereby reducing the growth of the particle weights. The non-Lagrangian part of the kinetic equation – e.g., collision operation, ionization, charge exchange, heat-source, radiative cooling, and others – can be operated directly on the phase space grid. Deviation of the particle distribution function on the velocity grid from a Maxwellian distribution function – driven by ionization, charge exchange and wall loss – is allowed to be arbitrarily large. The numerical scheme is implemented in the gyrokinetic particle code XGC1, which specializes in simulating the tokamak edge plasma that crosses the magnetic separatrix and is in contact with the material wall.« less

  6. High Order Semi-Lagrangian Advection Scheme

    NASA Astrophysics Data System (ADS)

    Malaga, Carlos; Mandujano, Francisco; Becerra, Julian

    2014-11-01

    In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).

  7. Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

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

    Cheng, Juan, E-mail: cheng_juan@iapcm.ac.cn; Shu, Chi-Wang, E-mail: shu@dam.brown.edu

    In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, basedmore » on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.« less

  8. A second-order shock-adaptive Godunov scheme based on the generalized Lagrangian formulation

    NASA Astrophysics Data System (ADS)

    Lepage, Claude

    Application of the Godunov scheme to the Euler equations of gas dynamics, based on the Eulerian 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 Lagrangian 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.

  9. A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids

    NASA Astrophysics Data System (ADS)

    Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard

    2013-02-01

    In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.

  10. A nominally second-order cell-centered Lagrangian scheme for simulating elastic–plastic flows on two-dimensional unstructured grids

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

    Maire, Pierre-Henri, E-mail: maire@celia.u-bordeaux1.fr; Abgrall, Rémi, E-mail: remi.abgrall@math.u-bordeau1.fr; Breil, Jérôme, E-mail: breil@celia.u-bordeaux1.fr

    2013-02-15

    In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic–plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs themore » von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.« less

  11. A hybrid Lagrangian Voronoi-SPH scheme

    NASA Astrophysics Data System (ADS)

    Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.

    2018-07-01

    A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

  12. A hybrid Lagrangian Voronoi-SPH scheme

    NASA Astrophysics Data System (ADS)

    Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.

    2017-11-01

    A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.

  13. An online-coupled NWP/ACT model with conserved Lagrangian levels

    NASA Astrophysics Data System (ADS)

    Sørensen, B.; Kaas, E.; Lauritzen, P. H.

    2012-04-01

    Numerical weather and climate modelling is under constant development. Semi-implicit semi-Lagrangian (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-Lagrangian schemes with quasi-Lagrangian vertical coordinates the Lagrangian levels are remapped to Eulerian 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-Lagrangian advection method is introduced, it combines an inherently mass conserving 2D semi-Lagrangian scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully Lagrangian 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 Lagrangian levels suffer from traditional Lagrangian limitations caused by the convergence and divergence of the flow, remappings to the Eulerian 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.

  14. A second-order cell-centered Lagrangian ADER-MOOD finite volume scheme on multidimensional unstructured meshes for hydrodynamics

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri

    2018-04-01

    In this paper we develop a conservative cell-centered Lagrangian finite volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.

  15. Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

    NASA Astrophysics Data System (ADS)

    Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri

    2016-05-01

    One of the main issues in the field of numerical schemes is to ally robustness with accuracy. Considering gas dynamics, numerical approximations may generate negative density or pressure, which may lead to nonlinear instability and crash of the code. This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation. Furthermore, most of the problems studied in this framework contain very intense rarefaction and shock waves. In this paper, the admissibility of numerical solutions obtained by high-order finite-volume-scheme-based methods, such as the discontinuous Galerkin (DG) method, the essentially non-oscillatory (ENO) and the weighted ENO (WENO) finite volume schemes, is addressed in the one-dimensional Lagrangian gas dynamics framework. After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume schemes to be positive, is then given. This study is conducted for both ideal gas and non-ideal gas equations of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Mie-Grüneisen (MG) EOS, and relies on two different techniques: either a particular definition of the local approximation of the acoustic impedances arising from the approximate Riemann solver, or an additional time step constraint relative to the cell volume variation. Then, making use of the work presented in [89,90,22], this positivity study is extended to high-orders of accuracy, where new time step constraints are obtained, and proper limitation is required. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. This paper is the first part of a series of two. The whole analysis presented here is extended to the two-dimensional case in [85], and proves to fit a wide

  16. Testing higher-order Lagrangian perturbation theory against numerical simulations. 2: Hierarchical models

    NASA Technical Reports Server (NTRS)

    Melott, A. L.; Buchert, T.; Weib, A. G.

    1995-01-01

    We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of scales. The Lagrangian theory of gravitational instability of Friedmann-Lemaitre cosmogonies is compared with numerical simulations. We study the dynamics of hierarchical models as a second step. In the first step we analyzed the performance of the Lagrangian schemes for pancake models, the difference being that in the latter models the initial power spectrum is truncated. This work probed the quasi-linear and weakly non-linear regimes. We here explore whether the results found for pancake models carry over to hierarchical models which are evolved deeply into the non-linear regime. We smooth the initial data by using a variety of filter types and filter scales in order to determine the optimal performance of the analytical models, as has been done for the 'Zel'dovich-approximation' - hereafter TZA - in previous work. We find that for spectra with negative power-index the second-order scheme performs considerably better than TZA in terms of statistics which probe the dynamics, and slightly better in terms of low-order statistics like the power-spectrum. However, in contrast to the results found for pancake models, where the higher-order schemes get worse than TZA at late non-linear stages and on small scales, we here find that the second-order model is as robust as TZA, retaining the improvement at later stages and on smaller scales. In view of these results we expect that the second-order truncated Lagrangian model is especially useful for the modelling of standard dark matter models such as Hot-, Cold-, and Mixed-Dark-Matter.

  17. An improved bounded semi-Lagrangian scheme for the turbulent transport of passive scalars

    NASA Astrophysics Data System (ADS)

    Verma, Siddhartha; Xuan, Y.; Blanquart, G.

    2014-09-01

    An improved bounded semi-Lagrangian 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 Eulerian scheme.

  18. Modified Mixed Lagrangian-Eulerian Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.

    PubMed

    Suk, Heejun

    2016-07-01

    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 Lagrangian 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 Lagrangian concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the finite element method (FEM) and the Eulerian-Lagrangian 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.

  19. Implications of Lagrangian transport for coupled chemistry-climate simulations

    NASA Astrophysics Data System (ADS)

    Stenke, A.; Dameris, M.; Grewe, V.; Garny, H.

    2008-10-01

    For the first time a purely Lagrangian transport algorithm is applied in a fully coupled chemistry-climate model (CCM). We use the Lagrangian 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 Lagrangian approach is that it is numerically non-diffusive and therefore maintains steeper and more realistic gradients than the operational semi-Lagrangian 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 Lagrangian 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-Lagrangian 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 Lagrangian 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

  20. A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

    NASA Astrophysics Data System (ADS)

    Jaouen, Stéphane

    2007-07-01

    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 Lagrangian 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 Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian 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 Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

  1. Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Dumbser, Michael

    2017-10-01

    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-Lagrangian-Eulerian (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

  2. Lagrangian motion, coherent structures, and lines of persistent material strain.

    PubMed

    Samelson, R M

    2013-01-01

    Lagrangian 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 Lagrangian 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, Lagrangian regime boundaries may often be indicated as material curves on which the Lagrangian-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 Lagrangian regime boundaries and lines of principal Lagrangian strain (also called Lagrangian coherent structures) are divided into parcel and bundle schemes; the latter include the finite-time and finite-size Lyapunov exponent/Lagrangian 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.

  3. Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

    NASA Technical Reports Server (NTRS)

    Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.

    1990-01-01

    A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

  4. Numerical Simulations of Homogeneous Turbulence Using Lagrangian-Averaged Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Mohseni, Kamran; Shkoller, Steve; Kosovic, Branko; Marsden, Jerrold E.; Carati, Daniele; Wray, Alan; Rogallo, Robert

    2000-01-01

    The Lagrangian-averaged Navier-Stokes (LANS) equations are numerically evaluated as a turbulence closure. They are derived from a novel Lagrangian averaging procedure on the space of all volume-preserving maps and can be viewed as a numerical algorithm which removes the energy content from the small scales (smaller than some a priori fixed spatial scale alpha) using a dispersive rather than dissipative mechanism, thus maintaining the crucial features of the large scale flow. We examine the modeling capabilities of the LANS equations for decaying homogeneous turbulence, ascertain their ability to track the energy spectrum of fully resolved direct numerical simulations (DNS), compare the relative energy decay rates, and compare LANS with well-accepted large eddy simulation (LES) models.

  5. Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

    NASA Astrophysics Data System (ADS)

    Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

    2007-10-01

    Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

  6. Age-of-Air, Tape Recorder, and Vertical Transport Schemes

    NASA Technical Reports Server (NTRS)

    Lin, S.-J.; Einaudi, Franco (Technical Monitor)

    2000-01-01

    A numerical-analytic investigation of the impacts of vertical transport schemes on the model simulated age-of-air and the so-called 'tape recorder' will be presented using an idealized 1-D column transport model as well as a more realistic 3-D dynamical model. By comparing to the 'exact' solutions of 'age-of-air' and the 'tape recorder' obtainable in the 1-D setting, useful insight is gained on the impacts of numerical diffusion and dispersion of numerical schemes used in global models. Advantages and disadvantages of Eulerian, semi-Lagrangian, and Lagrangian transport schemes will be discussed. Vertical resolution requirement for numerical schemes as well as observing systems for capturing the fine details of the 'tape recorder' or any upward propagating wave-like structures can potentially be derived from the 1-D analytic model.

  7. A high order cell-centered semi-Lagrangian scheme for multi-dimensional kinetic simulations of neutral gas flows

    NASA Astrophysics Data System (ADS)

    Güçlü, Y.; Hitchon, W. N. G.

    2012-04-01

    The term 'Convected Scheme' (CS) refers to a family of algorithms, most usually applied to the solution of Boltzmann's equation, which uses a method of characteristics in an integral form to project an initial cell forward to a group of final cells. As such the CS is a 'forward-trajectory' semi-Lagrangian scheme. For multi-dimensional simulations of neutral gas flows, the cell-centered version of this semi-Lagrangian (CCSL) scheme has advantages over other options due to its implementation simplicity, low memory requirements, and easier treatment of boundary conditions. The main drawback of the CCSL-CS to date has been its high numerical diffusion in physical space, because of the 2nd order remapping that takes place at the end of each time step. By means of a modified equation analysis, it is shown that a high order estimate of the remapping error can be obtained a priori, and a small correction to the final position of the cells can be applied upon remapping, in order to achieve full compensation of this error. The resulting scheme is 4th order accurate in space while retaining the desirable properties of the CS: it is conservative and positivity-preserving, and the overall algorithm complexity is not appreciably increased. Two monotone (i.e. non-oscillating) versions of the fourth order CCSL-CS are also presented: one uses a common flux-limiter approach; the other uses a non-polynomial reconstruction to evaluate the derivatives of the density function. The method is illustrated in simple one- and two-dimensional examples, and a fully 3D solution of the Boltzmann equation describing expansion of a gas into vacuum through a cylindrical tube.

  8. 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.

  9. Numerical considerations for Lagrangian stochastic dispersion models: Eliminating rogue trajectories, and the importance of numerical accuracy

    USDA-ARS?s Scientific Manuscript database

    When Lagrangian stochastic models for turbulent dispersion are applied to complex flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behavior in the numerical solution. This paper discusses numerical considerations when solving the Langevin-based particle velo...

  10. 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.

  11. 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.

  12. A Shock-Adaptive Godunov Scheme Based on the Generalised Lagrangian Formulation

    NASA Astrophysics Data System (ADS)

    Lepage, C. Y.; Hui, W. H.

    1995-12-01

    Application of the Godunov scheme to the Euler equations of gas dynamics based on the Eulerian 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 Lagrangian 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.

  13. Lagrangian numerical methods for ocean biogeochemical simulations

    NASA Astrophysics Data System (ADS)

    Paparella, Francesco; Popolizio, Marina

    2018-05-01

    We propose two closely-related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and the Péclet numbers are so high that resolving all the scales of motion is unfeasible. This is commonplace in ocean flows. Our methods consist in augmenting the method of characteristics, which is suitable for advection-reaction problems, with couplings among nearby particles, producing fluxes that mimic diffusion, or unresolved small-scale transport. The methods conserve mass, obey the maximum principle, and allow to tune the strength of the diffusive terms down to zero, while avoiding unwanted numerical dissipation effects.

  14. Multi-Scale Analysis for Characterizing Near-Field Constituent Concentrations in the Context of a Macro-Scale Semi-Lagrangian Numerical Model

    NASA Astrophysics Data System (ADS)

    Yearsley, J. R.

    2017-12-01

    The semi-Lagrangian numerical scheme employed by RBM, a model for simulating time-dependent, one-dimensional water quality constituents in advection-dominated rivers, is highly scalable both in time and space. Although the model has been used at length scales of 150 meters and time scales of three hours, the majority of applications have been at length scales of 1/16th degree latitude/longitude (about 5 km) or greater and time scales of one day. Applications of the method at these scales has proven successful for characterizing the impacts of climate change on water temperatures in global rivers and on the vulnerability of thermoelectric power plants to changes in cooling water temperatures in large river systems. However, local effects can be very important in terms of ecosystem impacts, particularly in the case of developing mixing zones for wastewater discharges with pollutant loadings limited by regulations imposed by the Federal Water Pollution Control Act (FWPCA). Mixing zone analyses have usually been decoupled from large-scale watershed influences by developing scenarios that represent critical scenarios for external processes associated with streamflow and weather conditions . By taking advantage of the particle-tracking characteristics of the numerical scheme, RBM can provide results at any point in time within the model domain. We develop a proof of concept for locations in the river network where local impacts such as mixing zones may be important. Simulated results from the semi-Lagrangian numerical scheme are treated as input to a finite difference model of the two-dimensional diffusion equation for water quality constituents such as water temperature or toxic substances. Simulations will provide time-dependent, two-dimensional constituent concentration in the near-field in response to long-term basin-wide processes. These results could provide decision support to water quality managers for evaluating mixing zone characteristics.

  15. 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.

  16. A strong shock tube problem calculated by different numerical schemes

    NASA Astrophysics Data System (ADS)

    Lee, Wen Ho; Clancy, Sean P.

    1996-05-01

    Calculated results are presented for the solution of a very strong shock tube problem on a coarse mesh using (1) MESA code, (2) UNICORN code, (3) Schulz hydro, and (4) modified TVD scheme. The first two codes are written in Eulerian coordinates, whereas methods (3) and (4) are in Lagrangian coordinates. MESA and UNICORN codes are both of second order and use different monotonic advection method to avoid the Gibbs phenomena. Code (3) uses typical artificial viscosity for inviscid flow, whereas code (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 Lagrangian methods.

  17. An efficient and stable hybrid extended Lagrangian/self-consistent field scheme for solving classical mutual induction

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

    Albaugh, Alex; Demerdash, Omar; Head-Gordon, Teresa, E-mail: thg@berkeley.edu

    2015-11-07

    We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the coursemore » of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well.« less

  18. 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 Eulerian <span class="hlt">schemes</span> in detail to tackle with the turbulence-generated collection.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.353..460F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.353..460F"><span>Efficient <span class="hlt">numerical</span> <span class="hlt">schemes</span> for viscoplastic avalanches. Part 2: The 2D case</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fernández-Nieto, Enrique D.; Gallardo, José M.; Vigneaux, Paul</p> <p>2018-01-01</p> <p>This paper deals with the <span class="hlt">numerical</span> resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite volume <span class="hlt">schemes</span> are used together with duality methods (namely Augmented <span class="hlt">Lagrangian</span> and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new <span class="hlt">schemes</span> need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. Here we derive such <span class="hlt">schemes</span> in 2D as the follow up of the companion paper treating the 1D case. <span class="hlt">Numerical</span> tests include in particular a generalized 2D benchmark for Bingham codes (the Bingham-Couette flow with two non-zero boundary conditions on the velocity) and a simulation of the avalanche path of Taconnaz in Chamonix-Mont-Blanc to show the usability of these <span class="hlt">schemes</span> on real topographies from digital elevation models (DEM).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900001315','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900001315"><span>A high-order <span class="hlt">Lagrangian</span>-decoupling method for the incompressible Navier-Stokes equations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.</p> <p>1989-01-01</p> <p>A high-order <span class="hlt">Lagrangian</span>-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) <span class="hlt">Lagrangian</span> variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference <span class="hlt">schemes</span> for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping <span class="hlt">schemes</span> for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection <span class="hlt">schemes</span> for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. <span class="hlt">Numerous</span> <span class="hlt">numerical</span> examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.</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('http://adsabs.harvard.edu/abs/2017JCoPh.349..137C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.349..137C"><span>A third-order moving mesh cell-centered <span class="hlt">scheme</span> for one-dimensional elastic-plastic flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cheng, Jun-Bo; Huang, Weizhang; Jiang, Song; Tian, Baolin</p> <p>2017-11-01</p> <p>A third-order moving mesh cell-centered <span class="hlt">scheme</span> without the remapping of physical variables is developed for the <span class="hlt">numerical</span> solution of one-dimensional elastic-plastic flows with the Mie-Grüneisen equation of state, the Wilkins constitutive model, and the von Mises yielding criterion. The <span class="hlt">scheme</span> combines the <span class="hlt">Lagrangian</span> method with the MMPDE moving mesh method and adaptively moves the mesh to better resolve shock and other types of waves while preventing the mesh from crossing and tangling. It can be viewed as a direct arbitrarily <span class="hlt">Lagrangian</span>-Eulerian method but can also be degenerated to a purely <span class="hlt">Lagrangian</span> <span class="hlt">scheme</span>. It treats the relative velocity of the fluid with respect to the mesh as constant in time between time steps, which allows high-order approximation of free boundaries. A time dependent scaling is used in the monitor function to avoid possible sudden movement of the mesh points due to the creation or diminishing of shock and rarefaction waves or the steepening of those waves. A two-rarefaction Riemann solver with elastic waves is employed to compute the Godunov values of the density, pressure, velocity, and deviatoric stress at cell interfaces. <span class="hlt">Numerical</span> results are presented for three examples. The third-order convergence of the <span class="hlt">scheme</span> and its ability to concentrate mesh points around shock and elastic rarefaction waves are demonstrated. The obtained <span class="hlt">numerical</span> results are in good agreement with those in literature. The new <span class="hlt">scheme</span> is also shown to be more accurate in resolving shock and rarefaction waves than an existing third-order cell-centered <span class="hlt">Lagrangian</span> <span class="hlt">scheme</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1194069','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1194069"><span>A Godunov-like point-centered essentially <span class="hlt">Lagrangian</span> hydrodynamic approach</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>Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.</p> <p></p> <p>We present an essentially <span class="hlt">Lagrangian</span> hydrodynamic <span class="hlt">scheme</span> suitable for modeling complex compressible flows on tetrahedron meshes. The <span class="hlt">scheme</span> reduces to a purely <span class="hlt">Lagrangian</span> approach when the flow is linear or if the mesh size is equal to zero; as a result, we use the term essentially <span class="hlt">Lagrangian</span> for the proposed approach. The motivation for developing a hydrodynamic method for tetrahedron meshes is because tetrahedron meshes have some advantages over other mesh topologies. Notable advantages include reduced complexity in generating conformal meshes, reduced complexity in mesh reconnection, and preserving tetrahedron cells with automatic mesh refinement. A challenge, however, is tetrahedron meshesmore » do not correctly deform with a lower order (i.e. piecewise constant) staggered-grid hydrodynamic <span class="hlt">scheme</span> (SGH) or with a cell-centered hydrodynamic (CCH) <span class="hlt">scheme</span>. The SGH and CCH approaches calculate the strain via the tetrahedron, which can cause artificial stiffness on large deformation problems. To resolve the stiffness problem, we adopt the point-centered hydrodynamic approach (PCH) and calculate the evolution of the flow via an integration path around the node. The PCH approach stores the conserved variables (mass, momentum, and total energy) at the node. The evolution equations for momentum and total energy are discretized using an edge-based finite element (FE) approach with linear basis functions. A multidirectional Riemann-like problem is introduced at the center of the tetrahedron to account for discontinuities in the flow such as a shock. Conservation is enforced at each tetrahedron center. The multidimensional Riemann-like problem used here is based on <span class="hlt">Lagrangian</span> CCH work [8, 19, 37, 38, 44] and recent <span class="hlt">Lagrangian</span> SGH work [33-35, 39, 45]. In addition, an approximate 1D Riemann problem is solved on each face of the nodal control volume to advect mass, momentum, and total energy. The 1D Riemann problem produces fluxes [18] that remove a volume error in the PCH</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1194069-godunov-like-point-centered-essentially-lagrangian-hydrodynamic-approach','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1194069-godunov-like-point-centered-essentially-lagrangian-hydrodynamic-approach"><span>A Godunov-like point-centered essentially <span class="hlt">Lagrangian</span> hydrodynamic approach</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>2014-10-28</p> <p>We present an essentially <span class="hlt">Lagrangian</span> hydrodynamic <span class="hlt">scheme</span> suitable for modeling complex compressible flows on tetrahedron meshes. The <span class="hlt">scheme</span> reduces to a purely <span class="hlt">Lagrangian</span> approach when the flow is linear or if the mesh size is equal to zero; as a result, we use the term essentially <span class="hlt">Lagrangian</span> for the proposed approach. The motivation for developing a hydrodynamic method for tetrahedron meshes is because tetrahedron meshes have some advantages over other mesh topologies. Notable advantages include reduced complexity in generating conformal meshes, reduced complexity in mesh reconnection, and preserving tetrahedron cells with automatic mesh refinement. A challenge, however, is tetrahedron meshesmore » do not correctly deform with a lower order (i.e. piecewise constant) staggered-grid hydrodynamic <span class="hlt">scheme</span> (SGH) or with a cell-centered hydrodynamic (CCH) <span class="hlt">scheme</span>. The SGH and CCH approaches calculate the strain via the tetrahedron, which can cause artificial stiffness on large deformation problems. To resolve the stiffness problem, we adopt the point-centered hydrodynamic approach (PCH) and calculate the evolution of the flow via an integration path around the node. The PCH approach stores the conserved variables (mass, momentum, and total energy) at the node. The evolution equations for momentum and total energy are discretized using an edge-based finite element (FE) approach with linear basis functions. A multidirectional Riemann-like problem is introduced at the center of the tetrahedron to account for discontinuities in the flow such as a shock. Conservation is enforced at each tetrahedron center. The multidimensional Riemann-like problem used here is based on <span class="hlt">Lagrangian</span> CCH work [8, 19, 37, 38, 44] and recent <span class="hlt">Lagrangian</span> SGH work [33-35, 39, 45]. In addition, an approximate 1D Riemann problem is solved on each face of the nodal control volume to advect mass, momentum, and total energy. The 1D Riemann problem produces fluxes [18] that remove a volume error in the PCH</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 <span class="hlt">schemes</span> can have severe implications for the overall model performance. Traditional Eulerian 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 <span class="hlt">schemes</span> show a considerable <span class="hlt">numerical</span> diffusion. <span class="hlt">Lagrangian</span> approaches, on the other hand, combine a number of favourable <span class="hlt">numerical</span> properties: They are strictly mass-conserving and do not suffer from <span class="hlt">numerical</span> 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 <span class="hlt">scheme</span> has been replaced with the purely <span class="hlt">Lagrangian</span> <span class="hlt">scheme</span> 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> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..SHK.H4002D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..SHK.H4002D"><span>Modeling and <span class="hlt">Numerical</span> Challenges in Eulerian-<span class="hlt">Lagrangian</span> Computations of Shock-driven 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>Diggs, Angela; Balachandar, Sivaramakrishnan</p> <p>2015-06-01</p> <p>The present work addresses the <span class="hlt">numerical</span> methods required for particle-gas and particle-particle interactions in Eulerian-<span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> quantities. Most importantly, we will show that such careful attention to <span class="hlt">numerical</span> 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.</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 Eulerian and <span class="hlt">Lagrangian</span> <span class="hlt">schemes</span></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 Eulerian and <span class="hlt">Lagrangian</span> modeling approaches to describe the particulate phase. Gradient-diffusion approximations are employed in the Eulerian 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 <span class="hlt">schemes</span> 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://adsabs.harvard.edu/abs/2017JChPh.146l4115V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JChPh.146l4115V"><span>Performance of extended <span class="hlt">Lagrangian</span> <span class="hlt">schemes</span> for molecular dynamics simulations with classical polarizable force fields and density functional theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M. N.; Head-Gordon, Teresa; Skylaris, Chris-Kriton</p> <p>2017-03-01</p> <p>Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent <span class="hlt">schemes</span> based on the extended <span class="hlt">Lagrangian</span> formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration <span class="hlt">schemes</span> with the same underlying extended <span class="hlt">Lagrangian</span> structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration <span class="hlt">schemes</span> are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28388116','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28388116"><span>Performance of extended <span class="hlt">Lagrangian</span> <span class="hlt">schemes</span> for molecular dynamics simulations with classical polarizable force fields and density functional theory.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; Niklasson, Anders M N; Head-Gordon, Teresa; Skylaris, Chris-Kriton</p> <p>2017-03-28</p> <p>Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent <span class="hlt">schemes</span> based on the extended <span class="hlt">Lagrangian</span> formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration <span class="hlt">schemes</span> with the same underlying extended <span class="hlt">Lagrangian</span> structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration <span class="hlt">schemes</span> are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1414137-performance-extended-lagrangian-schemes-molecular-dynamics-simulations-classical-polarizable-force-fields-density-functional-theory','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1414137-performance-extended-lagrangian-schemes-molecular-dynamics-simulations-classical-polarizable-force-fields-density-functional-theory"><span>Performance of extended <span class="hlt">Lagrangian</span> <span class="hlt">schemes</span> for molecular dynamics simulations with classical polarizable force fields and density functional theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex; ...</p> <p>2017-03-28</p> <p>Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent <span class="hlt">schemes</span> based on the extended <span class="hlt">Lagrangian</span> formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration <span class="hlt">schemes</span> with the same underlying extended <span class="hlt">Lagrangian</span> structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration <span class="hlt">schemes</span> are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1414137','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1414137"><span>Performance of extended <span class="hlt">Lagrangian</span> <span class="hlt">schemes</span> for molecular dynamics simulations with classical polarizable force fields and density functional 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>Vitale, Valerio; Dziedzic, Jacek; Albaugh, Alex</p> <p></p> <p>Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent <span class="hlt">schemes</span> based on the extended <span class="hlt">Lagrangian</span> formalism, where the initial guesses for the optimized quantities aremore » treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration <span class="hlt">schemes</span> with the same underlying extended <span class="hlt">Lagrangian</span> structure, which we both employ in two radically distinct regimes—in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Furthermore, both integration <span class="hlt">schemes</span> are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015GMDD....8.4221C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015GMDD....8.4221C"><span>A semi-<span class="hlt">Lagrangian</span> advection <span class="hlt">scheme</span> for radioactive tracers in a regional spectral model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chang, E.-C.; Yoshimura, K.</p> <p>2015-06-01</p> <p>In this study, the non-iteration dimensional-split semi-<span class="hlt">Lagrangian</span> (NDSL) advection <span class="hlt">scheme</span> is applied to the National Centers for Environmental Prediction (NCEP) regional spectral model (RSM) to alleviate the Gibbs phenomenon. The Gibbs phenomenon is a problem wherein negative values of positive-definite quantities (e.g., moisture and tracers) are generated by the spectral space transformation in a spectral model system. To solve this problem, the spectral prognostic specific humidity and radioactive tracer advection <span class="hlt">scheme</span> is replaced by the NDSL advection <span class="hlt">scheme</span>, which considers advection of tracers in a grid system without spectral space transformations. A regional version of the NDSL is developed in this study and is applied to the RSM. Idealized experiments show that the regional version of the NDSL is successful. The model runs for an actual case study suggest that the NDSL can successfully advect radioactive tracers (iodine-131 and cesium-137) without noise from the Gibbs phenomenon. The NDSL can also remove negative specific humidity values produced in spectral calculations without losing detailed features.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1013709','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1013709"><span>Bayesian Nonlinear Assimilation of Eulerian and <span class="hlt">Lagrangian</span> Coastal Flow Data</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><span class="hlt">Lagrangian</span> Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, <span class="hlt">schemes</span> and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and <span class="hlt">Lagrangian</span> coastal flow data...coastal ocean fields, both in Eulerian and <span class="hlt">Lagrangian</span> forms. - Further develop and implement our GMM-DO <span class="hlt">schemes</span> for robust Bayesian nonlinear estimation</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</span>-Eulerian finite volume <span class="hlt">schemes</span> 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</span>-Eulerian (ALE) finite volume <span class="hlt">scheme</span> 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 <span class="hlt">schemes</span>, which are expressly designed to deal with source terms written via non-conservative products, with ALE <span class="hlt">schemes</span> on moving grids, which exhibit only very little <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> 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/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 <span class="hlt">schemes</span> 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 <span class="hlt">scheme</span> 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 <span class="hlt">scheme</span> by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to Eulerian background coordinates with truncation of nonlinear terms.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950005164','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950005164"><span>A coupled Eulerian/<span class="hlt">Lagrangian</span> method for the solution of three-dimensional vortical flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Felici, Helene Marie</p> <p>1992-01-01</p> <p>A coupled Eulerian/<span class="hlt">Lagrangian</span> method is presented for the reduction of <span class="hlt">numerical</span> diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> state-vector along the particles trajectories. The <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/<span class="hlt">Lagrangian</span> <span class="hlt">scheme</span> results in substantially lower grid resolution requirements than the standard Eulerian <span class="hlt">scheme</span> for a given solution accuracy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017NPGeo..24..661P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017NPGeo..24..661P"><span>Network-based study of <span class="hlt">Lagrangian</span> transport and mixing</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Padberg-Gehle, Kathrin; Schneide, Christiane</p> <p>2017-10-01</p> <p>Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these <span class="hlt">Lagrangian</span> objects is a topic of intense current research. While established mathematical approaches such as variational methods or transfer-operator-based <span class="hlt">schemes</span> require full knowledge of the flow field or at least high-resolution trajectory data, this information may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from <span class="hlt">Lagrangian</span> trajectory data, that is, <span class="hlt">numerical</span> or measured time series of particle positions in a fluid flow. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where <span class="hlt">Lagrangian</span> particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting network. In particular, local network measures such as the node degree, the average degree of neighboring nodes, and the clustering coefficient serve as indicators of highly mixing regions, whereas spectral graph partitioning <span class="hlt">schemes</span> allow us to extract coherent sets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows - the Bickley jet as well as the Antarctic stratospheric polar vortex.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018GMD....11..575R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018GMD....11..575R"><span>Trajectory errors of different <span class="hlt">numerical</span> integration <span class="hlt">schemes</span> diagnosed with the MPTRAC advection module driven by ECMWF operational analyses</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rößler, Thomas; Stein, Olaf; Heng, Yi; Baumeister, Paul; Hoffmann, Lars</p> <p>2018-02-01</p> <p>The accuracy of trajectory calculations performed by <span class="hlt">Lagrangian</span> particle dispersion models (LPDMs) depends on various factors. The optimization of <span class="hlt">numerical</span> integration <span class="hlt">schemes</span> used to solve the trajectory equation helps to maximize the computational efficiency of large-scale LPDM simulations. We analyzed global truncation errors of six explicit integration <span class="hlt">schemes</span> of the Runge-Kutta family, which we implemented in the Massive-Parallel Trajectory Calculations (MPTRAC) advection module. The simulations were driven by wind fields from operational analysis and forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) at T1279L137 spatial resolution and 3 h temporal sampling. We defined separate test cases for 15 distinct regions of the atmosphere, covering the polar regions, the midlatitudes, and the tropics in the free troposphere, in the upper troposphere and lower stratosphere (UT/LS) region, and in the middle stratosphere. In total, more than 5000 different transport simulations were performed, covering the months of January, April, July, and October for the years 2014 and 2015. We quantified the accuracy of the trajectories by calculating transport deviations with respect to reference simulations using a fourth-order Runge-Kutta integration <span class="hlt">scheme</span> with a sufficiently fine time step. Transport deviations were assessed with respect to error limits based on turbulent diffusion. Independent of the <span class="hlt">numerical</span> <span class="hlt">scheme</span>, the global truncation errors vary significantly between the different regions. Horizontal transport deviations in the stratosphere are typically an order of magnitude smaller compared with the free troposphere. We found that the truncation errors of the six <span class="hlt">numerical</span> <span class="hlt">schemes</span> fall into three distinct groups, which mostly depend on the <span class="hlt">numerical</span> order of the <span class="hlt">scheme</span>. <span class="hlt">Schemes</span> of the same order differ little in accuracy, but some methods need less computational time, which gives them an advantage in efficiency. The selection of the integration</p> </li> <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 <span class="hlt">numerical</span> points of view. The formulation offers accuracy in <span class="hlt">numerical</span> solution by avoiding <span class="hlt">numerical</span> diffusion resulting from mixing of fluxes in the Eulerian 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('http://hdl.handle.net/2060/19830020667','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19830020667"><span><span class="hlt">Numerical</span> viscosity and the entropy condition for conservative difference <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Tadmor, E.</p> <p>1983-01-01</p> <p>Consider a scalar, nonlinear conservative difference <span class="hlt">scheme</span> satisfying the entropy condition. It is shown that difference <span class="hlt">schemes</span> containing more <span class="hlt">numerical</span> viscosity will necessarily converge to the unique, physically relevant weak solution of the approximated conservation equation. In particular, entropy satisfying convergence follows for E <span class="hlt">schemes</span> - those containing more <span class="hlt">numerical</span> viscosity than Godunov's <span class="hlt">scheme</span>.</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 <span class="hlt">scheme</span> is comparedmore » against an Eulerian scalar transport <span class="hlt">scheme</span>. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based Eulerian 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 Eulerian 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> </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('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 <span class="hlt">scheme</span> is comparedmore » against an Eulerian scalar transport <span class="hlt">scheme</span>. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based Eulerian 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 Eulerian 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('http://adsabs.harvard.edu/abs/2015GMD.....8.3247C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015GMD.....8.3247C"><span>A semi-<span class="hlt">Lagrangian</span> advection <span class="hlt">scheme</span> for radioactive tracers in the NCEP Regional Spectral Model (RSM)</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chang, E.-C.; Yoshimura, K.</p> <p>2015-10-01</p> <p>In this study, the non-iteration dimensional-split semi-<span class="hlt">Lagrangian</span> (NDSL) advection <span class="hlt">scheme</span> is applied to the National Centers for Environmental Prediction (NCEP) Regional Spectral Model (RSM) to alleviate the Gibbs phenomenon. The Gibbs phenomenon is a problem wherein negative values of positive-definite quantities (e.g., moisture and tracers) are generated by the spectral space transformation in a spectral model system. To solve this problem, the spectral prognostic specific humidity and radioactive tracer advection <span class="hlt">scheme</span> is replaced by the NDSL advection <span class="hlt">scheme</span>, which considers advection of tracers in a grid system without spectral space transformations. A regional version of the NDSL is developed in this study and is applied to the RSM. Idealized experiments show that the regional version of the NDSL is successful. The model runs for an actual case study suggest that the NDSL can successfully advect radioactive tracers (iodine-131 and cesium-137) without noise from the Gibbs phenomenon. The NDSL can also remove negative specific humidity values produced in spectral calculations without losing detailed features.</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> Eulerian 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 <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> demand for the solution as well as for the handling of mesh distortions. The two <span class="hlt">numerical</span> 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> Eulerian (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 Eulerian 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 <span class="hlt">numerical</span> simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and <span class="hlt">numerical</span> 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('https://www.osti.gov/biblio/21592603-fast-numerical-scheme-causal-relativistic-hydrodynamics-dissipation','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/21592603-fast-numerical-scheme-causal-relativistic-hydrodynamics-dissipation"><span>A fast <span class="hlt">numerical</span> <span class="hlt">scheme</span> for causal relativistic hydrodynamics with dissipation</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>Takamoto, Makoto, E-mail: takamoto@tap.scphys.kyoto-u.ac.jp; Inutsuka, Shu-ichiro</p> <p>2011-08-01</p> <p>Highlights: {yields} We have developed a new multi-dimensional <span class="hlt">numerical</span> <span class="hlt">scheme</span> for causal relativistic hydrodynamics with dissipation. {yields} Our new <span class="hlt">scheme</span> can calculate the evolution of dissipative relativistic hydrodynamics faster and more effectively than existing <span class="hlt">schemes</span>. {yields} Since we use the Riemann solver for solving the advection steps, our method can capture shocks very accurately. - Abstract: In this paper, we develop a stable and fast <span class="hlt">numerical</span> <span class="hlt">scheme</span> for relativistic dissipative hydrodynamics based on Israel-Stewart theory. Israel-Stewart theory is a stable and causal description of dissipation in relativistic hydrodynamics although it includes relaxation process with the timescale for collision of constituentmore » particles, which introduces stiff equations and makes practical <span class="hlt">numerical</span> calculation difficult. In our new <span class="hlt">scheme</span>, we use Strang's splitting method, and use the piecewise exact solutions for solving the extremely short timescale problem. In addition, since we split the calculations into inviscid step and dissipative step, Riemann solver can be used for obtaining <span class="hlt">numerical</span> flux for the inviscid step. The use of Riemann solver enables us to capture shocks very accurately. Simple <span class="hlt">numerical</span> examples are shown. The present <span class="hlt">scheme</span> can be applied to various high energy phenomena of astrophysics and nuclear physics.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920016575&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=19920016575&hterms=fun&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfun"><span>High order parallel <span class="hlt">numerical</span> <span class="hlt">schemes</span> for solving incompressible flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lin, Avi; Milner, Edward J.; Liou, May-Fun; Belch, Richard A.</p> <p>1992-01-01</p> <p>The use of parallel computers for <span class="hlt">numerically</span> solving flow fields has gained much importance in recent years. This paper introduces a new high order <span class="hlt">numerical</span> <span class="hlt">scheme</span> for computational fluid dynamics (CFD) specifically designed for parallel computational environments. A distributed MIMD system gives the flexibility of treating different elements of the governing equations with totally different <span class="hlt">numerical</span> <span class="hlt">schemes</span> in different regions of the flow field. The parallel decomposition of the governing operator to be solved is the primary parallel split. The primary parallel split was studied using a hypercube like architecture having clusters of shared memory processors at each node. The approach is demonstrated using examples of simple steady state incompressible flows. Future studies should investigate the secondary split because, depending on the <span class="hlt">numerical</span> <span class="hlt">scheme</span> that each of the processors applies and the nature of the flow in the specific subdomain, it may be possible for a processor to seek better, or higher order, <span class="hlt">schemes</span> for its particular subcase.</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 <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> implementation assumptions on predicting blood damage in cardiovascular devices using <span class="hlt">Lagrangian</span> methods with Eulerian 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 <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> implementation assumptions on predicting blood damage in cardiovascular devices using <span class="hlt">Lagrangian</span> methods with Eulerian 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> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CG.....89..200T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CG.....89..200T"><span>A majorized Newton-CG augmented <span class="hlt">Lagrangian</span>-based finite element method for 3D restoration of geological models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia</p> <p>2016-04-01</p> <p>In this paper, we propose a majorized Newton-CG augmented <span class="hlt">Lagrangian</span>-based finite element method for 3D elastic frictionless contact problems. In this <span class="hlt">scheme</span>, we discretize the restoration problem via the finite element method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented <span class="hlt">Lagrangian</span> method to solve the optimization problem, which is very suitable for the ill-conditioned case. <span class="hlt">Numerical</span> results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults.</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 <span class="hlt">schemes</span> for both Eulerian and <span class="hlt">Lagrangian</span> variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint Eulerian-<span class="hlt">Lagrangian</span> Bayesian data assimilation <span class="hlt">scheme</span>. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of Eulerian 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/2008CNSNS..13.2071W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008CNSNS..13.2071W"><span>A deterministic <span class="hlt">Lagrangian</span> particle separation-based method for advective-diffusion problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wong, Ken T. M.; Lee, Joseph H. W.; Choi, K. W.</p> <p>2008-12-01</p> <p>A simple and robust <span class="hlt">Lagrangian</span> particle <span class="hlt">scheme</span> is proposed to solve the advective-diffusion transport problem. The <span class="hlt">scheme</span> is based on relative diffusion concepts and simulates diffusion by regulating particle separation. This new approach generates a deterministic result and requires far less number of particles than the random walk method. For the advection process, particles are simply moved according to their velocity. The general <span class="hlt">scheme</span> is mass conservative and is free from <span class="hlt">numerical</span> diffusion. It can be applied to a wide variety of advective-diffusion problems, but is particularly suited for ecological and water quality modelling when definition of particle attributes (e.g., cell status for modelling algal blooms or red tides) is a necessity. The basic derivation, <span class="hlt">numerical</span> stability and practical implementation of the NEighborhood Separation Technique (NEST) are presented. The accuracy of the method is demonstrated through a series of test cases which embrace realistic features of coastal environmental transport problems. Two field application examples on the tidal flushing of a fish farm and the dynamics of vertically migrating marine algae are also presented.</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</span>-Eulerian ADER-WENO finite volume <span class="hlt">scheme</span> 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</span>-Eulerian (ALE) one-step ADER-WENO finite volume <span class="hlt">schemes</span> 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 <span class="hlt">scheme</span> 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 <span class="hlt">schemes</span> to the 3D Euler equations of compressible gas dynamics, for which a set of classical <span class="hlt">numerical</span> 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://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 Eulerian 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 <span class="hlt">scheme</span> 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 Eulerian 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 <span class="hlt">scheme</span> 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('https://www.ncbi.nlm.nih.gov/pubmed/28726683','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28726683"><span>Canonical-ensemble extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics for the linear scaling density functional theory.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hirakawa, Teruo; Suzuki, Teppei; Bowler, David R; Miyazaki, Tsuyoshi</p> <p>2017-10-11</p> <p>We discuss the development and implementation of a constant temperature (NVT) molecular dynamics <span class="hlt">scheme</span> that combines the Nosé-Hoover chain thermostat with the extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics (BOMD) <span class="hlt">scheme</span>, using a linear scaling density functional theory (DFT) approach. An integration <span class="hlt">scheme</span> for this canonical-ensemble extended <span class="hlt">Lagrangian</span> BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended <span class="hlt">Lagrangian</span> BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration <span class="hlt">scheme</span>. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.</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 <span class="hlt">scheme</span> to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS <span class="hlt">scheme</span> for seakeeping simulations is presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22617150-mean-field-type-control-congestion-ii-augmented-lagrangian-method','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22617150-mean-field-type-control-congestion-ii-augmented-lagrangian-method"><span>Mean Field Type Control with Congestion (II): An Augmented <span class="hlt">Lagrangian</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>Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Laurière, Mathieu</p> <p></p> <p>This work deals with a <span class="hlt">numerical</span> method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on <span class="hlt">numerical</span> methods: a monotone finite difference <span class="hlt">scheme</span> is proposed and shown to have a variational interpretation. Then an Alternating Direction Method of Multipliers for solving the variational problem is addressed. It is based on an augmented <span class="hlt">Lagrangian</span>. Two kinds of boundary conditionsmore » are considered: periodic conditions and more realistic boundary conditions associated to state constrained problems. Various test cases and <span class="hlt">numerical</span> results are presented.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19880002950','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19880002950"><span><span class="hlt">Numerical</span> experiments with a symmetric high-resolution shock-capturing <span class="hlt">scheme</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Yee, H. C.</p> <p>1986-01-01</p> <p>Characteristic-based explicit and implicit total variation diminishing (TVD) <span class="hlt">schemes</span> for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD <span class="hlt">schemes</span> other than Lax-Wendroff. The Roe and Davis <span class="hlt">schemes</span> can be viewed as a subset of the class of explicit methods. The main properties of the present class of <span class="hlt">schemes</span> are that they can be implicit, and, when steady-state calculations are sought, the <span class="hlt">numerical</span> solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD <span class="hlt">scheme</span> with an implicit upwind TVD <span class="hlt">scheme</span> originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more <span class="hlt">numerical</span> experiments are being conducted on time-accurate calculations and on the effect of grid topology, <span class="hlt">numerical</span> boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of <span class="hlt">scheme</span> and give guidelines for its use.</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 <span class="hlt">numerical</span> points of view. The formulation offers accuracy in <span class="hlt">numerical</span> solution by avoiding <span class="hlt">numerical</span> diffusion resulting from mixing of fluxes in the Eulerian 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://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=47068&Lab=NERL&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=47068&Lab=NERL&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>COMPARISON OF <span class="hlt">NUMERICAL</span> <span class="hlt">SCHEMES</span> FOR SOLVING A SPHERICAL PARTICLE 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>A new robust iterative <span class="hlt">numerical</span> <span class="hlt">scheme</span> was developed for a nonlinear diffusive model that described sorption dynamics in spherical particle suspensions. he <span class="hlt">numerical</span> <span class="hlt">scheme</span> had been applied to finite difference and finite element models that showed rapid convergence and stabilit...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950014634','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950014634"><span>A <span class="hlt">Lagrangian</span> dynamic subgrid-scale model turbulence</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Meneveau, C.; Lund, T. S.; Cabot, W.</p> <p>1994-01-01</p> <p>A new formulation of the dynamic subgrid-scale model is tested in which the error associated with the Germano identity is minimized over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to flows in complex geometries that do not possess homogeneous directions. The characteristic <span class="hlt">Lagrangian</span> time scale over which the averaging is performed is chosen such that the model is purely dissipative, guaranteeing <span class="hlt">numerical</span> stability when coupled with the Smagorinsky model. The formulation is tested successfully in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are superior to those of the plane-averaged dynamic model. The relationship between the averaged terms in the model and vortical structures (worms) that appear in the LES is investigated. Computational overhead is kept small (about 10 percent above the CPU requirements of the volume or plane-averaged dynamic model) by using an approximate <span class="hlt">scheme</span> to advance the <span class="hlt">Lagrangian</span> tracking through first-order Euler time integration and linear interpolation in space.</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('http://adsabs.harvard.edu/abs/2018E%26ES..121e2019W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018E%26ES..121e2019W"><span><span class="hlt">Numerical</span> study on flow over stepped spillway using <span class="hlt">Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wang, Junmin; Fu, Lei; Xu, Haibo; Jin, Yeechung</p> <p>2018-02-01</p> <p>Flow over stepped spillway has been studied for centuries, due to its unstable and the characteristics of cavity, the simulation of this type of spillway flow is always difficult. Most of the early studies of flow over stepped spillway are based on experiment, while in the recent decades, <span class="hlt">numerical</span> studies of flow over stepped spillway draw most of the researchers’ attentions due to its simplicity and efficiency. In this study, a new <span class="hlt">Lagrangian</span> based particle method is introduced to reproduce the phenomenon of flow over stepped spillway, the inherent advantages of this particle based method provide a convincing free surface and velocity profiles compared with previous experimental data. The capacity of this new method is proved and it is anticipated to be an alternative tool of traditional mesh based method in environmental engineering field such as the simulation of flow over stepped spillway.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018ResPh...9.1161G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018ResPh...9.1161G"><span><span class="hlt">Numerical</span> solution of special ultra-relativistic Euler equations using central upwind <span class="hlt">scheme</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul</p> <p>2018-06-01</p> <p>This article is concerned with the <span class="hlt">numerical</span> approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind <span class="hlt">scheme</span> is employed to solve the model equations. To avoid excessive <span class="hlt">numerical</span> diffusion, the considered <span class="hlt">scheme</span> avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed <span class="hlt">scheme</span>. After discussing the model equations and the <span class="hlt">numerical</span> technique, several 1D and 2D test problems are investigated. For all the <span class="hlt">numerical</span> test cases, our proposed <span class="hlt">scheme</span> demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central <span class="hlt">scheme</span> and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind <span class="hlt">scheme</span> is demonstrated by the <span class="hlt">numerical</span> results.</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> <span class="hlt">scheme</span> or an Arbitrary <span class="hlt">Lagrangian</span> Eulerian <span class="hlt">scheme</span> (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 <span class="hlt">numerical</span> experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM code 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/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 <span class="hlt">scheme</span> 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> <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 <span class="hlt">numerical</span> points of view. The formulation offers accuracy in <span class="hlt">numerical</span> solution by avoiding <span class="hlt">numerical</span> diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary <span class="hlt">Lagrangian</span>-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline <span class="hlt">numerical</span> 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 code 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://hdl.handle.net/2060/20040031690','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040031690"><span>A Eulerian-<span class="hlt">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 Eulerian-<span class="hlt">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 Eulerian-<span class="hlt">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 <span class="hlt">numerical</span> <span class="hlt">scheme</span> for unstructured grids developed by Mahesh et al. (2003) for incompressible flows is modified to take into account the droplet volume fraction. The <span class="hlt">numerical</span> framework is directly applicable to realistic combustor geometries. Our main objectives in this work are: Develop a <span class="hlt">numerical</span> formulation based on Eulerian-<span class="hlt">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('https://ntrs.nasa.gov/search.jsp?R=20070003473&hterms=levels+law&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3DA%2Blevels%2Blaw','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20070003473&hterms=levels+law&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3DA%2Blevels%2Blaw"><span><span class="hlt">Numerical</span> <span class="hlt">Schemes</span> for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Barth, Timothy J.; Sethian, James A.</p> <p>1997-01-01</p> <p>Borrowing from techniques developed for conservation law equations, <span class="hlt">numerical</span> <span class="hlt">schemes</span> which discretize the Hamilton-Jacobi (H-J), level set, and Eikonal equations on triangulated domains are presented. The first <span class="hlt">scheme</span> is a provably monotone discretization for certain forms of the H-J equations. Unfortunately, the basic <span class="hlt">scheme</span> lacks proper Lipschitz continuity of the <span class="hlt">numerical</span> Hamiltonian. By employing a virtual edge flipping technique, Lipschitz continuity of the <span class="hlt">numerical</span> flux is restored on acute triangulations. Next, <span class="hlt">schemes</span> are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These <span class="hlt">schemes</span> possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the <span class="hlt">numerical</span> Hamiltonian. Finally, a class of Petrov-Galerkin approximations are considered. These <span class="hlt">schemes</span> are stabilized via a least-squares bilinear form. The Petrov-Galerkin <span class="hlt">schemes</span> do not possess a discrete maximum principle but generalize to high order accuracy.</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 <span class="hlt">scheme</span></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 <span class="hlt">numerical</span> 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> <span class="hlt">schemes</span> have evolved into Arbitrary <span class="hlt">Lagrangian</span>-Eulerian (ALE) methods [39] that combine the best properties of <span class="hlt">Lagrangian</span> and Eulerian 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 <span class="hlt">scheme</span> 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 <span class="hlt">numerical</span> 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('http://adsabs.harvard.edu/abs/2018JCoPh.354...67G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.354...67G"><span>Unconditionally energy stable <span class="hlt">numerical</span> <span class="hlt">schemes</span> for phase-field vesicle membrane model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Guillén-González, F.; Tierra, G.</p> <p>2018-02-01</p> <p><span class="hlt">Numerical</span> <span class="hlt">schemes</span> to simulate the deformation of vesicles membranes via minimizing the bending energy have been widely studied in recent times due to its connection with many biological motivated problems. In this work we propose a new unconditionally energy stable <span class="hlt">numerical</span> <span class="hlt">scheme</span> for a vesicle membrane model that satisfies exactly the conservation of volume constraint and penalizes the surface area constraint. Moreover, we extend these ideas to present an unconditionally energy stable splitting <span class="hlt">scheme</span> decoupling the interaction of the vesicle with a surrounding fluid. Finally, the well behavior of the proposed <span class="hlt">schemes</span> are illustrated through several computational experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1134155-asymptotic-preserving-lagrangian-algorithm-time-dependent-anisotropic-heat-transport-equation','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1134155-asymptotic-preserving-lagrangian-algorithm-time-dependent-anisotropic-heat-transport-equation"><span>An asymptotic-preserving <span class="hlt">Lagrangian</span> algorithm for the time-dependent anisotropic heat transport 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>Chacon, Luis; del-Castillo-Negrete, Diego; Hauck, Cory D.</p> <p>2014-09-01</p> <p>We propose a <span class="hlt">Lagrangian</span> <span class="hlt">numerical</span> algorithm for a time-dependent, anisotropic temperature transport equation in magnetized plasmas in the large guide field regime. The approach is based on an analytical integral formal solution of the parallel (i.e., along the magnetic field) transport equation with sources, and it is able to accommodate both local and non-local parallel heat flux closures. The <span class="hlt">numerical</span> implementation is based on an operator-split formulation, with two straightforward steps: a perpendicular transport step (including sources), and a <span class="hlt">Lagrangian</span> (field-line integral) parallel transport step. Algorithmically, the first step is amenable to the use of modern iterative methods, while themore » second step has a fixed cost per degree of freedom (and is therefore scalable). Accuracy-wise, the approach is free from the <span class="hlt">numerical</span> pollution introduced by the discrete parallel transport term when the perpendicular to parallel transport coefficient ratio X ⊥ /X ∥ becomes arbitrarily small, and is shown to capture the correct limiting solution when ε = X⊥L 2 ∥/X1L 2 ⊥ → 0 (with L∥∙ L⊥ , the parallel and perpendicular diffusion length scales, respectively). Therefore, the approach is asymptotic-preserving. We demonstrate the capabilities of the <span class="hlt">scheme</span> with several <span class="hlt">numerical</span> experiments with varying magnetic field complexity in two dimensions, including the case of transport across a magnetic island.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29255342','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29255342"><span>A SEMI-<span class="hlt">LAGRANGIAN</span> TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Mang, Andreas; Biros, George</p> <p>2017-01-01</p> <p>We propose an efficient <span class="hlt">numerical</span> algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-<span class="hlt">Lagrangian</span> time stepping <span class="hlt">scheme</span> for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov <span class="hlt">scheme</span>. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new <span class="hlt">scheme</span>. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta <span class="hlt">scheme</span> for the <span class="hlt">numerical</span> time integration of the transport equations and a single-level preconditioner. Our improved <span class="hlt">scheme</span> delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/16383461','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/16383461"><span>Cancellation exponent and multifractal structure in two-dimensional magnetohydrodynamics: direct <span class="hlt">numerical</span> simulations and <span class="hlt">Lagrangian</span> averaged modeling.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Graham, Jonathan Pietarila; Mininni, Pablo D; Pouquet, Annick</p> <p>2005-10-01</p> <p>We present direct <span class="hlt">numerical</span> simulations and <span class="hlt">Lagrangian</span> averaged (also known as alpha model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at small scales is studied using both the cancellation exponent and the fractal dimension of the structures. The alpha model is found to have the same scaling behavior between positive and negative contributions as the direct <span class="hlt">numerical</span> simulations. The alpha model is also able to reproduce the time evolution of these quantities in free decaying turbulence. At large Reynolds numbers, an independence of the cancellation exponent with the Reynolds numbers is observed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26575769','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26575769"><span>Extended <span class="hlt">Lagrangian</span> Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Aradi, Bálint; Niklasson, Anders M N; Frauenheim, Thomas</p> <p>2015-07-14</p> <p>A computationally fast quantum mechanical molecular dynamics <span class="hlt">scheme</span> using an extended <span class="hlt">Lagrangian</span> density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The <span class="hlt">scheme</span> combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics. For systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation <span class="hlt">scheme</span> can be applied to a broad range of problems in materials science, chemistry, and biology.</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 <span class="hlt">numerical</span> experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and <span class="hlt">numerically</span> 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/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 <span class="hlt">Numerical</span> 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 <span class="hlt">numerical</span> method combined the Eulerian 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/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 <span class="hlt">numerical</span> experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and <span class="hlt">numerically</span> 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/2006CompM..38..294A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006CompM..38..294A"><span>Fractional Step Like <span class="hlt">Schemes</span> for Free Surface Problems with Thermal Coupling Using the <span class="hlt">Lagrangian</span> PFEM</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Aubry, R.; Oñate, E.; Idelsohn, S. R.</p> <p>2006-09-01</p> <p>The method presented in Aubry et al. (Comput Struc 83:1459-1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully <span class="hlt">Lagrangian</span> description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505-526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a <span class="hlt">Lagrangian</span> description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. <span class="hlt">Numerical</span> results are provided to assess the superiority of the modified algebraic splitting to the classical FS.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1227099','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1227099"><span>Extended <span class="hlt">Lagrangian</span> Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids</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>Aradi, Bálint; Niklasson, Anders M. N.; Frauenheim, Thomas</p> <p></p> <p>A computationally fast quantum mechanical molecular dynamics <span class="hlt">scheme</span> using an extended <span class="hlt">Lagrangian</span> density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The <span class="hlt">scheme</span> combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended <span class="hlt">Lagrangian</span> Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation <span class="hlt">scheme</span> can also be applied to a broad range of problems in materialsmore » science, chemistry, and biology.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1227099-extended-lagrangian-density-functional-tight-binding-molecular-dynamics-molecules-solids','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1227099-extended-lagrangian-density-functional-tight-binding-molecular-dynamics-molecules-solids"><span>Extended <span class="hlt">Lagrangian</span> Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Aradi, Bálint; Niklasson, Anders M. N.; Frauenheim, Thomas</p> <p>2015-06-26</p> <p>A computationally fast quantum mechanical molecular dynamics <span class="hlt">scheme</span> using an extended <span class="hlt">Lagrangian</span> density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The <span class="hlt">scheme</span> combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended <span class="hlt">Lagrangian</span> Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation <span class="hlt">scheme</span> can also be applied to a broad range of problems in materialsmore » science, chemistry, and biology.« less</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</span>-Eulerian) multi-material finite element code 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 <span class="hlt">numerical</span> implementation of the Alegra continuum hydrodynamics algorithm.</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://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> <span class="hlt">numerical</span> <span class="hlt">scheme</span> is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian 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('http://adsabs.harvard.edu/abs/2008JCoAM.218..270T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008JCoAM.218..270T"><span><span class="hlt">Numerical</span> pricing of options using high-order compact finite difference <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tangman, D. Y.; Gopaul, A.; Bhuruth, M.</p> <p>2008-09-01</p> <p>We consider high-order compact (HOC) <span class="hlt">schemes</span> for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the <span class="hlt">numerical</span> pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC <span class="hlt">schemes</span> attain clear fourth-order convergence but fail if non-smooth payoff conditions are used. To restore the fourth-order convergence, we use a grid stretching that concentrates grid nodes at the strike price for European options. For an American option, an efficient procedure is also described to compute the option price, Greeks and the optimal exercise curve. Comparisons with a fourth-order non-compact <span class="hlt">scheme</span> are also done. However, fourth-order convergence is not experienced with this strategy. To improve the convergence rate for American options, we discuss the use of a front-fixing transformation with the HOC <span class="hlt">scheme</span>. We also show that the HOC <span class="hlt">scheme</span> with grid stretching along the asset price dimension gives accurate <span class="hlt">numerical</span> solutions for European options under stochastic volatility.</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 <span class="hlt">scheme</span> 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('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> <span class="hlt">schemes</span> are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eulerian solutions available for simplified FDMs. <span class="hlt">Numerical</span> 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://pubs.er.usgs.gov/publication/70177969','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70177969"><span>Bounded fractional diffusion in geological media: Definition and <span class="hlt">Lagrangian</span> approximation</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang</p> <p>2016-01-01</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 non-zero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing non-zero-value spatial-nonlocal boundary conditions with directional super-diffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New <span class="hlt">Lagrangian</span> <span class="hlt">schemes</span> are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or Eularian solutions available for simplified FDMs. <span class="hlt">Numerical</span> 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 non-local and non-symmetric fractional diffusion. For a non-zero-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 do mains to those with any size and boundary conditions.</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 Eulerian 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 Eulerian grid. The markers are not stored and the <span class="hlt">Lagrangian</span> data-structure is not modified. The proposed <span class="hlt">scheme</span> 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/2017AGUFM.A22E..06K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A22E..06K"><span><span class="hlt">Lagrangian</span> Particle Tracking Simulation for Warm-Rain Processes in Quasi-One-Dimensional Domain</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kunishima, Y.; Onishi, R.</p> <p>2017-12-01</p> <p>Conventional cloud simulations are based on the Euler method and compute each microphysics process in a stochastic way assuming infinite numbers of particles within each <span class="hlt">numerical</span> grid. They therefore cannot provide the <span class="hlt">Lagrangian</span> statistics of individual particles in cloud microphysics (i.e., aerosol particles, cloud particles, and rain drops) nor discuss the statistical fluctuations due to finite number of particles. We here simulate the entire precipitation process of warm-rain, with tracking individual particles. We use the <span class="hlt">Lagrangian</span> Cloud Simulator (LCS), which is based on the Euler-<span class="hlt">Lagrangian</span> framework. In that framework, flow motion and scalar transportation are computed with the Euler method, and particle motion with the <span class="hlt">Lagrangian</span> one. The LCS tracks particle motions and collision events individually with considering the hydrodynamic interaction between approaching particles with a superposition method, that is, it can directly represent the collisional growth of cloud particles. It is essential for trustworthy collision detection to take account of the hydrodynamic interaction. In this study, we newly developed a stochastic model based on the Twomey cloud condensation nuclei (CCN) activation for the <span class="hlt">Lagrangian</span> tracking simulation and integrated it into the LCS. Coupling with the Euler computation for water vapour and temperature fields, the initiation and condensational growth of water droplets were computed in the <span class="hlt">Lagrangian</span> way. We applied the integrated LCS for a kinematic simulation of warm-rain processes in a vertically-elongated domain of, at largest, 0.03×0.03×3000 (m3) with horizontal periodicity. Aerosol particles with a realistic number density, 5×107 (m3), were evenly distributed over the domain at the initial state. Prescribed updraft at the early stage initiated development of a precipitating cloud. We have confirmed that the obtained bulk statistics fairly agree with those from a conventional spectral-bin <span class="hlt">scheme</span> for a vertical column</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 Eulerian 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 <span class="hlt">scheme</span> where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in Eulerian bin microphysics <span class="hlt">schemes</span>. 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('http://adsabs.harvard.edu/abs/2014EGUGA..1613316G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..1613316G"><span>Eulerian <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> linear system on adaptive grid because each Fup coefficient is obtained by predefined formulas equalizing Fup expansion around corresponding collocation point and particular collocation operator based on few surrounding solution values. Furthermore, each Fup coefficient can be obtained independently which is perfectly suited for parallel processing. Adaptive grid in each time step is obtained from solution of the last time step or initial conditions and advective <span class="hlt">Lagrangian</span> step in the current time step according to the velocity field and continuous streamlines. On the other side, we implement explicit stabilized routine SERK2 for dispersive Eulerian part of solution in the current time step on obtained spatial adaptive grid. Overall adaptive concept does not require the solving of large linear systems for the spatial and temporal approximation of conservative transport. Also, this new Eulerian-<span class="hlt">Lagrangian</span>-Collocation <span class="hlt">scheme</span> resolves all mentioned <span class="hlt">numerical</span> problems due to its adaptive nature and ability to control <span class="hlt">numerical</span> errors in space and time. Proposed method solves advection in <span class="hlt">Lagrangian</span> way eliminating problems in Eulerian methods, while optimal collocation grid efficiently describes solution and boundary conditions eliminating usage of large number of particles and other problems in <span class="hlt">Lagrangian</span> methods. Finally, <span class="hlt">numerical</span> tests show that this approach enables not only accurate velocity field, but also conservative transport even in highly heterogeneous porous media resolving all spatial and temporal scales of concentration field.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900019812','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900019812"><span><span class="hlt">Numerical</span> experiments on the accuracy of ENO and modified ENO <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shu, Chi-Wang</p> <p>1990-01-01</p> <p>Further <span class="hlt">numerical</span> experiments are made assessing an accuracy degeneracy phenomena. A modified essentially non-oscillatory (ENO) <span class="hlt">scheme</span> is proposed, which recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives comparable results with the original ENO <span class="hlt">schemes</span> for discontinuous problems.</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 <span class="hlt">numerical</span> investigations of such problems use an Eulerian formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an Eulerian reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the Eulerian and <span class="hlt">Lagrangian</span> computational techniques.</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 <span class="hlt">scheme</span>, 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 Eulerian formulation, but at higher z the Eulerian 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 <span class="hlt">scheme</span>, 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 Eulerian formulation, but at higher z the Eulerian 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 <span class="hlt">scheme</span>, 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 Eulerian formulation, but at higher z the Eulerian 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/pages/biblio/1369441-lagrangian-particle-method-remeshing-tracer-transport-sphere','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1369441-lagrangian-particle-method-remeshing-tracer-transport-sphere"><span>A <span class="hlt">Lagrangian</span> particle method with remeshing for tracer transport on the sphere</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Bosler, Peter Andrew; Kent, James; Krasny, Robert; ...</p> <p>2017-03-30</p> <p>A <span class="hlt">Lagrangian</span> particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular <span class="hlt">Lagrangian</span> panels. Remeshing is applied to control particle disorder and two <span class="hlt">schemes</span> are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume <span class="hlt">scheme</span>. An adaptive particle/panel refinement <span class="hlt">scheme</span> is demonstrated.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1369441','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1369441"><span>A <span class="hlt">Lagrangian</span> particle method with remeshing for tracer transport on the sphere</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>Bosler, Peter Andrew; Kent, James; Krasny, Robert</p> <p></p> <p>A <span class="hlt">Lagrangian</span> particle method (called LPM) based on the flow map is presented for tracer transport on the sphere. The particles carry tracer values and are located at the centers and vertices of triangular <span class="hlt">Lagrangian</span> panels. Remeshing is applied to control particle disorder and two <span class="hlt">schemes</span> are compared, one using direct tracer interpolation and another using inverse flow map interpolation with sampling of the initial tracer density. Test cases include a moving-vortices flow and reversing-deformational flow with both zero and nonzero divergence, as well as smooth and discontinuous tracers. We examine the accuracy of the computed tracer density and tracermore » integral, and preservation of nonlinear correlation in a pair of tracers. Here, we compare results obtained using LPM and the Lin–Rood finite-volume <span class="hlt">scheme</span>. An adaptive particle/panel refinement <span class="hlt">scheme</span> is demonstrated.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015SSEle.114...80K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015SSEle.114...80K"><span><span class="hlt">Numerical</span> study of read <span class="hlt">scheme</span> in one-selector one-resistor crossbar array</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kim, Sungho; Kim, Hee-Dong; Choi, Sung-Jin</p> <p>2015-12-01</p> <p>A comprehensive <span class="hlt">numerical</span> circuit analysis of read <span class="hlt">schemes</span> of a one selector-one resistance change memory (1S1R) crossbar array is carried out. Three <span class="hlt">schemes</span>-the ground, V/2, and V/3 <span class="hlt">schemes</span>-are compared with each other in terms of sensing margin and power consumption. Without the aid of a complex analytical approach or SPICE-based simulation, a simple <span class="hlt">numerical</span> iteration method is developed to simulate entire current flows and node voltages within a crossbar array. Understanding such phenomena is essential in successfully evaluating the electrical specifications of selectors for suppressing intrinsic drawbacks of crossbar arrays, such as sneaky current paths and series line resistance problems. This method provides a quantitative tool for the accurate analysis of crossbar arrays and provides guidelines for developing an optimal read <span class="hlt">scheme</span>, array configuration, and selector device specifications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1996IJMPA..11.1353B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1996IJMPA..11.1353B"><span>On the Perturbative Equivalence Between the Hamiltonian and <span class="hlt">Lagrangian</span> Quantizations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Batalin, I. A.; Tyutin, I. V.</p> <p></p> <p>The Hamiltonian (BFV) and <span class="hlt">Lagrangian</span> (BV) quantization <span class="hlt">schemes</span> are proved to be perturbatively equivalent to each other. It is shown in particular that the quantum master equation being treated perturbatively possesses a local formal solution.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1411348-compatible-energy-conserving-bounds-preserving-remap-hydrodynamic-fields-extended-ale-scheme','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1411348-compatible-energy-conserving-bounds-preserving-remap-hydrodynamic-fields-extended-ale-scheme"><span>Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE <span class="hlt">scheme</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Burton, Donald E.; Morgan, Nathaniel Ray; Charest, Marc Robert Joseph; ...</p> <p>2017-11-22</p> <p>From the very origins of <span class="hlt">numerical</span> 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> <span class="hlt">schemes</span> have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of <span class="hlt">Lagrangian</span> and Eulerian 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 <span class="hlt">scheme</span> that is extended in the sense thatmore » 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. Particularly, 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. Our paper presents a derivation of the methods, details of implementation, and <span class="hlt">numerical</span> 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.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1411348-compatible-energy-conserving-bounds-preserving-remap-hydrodynamic-fields-extended-ale-scheme','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1411348-compatible-energy-conserving-bounds-preserving-remap-hydrodynamic-fields-extended-ale-scheme"><span>Compatible, energy conserving, bounds preserving remap of hydrodynamic fields for an extended ALE <span class="hlt">scheme</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>Burton, Donald E.; Morgan, Nathaniel Ray; Charest, Marc Robert Joseph</p> <p></p> <p>From the very origins of <span class="hlt">numerical</span> 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> <span class="hlt">schemes</span> have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of <span class="hlt">Lagrangian</span> and Eulerian 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 <span class="hlt">scheme</span> that is extended in the sense thatmore » 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. Particularly, 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. Our paper presents a derivation of the methods, details of implementation, and <span class="hlt">numerical</span> 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.« 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_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/2060/20040161131','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040161131"><span>Adaptive <span class="hlt">Numerical</span> Dissipative Control in High Order <span class="hlt">Schemes</span> for Multi-D Non-Ideal MHD</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Yee, H. C.; Sjoegreen, B.</p> <p>2004-01-01</p> <p>The goal is to extend our adaptive <span class="hlt">numerical</span> dissipation control in high order filter <span class="hlt">schemes</span> and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of <span class="hlt">numerical</span> dissipation/filter where needed and leave the rest of the region free of <span class="hlt">numerical</span> dissipation contamination. These <span class="hlt">scheme</span>-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) <span class="hlt">numerical</span> error. The filter <span class="hlt">scheme</span> consists of spatially sixth order or higher non-dissipative spatial difference operators as the base <span class="hlt">scheme</span> for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base <span class="hlt">scheme</span>. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base <span class="hlt">scheme</span> step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing <span class="hlt">scheme</span>. In addition, the <span class="hlt">scheme</span> independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base <span class="hlt">schemes</span>. The ACM and wavelet filter <span class="hlt">schemes</span> using the dissipative portion of a second-order shock-capturing <span class="hlt">scheme</span> with sixth-order spatial central base <span class="hlt">scheme</span> for both the inviscid and viscous MHD flux</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018ResPh...9.1411G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018ResPh...9.1411G"><span>An efficient <span class="hlt">numerical</span> <span class="hlt">scheme</span> for the study of equal width equation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ghafoor, Abdul; Haq, Sirajul</p> <p>2018-06-01</p> <p>In this work a new <span class="hlt">numerical</span> <span class="hlt">scheme</span> is proposed in which Haar wavelet method is coupled with finite difference <span class="hlt">scheme</span> for the solution of a nonlinear partial differential equation. The <span class="hlt">scheme</span> transforms the partial differential equation to a system of algebraic equations which can be solved easily. The technique is applied to equal width equation in order to study the behaviour of one, two, three solitary waves, undular bore and soliton collision. For efficiency and accuracy of the <span class="hlt">scheme</span>, L2 and L∞ norms and invariants are computed. The results obtained are compared with already existing results in literature.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930041272&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=19930041272&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian"><span>A global multilevel atmospheric model using a vector semi-<span class="hlt">Lagrangian</span> finite-difference <span class="hlt">scheme</span>. I - Adiabatic formulation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bates, J. R.; Moorthi, S.; Higgins, R. W.</p> <p>1993-01-01</p> <p>An adiabatic global multilevel primitive equation model using a two time-level, semi-<span class="hlt">Lagrangian</span> semi-implicit finite-difference integration <span class="hlt">scheme</span> is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009PhFl...21f5101K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009PhFl...21f5101K"><span><span class="hlt">Lagrangian</span> particles with mixing. I. Simulating scalar transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Klimenko, A. Y.</p> <p>2009-06-01</p> <p>The physical similarity and mathematical equivalence of continuous diffusion and particle random walk forms one of the cornerstones of modern physics and the theory of stochastic processes. The randomly walking particles do not need to posses any properties other than location in physical space. However, particles used in many models dealing with simulating turbulent transport and turbulent combustion do posses a set of scalar properties and mixing between particle properties is performed to reflect the dissipative nature of the diffusion processes. We show that the continuous scalar transport and diffusion can be accurately specified by means of localized mixing between randomly walking <span class="hlt">Lagrangian</span> particles with scalar properties and assess errors associated with this <span class="hlt">scheme</span>. Particles with scalar properties and localized mixing represent an alternative formulation for the process, which is selected to represent the continuous diffusion. Simulating diffusion by <span class="hlt">Lagrangian</span> particles with mixing involves three main competing requirements: minimizing stochastic uncertainty, minimizing bias introduced by <span class="hlt">numerical</span> diffusion, and preserving independence of particles. These requirements are analyzed for two limited cases of mixing between two particles and mixing between a large number of particles. The problem of possible dependences between particles is most complicated. This problem is analyzed using a coupled chain of equations that has similarities with Bogolubov-Born-Green-Kirkwood-Yvon chain in statistical physics. Dependences between particles can be significant in close proximity of the particles resulting in a reduced rate of mixing. This work develops further ideas introduced in the previously published letter [Phys. Fluids 19, 031702 (2007)]. Paper I of this work is followed by Paper II [Phys. Fluids 19, 065102 (2009)] where modeling of turbulent reacting flows by <span class="hlt">Lagrangian</span> particles with localized mixing is specifically considered.</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 <span class="hlt">numerically</span> solve the convective term of the convection-diffusion equation and provides significant <span class="hlt">numerical</span> advantages over the more commonly used Eulerian 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/2014CNSNS..19.1836T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CNSNS..19.1836T"><span>Building fast well-balanced two-stage <span class="hlt">numerical</span> <span class="hlt">schemes</span> for a model of two-phase flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Thanh, Mai Duc</p> <p>2014-06-01</p> <p>We present a set of well-balanced two-stage <span class="hlt">schemes</span> for an isentropic model of two-phase flows arisen from the modeling of deflagration-to-detonation transition in granular materials. The first stage is to absorb the source term in nonconservative form into equilibria. Then in the second stage, these equilibria will be composed into a <span class="hlt">numerical</span> flux formed by using a convex combination of the <span class="hlt">numerical</span> flux of a stable Lax-Friedrichs-type <span class="hlt">scheme</span> and the one of a higher-order Richtmyer-type <span class="hlt">scheme</span>. <span class="hlt">Numerical</span> <span class="hlt">schemes</span> constructed in such a way are expected to get the interesting property: they are fast and stable. Tests show that the method works out until the parameter takes on the value CFL, and so any value of the parameter between zero and this value is expected to work as well. All the <span class="hlt">schemes</span> in this family are shown to capture stationary waves and preserves the positivity of the volume fractions. The special values of the parameter 0,1/2,1/(1+CFL), and CFL in this family define the Lax-Friedrichs-type, FAST1, FAST2, and FAST3 <span class="hlt">schemes</span>, respectively. These <span class="hlt">schemes</span> are shown to give a desirable accuracy. The errors and the CPU time of these <span class="hlt">schemes</span> and the Roe-type <span class="hlt">scheme</span> are calculated and compared. The constructed <span class="hlt">schemes</span> are shown to be well-balanced and faster than the Roe-type <span class="hlt">scheme</span>.</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>Eulerian-<span class="hlt">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 <span class="hlt">numerical</span> investigations of transport phenomena use an Eulerian formulation for the convenience that the computational grids are fixed in space. An Eulerian-<span class="hlt">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 Eulerian 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 <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> examples are given to further substantiate the results of the present analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20010066844&hterms=sensitivity+scale&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsensitivity%2Bscale','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20010066844&hterms=sensitivity+scale&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsensitivity%2Bscale"><span>Sensitivity of Age-of-Air Calculations to the Choice of Advection <span class="hlt">Scheme</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Eluszkiewicz, Janusz; Hemler, Richard S.; Mahlman, Jerry D.; Bruhwiler, Lori; Takacs, Lawrence L.</p> <p>2000-01-01</p> <p>The age of air has recently emerged as a diagnostic of atmospheric transport unaffected by chemical parameterizations, and the features in the age distributions computed in models have been interpreted in terms of the models' large-scale circulation field. This study shows, however, that in addition to the simulated large-scale circulation, three-dimensional age calculations can also be affected by the choice of advection <span class="hlt">scheme</span> employed in solving the tracer continuity equation, Specifically, using the 3.0deg latitude X 3.6deg longitude and 40 vertical level version of the Geophysical Fluid Dynamics Laboratory SKYHI GCM and six online transport <span class="hlt">schemes</span> ranging from Eulerian through semi-<span class="hlt">Lagrangian</span> to fully <span class="hlt">Lagrangian</span>, it will be demonstrated that the oldest ages are obtained using the nondiffusive centered-difference <span class="hlt">schemes</span> while the youngest ages are computed with a semi-<span class="hlt">Lagrangian</span> transport (SLT) <span class="hlt">scheme</span>. The centered- difference <span class="hlt">schemes</span> are capable of producing ages older than 10 years in the mesosphere, thus eliminating the "young bias" found in previous age-of-air calculations. At this stage, only limited intuitive explanations can be advanced for this sensitivity of age-of-air calculations to the choice of advection <span class="hlt">scheme</span>, In particular, age distributions computed online with the National Center for Atmospheric Research Community Climate Model (MACCM3) using different varieties of the SLT <span class="hlt">scheme</span> are substantially older than the SKYHI SLT distribution. The different varieties, including a noninterpolating-in-the-vertical version (which is essentially centered-difference in the vertical), also produce a narrower range of age distributions than the suite of advection <span class="hlt">schemes</span> employed in the SKYHI model. While additional MACCM3 experiments with a wider range of <span class="hlt">schemes</span> would be necessary to provide more definitive insights, the older and less variable MACCM3 age distributions can plausibly be interpreted as being due to the semi-implicit semi-<span class="hlt">Lagrangian</span></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 Eulerian-<span class="hlt">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 Eulerian-<span class="hlt">Lagrangian</span> approach, are discussed. In the first part of this paper the results of <span class="hlt">numerical</span> analyses for an explicit Eulerian-<span class="hlt">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 <span class="hlt">scheme</span>. 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 Eulerian-<span class="hlt">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. <span class="hlt">Numerical</span> results support properties given by the stability and error analyses. ?? 1990.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21045898','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21045898"><span>A <span class="hlt">numerical</span> <span class="hlt">scheme</span> for nonlinear Helmholtz equations with strong nonlinear optical effects.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Xu, Zhengfu; Bao, Gang</p> <p>2010-11-01</p> <p>A <span class="hlt">numerical</span> <span class="hlt">scheme</span> is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, <span class="hlt">numerical</span> methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable <span class="hlt">numerical</span> <span class="hlt">scheme</span> is designed to simulate the NLH equations with strong nonlinearity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010WRR....4610510C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010WRR....4610510C"><span>Ancient <span class="hlt">numerical</span> daemons of conceptual hydrological modeling: 1. Fidelity and efficiency of time stepping <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Clark, Martyn P.; Kavetski, Dmitri</p> <p>2010-10-01</p> <p>A major neglected weakness of many current hydrological models is the <span class="hlt">numerical</span> method used to solve the governing model equations. This paper thoroughly evaluates several classes of time stepping <span class="hlt">schemes</span> in terms of <span class="hlt">numerical</span> reliability and computational efficiency in the context of conceptual hydrological modeling. <span class="hlt">Numerical</span> experiments are carried out using 8 distinct time stepping algorithms and 6 different conceptual rainfall-runoff models, applied in a densely gauged experimental catchment, as well as in 12 basins with diverse physical and hydroclimatic characteristics. Results show that, over vast regions of the parameter space, the <span class="hlt">numerical</span> errors of fixed-step explicit <span class="hlt">schemes</span> commonly used in hydrology routinely dwarf the structural errors of the model conceptualization. This substantially degrades model predictions, but also, disturbingly, generates fortuitously adequate performance for parameter sets where <span class="hlt">numerical</span> errors compensate for model structural errors. Simply running fixed-step explicit <span class="hlt">schemes</span> with shorter time steps provides a poor balance between accuracy and efficiency: in some cases daily-step adaptive explicit <span class="hlt">schemes</span> with moderate error tolerances achieved comparable or higher accuracy than 15 min fixed-step explicit approximations but were nearly 10 times more efficient. From the range of simple time stepping <span class="hlt">schemes</span> investigated in this work, the fixed-step implicit Euler method and the adaptive explicit Heun method emerge as good practical choices for the majority of simulation scenarios. In combination with the companion paper, where impacts on model analysis, interpretation, and prediction are assessed, this two-part study vividly highlights the impact of <span class="hlt">numerical</span> errors on critical performance aspects of conceptual hydrological models and provides practical guidelines for robust <span class="hlt">numerical</span> implementation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007TellA..59..661R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007TellA..59..661R"><span>Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: <span class="hlt">numerical</span> testing</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko</p> <p>2007-10-01</p> <p>The semi-implicit semi-<span class="hlt">Lagrangian</span> (SISL), two-time-level, non-hydrostatic <span class="hlt">numerical</span> <span class="hlt">scheme</span>, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the <span class="hlt">numerical</span> accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak secondary wave reproduction in some cases) consistency of the <span class="hlt">numerical</span> modelling results with known stationary linear test solutions. <span class="hlt">Numerical</span> stability of the developed model is investigated with respect to the reference state choice, modelling dynamics of a stationary front. The horizontally area-mean reference temperature proves to be the optimal stability warrant. The <span class="hlt">numerical</span> <span class="hlt">scheme</span> with explicit residual in the vertical forcing term becomes unstable for cross-frontal temperature differences exceeding 30 K. Stability is restored, if the vertical forcing is treated implicitly, which enables to use time steps, comparable with the hydrostatic SISL.</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, <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> current fields, as far as forecasts of <span class="hlt">Lagrangian</span> dispersion are concerned.</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 code</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 <span class="hlt">numerical</span> diffusion, they are considered a promising alternative to more traditional semi-<span class="hlt">Lagrangian</span> <span class="hlt">schemes</span> (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 codes (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/2016ESASP.740E.214G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ESASP.740E.214G"><span><span class="hlt">Lagrangian</span>-based Backtracking of Oil Spill Dynamics from SAR Images: Application to Montara Case</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gautama, Budhi Gunadharma; Mercier, Gregoire; Fablet, Ronan; Longepe, Nicolas</p> <p>2016-08-01</p> <p>Within the framework of INDESO project (Infrastructure Development Space Oceanography), we address the issue of oilspill and aim at developing an operational SAR- based system for monitoring this issue in Indonesian waters from space. In this work, we focus on the backtrack- ing of an oilspill detected from SAR observations. As a case-study, we consider one large oil spill event that happened in Indonesian waters in 2009, referred to as the Montara oilspill. On 21 August 2009, the Montara Wellhead Platform had an uncontrolled release of hydrocarbons from one of the platform wells. It was estimated that 400 barrels (or approximately 64 tonnes) of crude oil were being lost per day. The uncontrolled release continued until 3 November 2009 and response operations continued until 3 December 2009. In this work, we develop a Langragian analysis and associated <span class="hlt">numerical</span> inversion tools with a view to further analyzing the oil spread due to the Montara Wellhead Platform. Our model relies on a 2D <span class="hlt">Lagrangian</span> transport model developed by CLS (Collecte Localisation Satellite). Our model involves four main parameters : the weights of wind- related and current-related advection, the origin and the duration of the oil leakage. Given SAR oilspill detections, we propose a <span class="hlt">numerical</span> inversion of the parameters of the <span class="hlt">Lagrangian</span> model, so that the simulated drift match the SAR observations of the oil spill. We demonstrate the relevance of the proposed model and <span class="hlt">numerical</span> <span class="hlt">scheme</span> for the Montara oilspill and further discuss their operational interest for the space-based oilspill backtracking and forecasting.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1342896-weighted-non-linear-compact-schemes-direct-numerical-simulation-compressible-turbulent-flows','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1342896-weighted-non-linear-compact-schemes-direct-numerical-simulation-compressible-turbulent-flows"><span>Weighted Non-linear Compact <span class="hlt">Schemes</span> for the Direct <span class="hlt">Numerical</span> Simulation of Compressible, Turbulent 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>Ghosh, Debojyoti; Baeder, James D.</p> <p>2014-01-21</p> <p>A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) <span class="hlt">schemes</span> were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO <span class="hlt">schemes</span> use solution-dependent weights to combine lower-order compact interpolation <span class="hlt">schemes</span> and yield a high-order compact <span class="hlt">scheme</span> for smooth solutions and a non-oscillatory compact <span class="hlt">scheme</span> near discontinuities. The new <span class="hlt">schemes</span> result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) <span class="hlt">scheme</span> of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed inmore » the literature in the context of the WENO <span class="hlt">schemes</span>, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO <span class="hlt">schemes</span> and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the <span class="hlt">numerical</span> properties of the CRWENO <span class="hlt">schemes</span> and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the <span class="hlt">schemes</span> for the direct <span class="hlt">numerical</span> simulation of compressible, turbulent flows« less</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 <span class="hlt">scheme</span> 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> <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 <span class="hlt">numerical</span> 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('http://adsabs.harvard.edu/abs/2017JCoPh.350..607X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.350..607X"><span>On <span class="hlt">numerical</span> instabilities of Godunov-type <span class="hlt">schemes</span> for strong shocks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Xie, Wenjia; Li, Wei; Li, Hua; Tian, Zhengyu; Pan, Sha</p> <p>2017-12-01</p> <p>It is well known that low diffusion Riemann solvers with minimal smearing on contact and shear waves are vulnerable to shock instability problems, including the carbuncle phenomenon. In the present study, we concentrate on exploring where the instability grows out and how the dissipation inherent in Riemann solvers affects the unstable behaviors. With the help of <span class="hlt">numerical</span> experiments and a linearized analysis method, it has been found that the shock instability is strongly related to the unstable modes of intermediate states inside the shock structure. The consistency of mass flux across the normal shock is needed for a Riemann solver to capture strong shocks stably. The famous carbuncle phenomenon is interpreted as the consequence of the inconsistency of mass flux across the normal shock for a low diffusion Riemann solver. Based on the results of <span class="hlt">numerical</span> experiments and the linearized analysis, a robust Godunov-type <span class="hlt">scheme</span> with a simple cure for the shock instability is suggested. With only the dissipation corresponding to shear waves introduced in the vicinity of strong shocks, the instability problem is circumvented. <span class="hlt">Numerical</span> results of several carefully chosen strong shock wave problems are investigated to demonstrate the robustness of the proposed <span class="hlt">scheme</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015EGUGA..17.5542M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015EGUGA..17.5542M"><span>Improved <span class="hlt">scheme</span> for parametrization of convection in the Met Office's <span class="hlt">Numerical</span> Atmospheric-dispersion Modelling Environment (NAME)</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Meneguz, Elena; Thomson, David; Witham, Claire; Kusmierczyk-Michulec, Jolanta</p> <p>2015-04-01</p> <p>NAME is a <span class="hlt">Lagrangian</span> atmospheric dispersion model used by the Met Office to predict the dispersion of both natural and man-made contaminants in the atmosphere, e.g. volcanic ash, radioactive particles and chemical species. Atmospheric convection is responsible for transport and mixing of air resulting in a large exchange of heat and energy above the boundary layer. Although convection can transport material through the whole troposphere, convective clouds have a small horizontal length scale (of the order of few kilometres). Therefore, for large-scale transport the horizontal scale on which the convection exists is below the global NWP resolution used as input to NAME and convection must be parametrized. Prior to the work presented here, the enhanced vertical mixing generated by non-resolved convection was reproduced by randomly redistributing <span class="hlt">Lagrangian</span> particles between the cloud base and cloud top with probability equal to 1/25th of the NWP predicted convective cloud fraction. Such a <span class="hlt">scheme</span> is essentially diffusive and it does not make optimal use of all the information provided by the driving meteorological model. To make up for these shortcomings and make the parametrization more physically based, the convection <span class="hlt">scheme</span> has been recently revised. The resulting version, presented in this paper, is now based on the balance equation between upward, entrainment and detrainment fluxes. In particular, upward mass fluxes are calculated with empirical formulas derived from Cloud Resolving Models and using the NWP convective precipitation diagnostic as closure. The fluxes are used to estimate how many particles entrain, move upward and detrain. Lastly, the <span class="hlt">scheme</span> is completed by applying a compensating subsidence flux. The performance of the updated convection <span class="hlt">scheme</span> is benchmarked against available observational data of passive tracers. In particular, radioxenon is a noble gas that can undergo significant long range transport: this study makes use of observations of</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/2014CPM.....1...85O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CPM.....1...85O"><span><span class="hlt">Lagrangian</span> analysis of multiscale particulate flows with the 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>Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy</p> <p>2014-05-01</p> <p>We present a <span class="hlt">Lagrangian</span> <span class="hlt">numerical</span> technique for the analysis of flows incorporating physical particles of different sizes. The <span class="hlt">numerical</span> approach is based on the particle finite element method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the <span class="hlt">Lagrangian</span> formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The <span class="hlt">numerical</span> technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.</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. <span class="hlt">Numerical</span> 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. <span class="hlt">Numerical</span> 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> <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 <span class="hlt">numerical</span> 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/2060/19980022720','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980022720"><span>Higher-Order Compact <span class="hlt">Schemes</span> for <span class="hlt">Numerical</span> Simulation of Incompressible Flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wilson, Robert V.; Demuren, Ayodeji O.; Carpenter, Mark</p> <p>1998-01-01</p> <p>A higher order accurate <span class="hlt">numerical</span> procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta <span class="hlt">schemes</span> for temporal discretization and fourth and sixth order compact finite-difference <span class="hlt">schemes</span> for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta <span class="hlt">schemes</span>. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/355654-numerical-study-axisymmetric-couette-taylor-problem-using-fast-high-resolution-second-order-central-scheme','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/355654-numerical-study-axisymmetric-couette-taylor-problem-using-fast-high-resolution-second-order-central-scheme"><span>A <span class="hlt">numerical</span> study of the axisymmetric Couette-Taylor problem using a fast high-resolution second-order central <span class="hlt">scheme</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>Kupferman, R.</p> <p></p> <p>The author presents a <span class="hlt">numerical</span> study of the axisymmetric Couette-Taylor problem using a finite difference <span class="hlt">scheme</span>. The <span class="hlt">scheme</span> is based on a staggered version of a second-order central-differencing method combined with a discrete Hodge projection. The use of central-differencing operators obviates the need to trace the characteristic flow associated with the hyperbolic terms. The result is a simple and efficient <span class="hlt">scheme</span> which is readily adaptable to other geometries and to more complicated flows. The <span class="hlt">scheme</span> exhibits competitive performance in terms of accuracy, resolution, and robustness. The <span class="hlt">numerical</span> results agree accurately with linear stability theory and with previous <span class="hlt">numerical</span> studies.</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> Eulerian 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> Eulerian (ALE) hydrodynamic <span class="hlt">scheme</span> 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 <span class="hlt">scheme</span> are discussed. Results from a range of <span class="hlt">numerical</span> test problems are presented.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001PhLA..284..184B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001PhLA..284..184B"><span>Multi-symplectic integrators: <span class="hlt">numerical</span> <span class="hlt">schemes</span> for Hamiltonian PDEs that conserve symplecticity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bridges, Thomas J.; Reich, Sebastian</p> <p>2001-06-01</p> <p>The symplectic <span class="hlt">numerical</span> integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate <span class="hlt">schemes</span>, e.g., for rigid body, constrained, and molecular dynamics. The <span class="hlt">numerical</span> integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic <span class="hlt">numerical</span> integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric <span class="hlt">numerical</span> <span class="hlt">schemes</span> for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003JCoAM.161..469F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003JCoAM.161..469F"><span><span class="hlt">Numerical</span> <span class="hlt">scheme</span> approximating solution and parameters in a beam equation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ferdinand, Robert R.</p> <p>2003-12-01</p> <p>We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation <span class="hlt">scheme</span> is used to estimate model solution. Infinite-dimensional model parameters are then estimated <span class="hlt">numerically</span> using an inverse method procedure which involves the minimization of a least-squares cost functional. <span class="hlt">Numerical</span> results are presented and future work to be done is discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AcGeo.tmp...28B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AcGeo.tmp...28B"><span>Stochastic porous media modeling and high-resolution <span class="hlt">schemes</span> for <span class="hlt">numerical</span> simulation of subsurface immiscible fluid flow transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah</p> <p>2018-04-01</p> <p>This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting <span class="hlt">schemes</span>, commonly used in conventional <span class="hlt">numerical</span> reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of <span class="hlt">numerical</span> smearing in first-order <span class="hlt">schemes</span>, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution <span class="hlt">schemes</span> of SUPERBEE flux limiter, weighted essentially non-oscillatory <span class="hlt">scheme</span> (WENO), and monotone upstream-centered <span class="hlt">schemes</span> for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order <span class="hlt">schemes</span> results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved <span class="hlt">numerically</span> using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable <span class="hlt">numerical</span> stability and convergence rate. A comparative and <span class="hlt">numerical</span> examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940020698','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940020698"><span>A Continuing Search for a Near-Perfect <span class="hlt">Numerical</span> Flux <span class="hlt">Scheme</span>. Part 1; [AUSM+</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>1994-01-01</p> <p>While enjoying demonstrated improvement in accuracy, efficiency, and robustness over existing <span class="hlt">schemes</span>, the Advection Upstream Splitting <span class="hlt">Scheme</span> (AUSM) was found to have some deficiencies in extreme cases. This recent progress towards improving the AUSM while retaining its advantageous features is described. The new <span class="hlt">scheme</span>, termed AUSM+, features: unification of velocity and Mach number splitting; exact capture of a single stationary shock; and improvement in accuracy. A general construction of the AUSM+ <span class="hlt">scheme</span> is layed out and then focus is on the analysis of the a <span class="hlt">scheme</span> and its mathematical properties, heretofore unreported. Monotonicity and positivity are proved, and a CFL-like condition is given for first and second order <span class="hlt">schemes</span> and for generalized curvilinear co-ordinates. Finally, results of <span class="hlt">numerical</span> tests on many problems are given to confirm the capability and improvements on a variety of problems including those failed by prominent <span class="hlt">schemes</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.341...44C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.341...44C"><span>Efficient and accurate <span class="hlt">numerical</span> <span class="hlt">schemes</span> for a hydro-dynamically coupled phase field diblock copolymer model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cheng, Qing; Yang, Xiaofeng; Shen, Jie</p> <p>2017-07-01</p> <p>In this paper, we consider <span class="hlt">numerical</span> approximations of a hydro-dynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching <span class="hlt">schemes</span> for this system using the "Invariant Energy Quadratization" approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting <span class="hlt">schemes</span> are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these <span class="hlt">schemes</span> are unconditionally energy stable. Various <span class="hlt">numerical</span> experiments are performed to validate the accuracy and energy stability of the proposed <span class="hlt">schemes</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DPPG10004R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DPPG10004R"><span>Applying Boundary Conditions Using a Time-Dependent <span class="hlt">Lagrangian</span> for Modeling Laser-Plasma Interactions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Reyes, Jonathan; Shadwick, B. A.</p> <p>2016-10-01</p> <p>Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. <span class="hlt">Numerical</span> models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the <span class="hlt">Lagrangian</span> density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the <span class="hlt">Lagrangian</span> which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization <span class="hlt">scheme</span> is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.</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 <span class="hlt">Numerical</span> 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 <span class="hlt">Numerical</span> 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('http://hdl.handle.net/2060/19960011642','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960011642"><span>Floating shock fitting via <span class="hlt">Lagrangian</span> adaptive meshes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Vanrosendale, John</p> <p>1995-01-01</p> <p>In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe <span class="hlt">scheme</span> discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting <span class="hlt">Lagrangian</span> Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.</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 code - 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 Eulerian <span class="hlt">schemes</span> 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 Eulerian 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 code 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 <span class="hlt">schemes</span>, the predictor-corrector <span class="hlt">Lagrangian</span>-remap code has great flexibility for application to a variety of astrophysical problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950012933','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950012933"><span>Testing higher-order <span class="hlt">Lagrangian</span> perturbation theory against <span class="hlt">numerical</span> simulation. 1: Pancake models</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Buchert, T.; Melott, A. L.; Weiss, A. G.</p> <p>1993-01-01</p> <p>We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The <span class="hlt">Lagrangian</span> theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with <span class="hlt">numerical</span> simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order <span class="hlt">Lagrangian</span> perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940010374','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940010374"><span>A new <span class="hlt">Lagrangian</span> method for three-dimensional steady supersonic 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>In this report, the new <span class="hlt">Lagrangian</span> method introduced by Loh and Hui is extended for three-dimensional, steady supersonic flow computation. The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) <span class="hlt">scheme</span> is presented. This new approach is accurate and robust, capable of handling complicated geometry and interactions between discontinuous waves. Test problems show that the extended <span class="hlt">Lagrangian</span> method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation). In this report, we also suggest a novel three dimensional Riemann problem in which interesting and intricate flow features are present.</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 <span class="hlt">numerical</span> 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('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> </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/1998JCoPh.144..662Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1998JCoPh.144..662Z"><span>High-Order Finite-Difference <span class="hlt">Schemes</span> for <span class="hlt">Numerical</span> Simulation of Hypersonic Boundary-Layer Transition</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhong, Xiaolin</p> <p>1998-08-01</p> <p>Direct <span class="hlt">numerical</span> simulation (DNS) has become a powerful tool in studying fundamental phenomena of laminar-turbulent transition of high-speed boundary layers. Previous DNS studies of supersonic and hypersonic boundary layer transition have been limited to perfect-gas flow over flat-plate boundary layers without shock waves. For hypersonic boundary layers over realistic blunt bodies, DNS studies of transition need to consider the effects of bow shocks, entropy layers, surface curvature, and finite-rate chemistry. It is necessary that <span class="hlt">numerical</span> methods for such studies are robust and high-order accurate both in resolving wide ranges of flow time and length scales and in resolving the interaction between the bow shocks and flow disturbance waves. This paper presents a new high-order shock-fitting finite-difference method for the DNS of the stability and transition of hypersonic boundary layers over blunt bodies with strong bow shocks and with (or without) thermo-chemical nonequilibrium. The proposed method includes a set of new upwind high-order finite-difference <span class="hlt">schemes</span> which are stable and are less dissipative than a straightforward upwind <span class="hlt">scheme</span> using an upwind-bias grid stencil, a high-order shock-fitting formulation, and third-order semi-implicit Runge-Kutta <span class="hlt">schemes</span> for temporal discretization of stiff reacting flow equations. The accuracy and stability of the new <span class="hlt">schemes</span> are validated by <span class="hlt">numerical</span> experiments of the linear wave equation and nonlinear Navier-Stokes equations. The algorithm is then applied to the DNS of the receptivity of hypersonic boundary layers over a parabolic leading edge to freestream acoustic disturbances.</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</span>-Eulerian 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> Eulerian (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 <span class="hlt">numerical</span> results that illustrate the advantages of the formulation with respect to current approaches.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28113769','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28113769"><span>A Combined Eulerian-<span class="hlt">Lagrangian</span> Data Representation for Large-Scale Applications.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Sauer, Franz; Xie, Jinrong; Ma, Kwan-Liu</p> <p>2017-10-01</p> <p>The Eulerian and <span class="hlt">Lagrangian</span> 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-<span class="hlt">Lagrangian</span> format. By reorganizing <span class="hlt">Lagrangian</span> 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 <span class="hlt">scheme</span>. 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.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017SPIE10420E..2JU','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017SPIE10420E..2JU"><span>Multiplicative noise removal through fractional order tv-based model and fast <span class="hlt">numerical</span> <span class="hlt">schemes</span> for its approximation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad</p> <p>2017-07-01</p> <p>This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two <span class="hlt">numerical</span> <span class="hlt">schemes</span> namely an iterative <span class="hlt">scheme</span> based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report <span class="hlt">numerical</span> simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. <span class="hlt">Numerical</span> experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative <span class="hlt">scheme</span>.</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 Eulerian 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 <span class="hlt">scheme</span>, 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 Eulerian 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 Eulerian 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/biblio/1375246-application-high-order-numerical-schemes-newton-krylov-method-two-phase-drift-flux-model','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1375246-application-high-order-numerical-schemes-newton-krylov-method-two-phase-drift-flux-model"><span>Application of high-order <span class="hlt">numerical</span> <span class="hlt">schemes</span> and Newton-Krylov method to two-phase drift-flux 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>Zou, Ling; Zhao, Haihua; Zhang, Hongbin</p> <p></p> <p>This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order <span class="hlt">numerical</span> <span class="hlt">schemes</span>. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order <span class="hlt">numerical</span> <span class="hlt">schemes</span> only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order <span class="hlt">numerical</span> <span class="hlt">schemes</span> were employed. In this study, a second-order spatial discretization <span class="hlt">scheme</span> that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. <span class="hlt">Numerical</span> verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization <span class="hlt">schemes</span>. Finally, the drift-flux model, along with <span class="hlt">numerical</span> methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1375246-application-high-order-numerical-schemes-newton-krylov-method-two-phase-drift-flux-model','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1375246-application-high-order-numerical-schemes-newton-krylov-method-two-phase-drift-flux-model"><span>Application of high-order <span class="hlt">numerical</span> <span class="hlt">schemes</span> and Newton-Krylov method to two-phase drift-flux model</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Zou, Ling; Zhao, Haihua; Zhang, Hongbin</p> <p>2017-08-07</p> <p>This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order <span class="hlt">numerical</span> <span class="hlt">schemes</span>. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order <span class="hlt">numerical</span> <span class="hlt">schemes</span> only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order <span class="hlt">numerical</span> <span class="hlt">schemes</span> were employed. In this study, a second-order spatial discretization <span class="hlt">scheme</span> that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. <span class="hlt">Numerical</span> verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization <span class="hlt">schemes</span>. Finally, the drift-flux model, along with <span class="hlt">numerical</span> methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.353...46D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.353...46D"><span>An efficient <span class="hlt">numerical</span> method for solving the Boltzmann equation in multidimensions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dimarco, Giacomo; Loubère, Raphaël; Narski, Jacek; Rey, Thomas</p> <p>2018-01-01</p> <p>In this paper we deal with the extension of the Fast Kinetic <span class="hlt">Scheme</span> (FKS) (Dimarco and Loubère, 2013 [26]) originally constructed for solving the BGK equation, to the more challenging case of the Boltzmann equation. The <span class="hlt">scheme</span> combines a robust and fast method for treating the transport part based on an innovative <span class="hlt">Lagrangian</span> technique supplemented with conservative fast spectral <span class="hlt">schemes</span> to treat the collisional operator by means of an operator splitting approach. This approach along with several implementation features related to the parallelization of the algorithm permits to construct an efficient simulation tool which is <span class="hlt">numerically</span> tested against exact and reference solutions on classical problems arising in rarefied gas dynamic. We present results up to the 3 D × 3 D case for unsteady flows for the Variable Hard Sphere model which may serve as benchmark for future comparisons between different <span class="hlt">numerical</span> methods for solving the multidimensional Boltzmann equation. For this reason, we also provide for each problem studied details on the computational cost and memory consumption as well as comparisons with the BGK model or the limit model of compressible Euler equations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010WRR....4610511K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010WRR....4610511K"><span>Ancient <span class="hlt">numerical</span> daemons of conceptual hydrological modeling: 2. Impact of time stepping <span class="hlt">schemes</span> on model analysis and prediction</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kavetski, Dmitri; Clark, Martyn P.</p> <p>2010-10-01</p> <p>Despite the widespread use of conceptual hydrological models in environmental research and operations, they remain frequently implemented using <span class="hlt">numerically</span> unreliable methods. This paper considers the impact of the time stepping <span class="hlt">scheme</span> on model analysis (sensitivity analysis, parameter optimization, and Markov chain Monte Carlo-based uncertainty estimation) and prediction. It builds on the companion paper (Clark and Kavetski, 2010), which focused on <span class="hlt">numerical</span> accuracy, fidelity, and computational efficiency. Empirical and theoretical analysis of eight distinct time stepping <span class="hlt">schemes</span> for six different hydrological models in 13 diverse basins demonstrates several critical conclusions. (1) Unreliable time stepping <span class="hlt">schemes</span>, in particular, fixed-step explicit methods, suffer from troublesome <span class="hlt">numerical</span> artifacts that severely deform the objective function of the model. These deformations are not rare isolated instances but can arise in any model structure, in any catchment, and under common hydroclimatic conditions. (2) Sensitivity analysis can be severely contaminated by <span class="hlt">numerical</span> errors, often to the extent that it becomes dominated by the sensitivity of truncation errors rather than the model equations. (3) Robust time stepping <span class="hlt">schemes</span> generally produce "better behaved" objective functions, free of spurious local optima, and with sufficient <span class="hlt">numerical</span> continuity to permit parameter optimization using efficient quasi Newton methods. When implemented within a multistart framework, modern Newton-type optimizers are robust even when started far from the optima and provide valuable diagnostic insights not directly available from evolutionary global optimizers. (4) Unreliable time stepping <span class="hlt">schemes</span> lead to inconsistent and biased inferences of the model parameters and internal states. (5) Even when interactions between hydrological parameters and <span class="hlt">numerical</span> errors provide "the right result for the wrong reason" and the calibrated model performance appears adequate, unreliable</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 Eulerian-<span class="hlt">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 Eulerian-<span class="hlt">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 <span class="hlt">scheme</span>, greatly facilitates mass conservation. The mass storage integral is <span class="hlt">numerically</span> 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('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 Eulerian mean fluid quantities by the fluctuating displacements of the <span class="hlt">Lagrangian</span> trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian 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('https://ntrs.nasa.gov/search.jsp?R=20050184193&hterms=acm&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dacm','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20050184193&hterms=acm&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dacm"><span>Adaptive <span class="hlt">Numerical</span> Dissipation Control in High Order <span class="hlt">Schemes</span> for Multi-D Non-Ideal MHD</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Yee, H. C.; Sjoegreen, B.</p> <p>2005-01-01</p> <p>The required type and amount of <span class="hlt">numerical</span> dissipation/filter to accurately resolve all relevant multiscales of complex MHD unsteady high-speed shock/shear/turbulence/combustion problems are not only physical problem dependent, but also vary from one flow region to another. In addition, proper and efficient control of the divergence of the magnetic field (Div(B)) <span class="hlt">numerical</span> error for high order shock-capturing methods poses extra requirements for the considered type of CPU intensive computations. The goal is to extend our adaptive <span class="hlt">numerical</span> dissipation control in high order filter <span class="hlt">schemes</span> and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of <span class="hlt">numerical</span> dissipation/filter where needed and leave the rest of the region free from <span class="hlt">numerical</span> dissipation contamination. These <span class="hlt">scheme</span>-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multiresolution wavelets (WAV) (for the above types of flow feature). These filters also provide a natural and efficient way for the minimization of Div(B) <span class="hlt">numerical</span> error.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940017007','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940017007"><span>A semi-<span class="hlt">Lagrangian</span> approach to the shallow water equation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bates, J. R.; Mccormick, Stephen F.; Ruge, John; Sholl, David S.; Yavneh, Irad</p> <p>1993-01-01</p> <p>We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-<span class="hlt">Lagrangian</span> time-stepping <span class="hlt">scheme</span> is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDQ15004O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDQ15004O"><span>Direct <span class="hlt">Lagrangian</span> tracking simulations of particles in vertically-developing atmospheric clouds</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Onishi, Ryo; Kunishima, Yuichi</p> <p>2017-11-01</p> <p>We have been developing the <span class="hlt">Lagrangian</span> Cloud Simulator (LCS), which follows the so-called Euler-<span class="hlt">Lagrangian</span> framework, where flow motion and scalar transportations (i.e., temperature and humidity) are computed with the Euler method and particle motion with the <span class="hlt">Lagrangian</span> method. The LCS simulation considers the hydrodynamic interaction between approaching particles for robust collision detection. This leads to reliable simulations of collision growth of cloud droplets. Recently the activation process, in which aerosol particles become tiny liquid droplets, has been implemented in the LCS. The present LCS can therefore consider the whole warm-rain precipitation processes -activation, condensation, collision and drop precipitation. In this talk, after briefly introducing the LCS, we will show kinematic simulations using the LCS for quasi-one dimensional domain, i.e., vertically elongated 3D domain. They are compared with one-dimensional kinematic simulations using a spectral-bin cloud microphysics <span class="hlt">scheme</span>, which is based on the Euler method. The comparisons show fairly good agreement with small discrepancies, the source of which will be presented. The <span class="hlt">Lagrangian</span> statistics, obtained for the first time for the vertical domain, will be the center of discussion. This research was supported by MEXT as ``Exploratory Challenge on Post-K computer'' (Frontiers of Basic Science: Challenging the Limits).</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 <span class="hlt">numerically</span> by tracking <span class="hlt">Lagrangian</span> fluid particles in direct <span class="hlt">numerical</span> simulation (DNS) datasets of the Eulerian flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that Eulerian 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> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1408834-multi-scale-residual-based-anti-hourglass-control-compatible-staggered-lagrangian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1408834-multi-scale-residual-based-anti-hourglass-control-compatible-staggered-lagrangian-hydrodynamics"><span>A multi-scale residual-based anti-hourglass control for compatible staggered <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>Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich</p> <p></p> <p>Hourglassing is a well-known pathological <span class="hlt">numerical</span> artifact affecting the robustness and accuracy of <span class="hlt">Lagrangian</span> methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible <span class="hlt">Lagrangian</span> methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add <span class="hlt">numerical</span> strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected <span class="hlt">numerical</span> problems.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1408834-multi-scale-residual-based-anti-hourglass-control-compatible-staggered-lagrangian-hydrodynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1408834-multi-scale-residual-based-anti-hourglass-control-compatible-staggered-lagrangian-hydrodynamics"><span>A multi-scale residual-based anti-hourglass control for compatible staggered <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich; ...</p> <p>2017-10-28</p> <p>Hourglassing is a well-known pathological <span class="hlt">numerical</span> artifact affecting the robustness and accuracy of <span class="hlt">Lagrangian</span> methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible <span class="hlt">Lagrangian</span> methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add <span class="hlt">numerical</span> strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the finite element approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected <span class="hlt">numerical</span> problems.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22570191-interface-discontinuity-aware-numerical-schemes-plasma-radiation-diffusion-two-three-dimensions','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22570191-interface-discontinuity-aware-numerical-schemes-plasma-radiation-diffusion-two-three-dimensions"><span>Interface- and discontinuity-aware <span class="hlt">numerical</span> <span class="hlt">schemes</span> for plasma 3-T radiation diffusion in two and three dimensions</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>Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.</p> <p>2015-11-01</p> <p>A set of <span class="hlt">numerical</span> <span class="hlt">schemes</span> is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The <span class="hlt">scheme</span> is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The <span class="hlt">scheme</span> is general in two and three dimensions on general polyhedral meshes. The features of the <span class="hlt">scheme</span> are demonstrated through <span class="hlt">numerical</span> examples for transient problems and steady states. The effects of some simplifications of <span class="hlt">numerical</span> <span class="hlt">schemes</span> are also shown through <span class="hlt">numerical</span> examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less</p> </li> <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('https://www.osti.gov/biblio/22570225-from-stochastic-processes-numerical-methods-new-scheme-solving-reaction-subdiffusion-fractional-partial-differential-equations','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22570225-from-stochastic-processes-numerical-methods-new-scheme-solving-reaction-subdiffusion-fractional-partial-differential-equations"><span>From stochastic processes to <span class="hlt">numerical</span> methods: A new <span class="hlt">scheme</span> for solving reaction subdiffusion fractional partial differential equations</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>Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au</p> <p></p> <p>We have introduced a new explicit <span class="hlt">numerical</span> method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The <span class="hlt">scheme</span> is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the <span class="hlt">numerical</span> <span class="hlt">scheme</span>. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide <span class="hlt">numerical</span> <span class="hlt">schemes</span> for partial differential equations, including fractional partial differential equations.« 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_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://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 EULERIAN-<span class="hlt">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 <span class="hlt">numerical</span> methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include Eulerian-<span class="hlt">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('http://hdl.handle.net/2060/19960001867','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960001867"><span>Full-Scale Direct <span class="hlt">Numerical</span> Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.</p> <p>1995-01-01</p> <p>A thin film draining on an inclined plate has been studied <span class="hlt">numerically</span> using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary <span class="hlt">Lagrangian</span> Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the <span class="hlt">numerical</span> <span class="hlt">scheme</span>. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.</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://ntrs.nasa.gov/search.jsp?R=19780037977&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=19780037977&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. I - Linear wave propagation. II - Nonlinear wave interactions</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>1977-01-01</p> <p>It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the <span class="hlt">Lagrangian</span> method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion <span class="hlt">scheme</span> described by Galloway and Kim (1971), and <span class="hlt">Lagrangians</span> to third order in perturbation are considered. Attention is given to the averaged-<span class="hlt">Lagrangian</span> density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.</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 <span class="hlt">numerical</span> 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('http://hdl.handle.net/2060/19950005461','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950005461"><span>Analysis and design of <span class="hlt">numerical</span> <span class="hlt">schemes</span> for gas dynamics. 2: Artificial diffusion and discrete shock structure</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jameson, Antony</p> <p>1994-01-01</p> <p>The effect of artificial diffusion on discrete shock structures is examined for a family of <span class="hlt">schemes</span> which includes scalar diffusion, convective upwind and split pressure (CUSP) <span class="hlt">schemes</span>, and upwind <span class="hlt">schemes</span> with characteristics splitting. The analysis leads to conditions on the diffusive flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a CUSP <span class="hlt">scheme</span> in which the coefficients of the pressure differences is fully determined by the coefficient of convective diffusion. It is also shown how both the characteristic and CUSP <span class="hlt">schemes</span> can be modified to preserve constant stagnation enthalpy in steady flow, leading to four variants, the E and H-characteristic <span class="hlt">schemes</span>, and the E and H-CUSP <span class="hlt">schemes</span>. <span class="hlt">Numerical</span> results are presented which confirm the properties of these <span class="hlt">schemes</span>.</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 <span class="hlt">numerically</span> 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/2017ECSS..194..263R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017ECSS..194..263R"><span><span class="hlt">Lagrangian</span> trajectories, residual currents and rectification process in the Northern Gulf of California</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rodríguez, Pablo Alonso; Carbajal, Noel; Rodríguez, Juan Heberto Gaviño</p> <p>2017-07-01</p> <p>Considering a semi-implicit approximation of the Coriolis terms, a <span class="hlt">numerical</span> solution of the vertically integrated equations of motion is proposed. To test the two-dimensional <span class="hlt">numerical</span> model, several experiments for the calculation of Euler, Stokes and Lagrange residual currents in the Gulf of California were carried out. To estimate the <span class="hlt">Lagrangian</span> residual current, trajectories of particles were also simulated. The applied tidal constituents were M2, S2, K2, N2, K1, P1 and O1. At spring tides, strong tidal velocities occur in the northern half of the gulf. In this region of complex geometry, depths change from a few meter in the northern shelf zone to more than 3000 m in the southern part. In the archipelago region, the presence of islands alters amplitude and direction of tidal currents producing a rectification process which is reflected in a clockwise circulation around Tiburón Island in the <span class="hlt">Lagrangian</span> residual current. The rectification process is explained by the superposition of the Euler and Stokes residual currents. Residual current patterns show several cyclonic and anticyclonic gyres in the Northern Gulf of California. <span class="hlt">Numerical</span> experiments for individual and combinations of several tidal constituents revealed a large variability of <span class="hlt">Lagrangian</span> trajectories.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1998A%26A...332.1159T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1998A%26A...332.1159T"><span>Implicit and semi-implicit <span class="hlt">schemes</span> in the Versatile Advection Code: <span class="hlt">numerical</span> tests</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Toth, G.; Keppens, R.; Botchev, M. A.</p> <p>1998-04-01</p> <p>We describe and evaluate various implicit and semi-implicit time integration <span class="hlt">schemes</span> applied to the <span class="hlt">numerical</span> simulation of hydrodynamical and magnetohydrodynamical problems. The <span class="hlt">schemes</span> were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional source terms. The main advantage of implicit solution strategies over explicit time integration is that the restrictive constraint on the allowed time step can be (partially) eliminated, thus the computational cost is reduced. The test problems cover one and two dimensional, steady state and time accurate computations, and the solutions contain discontinuities. For each test, we confront explicit with implicit solution strategies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ThCFD..26..225C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ThCFD..26..225C"><span>The effect of <span class="hlt">numerical</span> methods on the simulation of mid-ocean ridge hydrothermal models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Carpio, J.; Braack, M.</p> <p>2012-01-01</p> <p>This work considers the effect of the <span class="hlt">numerical</span> method on the simulation of a 2D model of hydrothermal systems located in the high-permeability axial plane of mid-ocean ridges. The behavior of hot plumes, formed in a porous medium between volcanic lava and the ocean floor, is very irregular due to convective instabilities. Therefore, we discuss and compare two different <span class="hlt">numerical</span> methods for solving the mathematical model of this system. In concrete, we consider two ways to treat the temperature equation of the model: a semi-<span class="hlt">Lagrangian</span> formulation of the advective terms in combination with a Galerkin finite element method for the parabolic part of the equations and a stabilized finite element <span class="hlt">scheme</span>. Both methods are very robust and accurate. However, due to physical instabilities in the system at high Rayleigh number, the effect of the <span class="hlt">numerical</span> method is significant with regard to the temperature distribution at a certain time instant. The good news is that relevant statistical quantities remain relatively stable and coincide for the two <span class="hlt">numerical</span> <span class="hlt">schemes</span>. The agreement is larger in the case of a mathematical model with constant water properties. In the case of a model with nonlinear dependence of the water properties on the temperature and pressure, the agreement in the statistics is clearly less pronounced. Hence, the presented work accentuates the need for a strengthened validation of the compatibility between <span class="hlt">numerical</span> <span class="hlt">scheme</span> (accuracy/resolution) and complex (realistic/nonlinear) models.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940024968','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940024968"><span>A new flux-conserving <span class="hlt">numerical</span> <span class="hlt">scheme</span> for the steady, incompressible Navier-Stokes equations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Scott, James R.</p> <p>1994-01-01</p> <p>This paper is concerned with the continued development of a new <span class="hlt">numerical</span> method, the space-time solution element (STS) method, for solving conservation laws. The present work focuses on the two-dimensional, steady, incompressible Navier-Stokes equations. Using first an integral approach, and then a differential approach, the discrete flux conservation equations presented in a recent paper are rederived. Here a simpler method for determining the flux expressions at cell interfaces is given; a systematic and rigorous derivation of the conditions used to simulate the differential form of the governing conservation law(s) is provided; necessary and sufficient conditions for a discrete approximation to satisfy a conservation law in E2 are derived; and an estimate of the local truncation error is given. A specific <span class="hlt">scheme</span> is then constructed for the solution of the thin airfoil boundary layer problem. <span class="hlt">Numerical</span> results are presented which demonstrate the ability of the <span class="hlt">scheme</span> to accurately resolve the developing boundary layer and wake regions using grids which are much coarser than those employed by other <span class="hlt">numerical</span> methods. It is shown that ten cells in the cross-stream direction are sufficient to accurately resolve the developing airfoil boundary layer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015EGUGA..1713489M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015EGUGA..1713489M"><span><span class="hlt">Lagrangian</span> <span class="hlt">numerical</span> techniques for modelling multicomponent flow in the presence of large viscosity contrasts: Markers-in-bulk versus Markers-in-chain</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mulyukova, Elvira; Dabrowski, Marcin; Steinberger, Bernhard</p> <p>2015-04-01</p> <p>Many problems in geodynamic applications may be described as viscous flow of chemically heterogeneous materials. Examples include subduction of compositionally stratified lithospheric plates, folding of rheologically layered rocks, and thermochemical convection of the Earth's mantle. The associated time scales are significantly shorter than that of chemical diffusion, which justifies the commonly featured phenomena in geodynamic flow models termed contact discontinuities. These are spatially sharp interfaces separating regions of different material properties. <span class="hlt">Numerical</span> modelling of advection of fields with sharp interfaces is challenging. Typical errors include <span class="hlt">numerical</span> diffusion, which arises due to the repeated action of <span class="hlt">numerical</span> interpolation. Mathematically, a material field can be represented by discrete indicator functions, whose values are interpreted as logical statements (e.g. whether or not the location is occupied by a given material). Interpolation of a discrete function boils down to determining where in the intermediate node-positions one material ends, and the other begins. The <span class="hlt">numerical</span> diffusion error thus manifests itself as an erroneous location of the material-interface. <span class="hlt">Lagrangian</span> advection-<span class="hlt">schemes</span> are known to be less prone to <span class="hlt">numerical</span> diffusion errors, compared to their Eulerian counterparts. The tracer-ratio method, where <span class="hlt">Lagrangian</span> markers are used to discretize the bulk of materials filling the entire domain, is a popular example of such methods. The Stokes equation in this case is solved on a separate, static grid, and in order to do it - material properties must be interpolated from the markers to the grid. This involves the difficulty related to interpolation of discrete fields. The material distribution, and thus material-properties like viscosity and density, seen by the grid is polluted by the interpolation error, which enters the solution of the momentum equation. Errors due to the uncertainty of interface-location can be</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22622258-mass-momentum-conserving-unsplit-semi-lagrangian-framework-simulating-multiphase-flows','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22622258-mass-momentum-conserving-unsplit-semi-lagrangian-framework-simulating-multiphase-flows"><span>A mass and momentum conserving unsplit semi-<span class="hlt">Lagrangian</span> framework for simulating multiphase 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>Owkes, Mark, E-mail: mark.owkes@montana.edu; Desjardins, Olivier</p> <p></p> <p>In this work, we present a computational methodology for convection and advection that handles discontinuities with second order accuracy and maintains conservation to machine precision. This method can transport a variety of discontinuous quantities and is used in the context of an incompressible gas–liquid flow to transport the phase interface, momentum, and scalars. The proposed method provides a modification to the three-dimensional, unsplit, second-order semi-<span class="hlt">Lagrangian</span> flux method of Owkes & Desjardins (JCP, 2014). The modification adds a refined grid that provides consistent fluxes of mass and momentum defined on a staggered grid and discrete conservation of mass and momentum, evenmore » for flows with large density ratios. Additionally, the refined grid doubles the resolution of the interface without significantly increasing the computational cost over previous non-conservative <span class="hlt">schemes</span>. This is possible due to a novel partitioning of the semi-<span class="hlt">Lagrangian</span> fluxes into a small number of simplices. The proposed <span class="hlt">scheme</span> is tested using canonical verification tests, rising bubbles, and an atomizing liquid jet.« less</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 <span class="hlt">numerical</span> 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 Eulerian 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 <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> 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 Eulerian 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 <span class="hlt">numerical</span> simulations and in vivo study. PMID:26578642</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012APS..APR.S1054C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012APS..APR.S1054C"><span>Asymptotic-preserving <span class="hlt">Lagrangian</span> approach for modeling anisotropic transport in magnetized plasmas</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</p> <p>2012-03-01</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 (the transport-coefficient ratio χ/χ˜10^10 in fusion plasmas). Recently, a novel <span class="hlt">Lagrangian</span> Green's function method has been proposedfootnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011); D. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, submitted (2011) to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids <span class="hlt">numerical</span> pollution, is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the <span class="hlt">Lagrangian</span> Green's function approach to include perpendicular transport terms and sources. We present an asymptotic-preserving <span class="hlt">numerical</span> formulation, which ensures a consistent <span class="hlt">numerical</span> discretization temporally and spatially for arbitrary χ/χ ratios. 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://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 Eulerian 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 Eulerian residual currents. When k is small, the first-order <span class="hlt">Lagrangian</span> residual is shown to be the sum of the Eulerian 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://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.ncbi.nlm.nih.gov/pubmed/29181888','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29181888"><span>Preconditioned augmented <span class="hlt">Lagrangian</span> formulation for nearly incompressible cardiac mechanics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Campos, Joventino Oliveira; Dos Santos, Rodrigo Weber; Sundnes, Joakim; Rocha, Bernardo Martins</p> <p>2018-04-01</p> <p>Computational modeling of the heart is a subject of substantial medical and scientific interest, which may contribute to increase the understanding of several phenomena associated with cardiac physiological and pathological states. Modeling the mechanics of the heart have led to considerable insights, but it still represents a complex and a demanding computational problem, especially in a strongly coupled electromechanical setting. Passive cardiac tissue is commonly modeled as hyperelastic and is characterized by quasi-incompressible, orthotropic, and nonlinear material behavior. These factors are known to be very challenging for the <span class="hlt">numerical</span> solution of the model. The near-incompressibility is known to cause <span class="hlt">numerical</span> issues such as the well-known locking phenomenon and ill-conditioning of the stiffness matrix. In this work, the augmented <span class="hlt">Lagrangian</span> method is used to handle the nearly incompressible condition. This approach can potentially improve computational performance by reducing the condition number of the stiffness matrix and thereby improving the convergence of iterative solvers. We also improve the performance of iterative solvers by the use of an algebraic multigrid preconditioner. <span class="hlt">Numerical</span> results of the augmented <span class="hlt">Lagrangian</span> method combined with a preconditioned iterative solver for a cardiac mechanics benchmark suite are presented to show its improved performance. Copyright © 2017 John Wiley & Sons, Ltd.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDD17004A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDD17004A"><span>Getting Things Sorted With <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>Atis, Severine; Peacock, Thomas; Environmental Dynamics Laboratory Team</p> <p>2014-11-01</p> <p>The dispersion of a tracer in a fluid flow is influenced by the <span class="hlt">Lagrangian</span> motion of fluid elements. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. For flows with arbitrary time-dependence, the modern approach of <span class="hlt">Lagrangian</span> Coherent Structures (LCSs) provide a method for identifying the key material lines that organize flow transport. When the advected tracer particles possess a finite size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. We present details of <span class="hlt">numerical</span> simulations and laboratory experiments that investigate the behavior of finite size particles in 2-dimensional chaotic flows. We show that the shape and the size of the particles alter the underlying LCSs, facilitating segregation between tracers of different shape in the same flow field.</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('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 <span class="hlt">numerical</span> code, written in Fortran programming language, has been used to perform the <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> <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('https://www.ncbi.nlm.nih.gov/pubmed/14683081','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/14683081"><span><span class="hlt">Numerical</span> viscosity and resolution of high-order weighted essentially nonoscillatory <span class="hlt">schemes</span> for compressible flows with high Reynolds numbers.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zhang, Yong-Tao; Shi, Jing; Shu, Chi-Wang; Zhou, Ye</p> <p>2003-10-01</p> <p>A quantitative study is carried out in this paper to investigate the size of <span class="hlt">numerical</span> viscosities and the resolution power of high-order weighted essentially nonoscillatory (WENO) <span class="hlt">schemes</span> for solving one- and two-dimensional Navier-Stokes equations for compressible gas dynamics with high Reynolds numbers. A one-dimensional shock tube problem, a one-dimensional example with parameters motivated by supernova and laser experiments, and a two-dimensional Rayleigh-Taylor instability problem are used as <span class="hlt">numerical</span> test problems. For the two-dimensional Rayleigh-Taylor instability problem, or similar problems with small-scale structures, the details of the small structures are determined by the physical viscosity (therefore, the Reynolds number) in the Navier-Stokes equations. Thus, to obtain faithful resolution to these small-scale structures, the <span class="hlt">numerical</span> viscosity inherent in the <span class="hlt">scheme</span> must be small enough so that the physical viscosity dominates. A careful mesh refinement study is performed to capture the threshold mesh for full resolution, for specific Reynolds numbers, when WENO <span class="hlt">schemes</span> of different orders of accuracy are used. It is demonstrated that high-order WENO <span class="hlt">schemes</span> are more CPU time efficient to reach the same resolution, both for the one-dimensional and two-dimensional test problems.</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 <span class="hlt">numerical</span> 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('http://adsabs.harvard.edu/abs/2015AGUFMNH13E..07R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFMNH13E..07R"><span>Influence of the <span class="hlt">Numerical</span> <span class="hlt">Scheme</span> on the Solution Quality of the SWE for Tsunami <span class="hlt">Numerical</span> Codes: The Tohoku-Oki, 2011Example.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Reis, C.; Clain, S.; Figueiredo, J.; Baptista, M. A.; Miranda, J. M. A.</p> <p>2015-12-01</p> <p><span class="hlt">Numerical</span> tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly depends on the <span class="hlt">numerical</span> tool quality and the design of efficient <span class="hlt">numerical</span> <span class="hlt">schemes</span> still receives important attention to provide robust and accurate solutions. In this study we propose a comparative study between the efficiency of two volume finite <span class="hlt">numerical</span> codes with second-order discretization implemented with different method to solve the non-conservative shallow water equations, the MUSCL (Monotonic Upstream-Centered <span class="hlt">Scheme</span> for Conservation Laws) and the MOOD methods (Multi-dimensional Optimal Order Detection) which optimize the accuracy of the approximation in function of the solution local smoothness. The MUSCL is based on a priori criteria where the limiting procedure is performed before updated the solution to the next time-step leading to non-necessary accuracy reduction. On the contrary, the new MOOD technique uses a posteriori detectors to prevent the solution from oscillating in the vicinity of the discontinuities. Indeed, a candidate solution is computed and corrections are performed only for the cells where non-physical oscillations are detected. Using a simple one-dimensional analytical benchmark, 'Single wave on a sloping beach', we show that the classical 1D shallow-water system can be accurately solved with the finite volume method equipped with the MOOD technique and provide better approximation with sharper shock and less <span class="hlt">numerical</span> diffusion. For the code validation, we also use the Tohoku-Oki 2011 tsunami and reproduce two DART records, demonstrating that the quality of the solution may deeply interfere with the scenario one can assess. This work is funded by the Portugal-France research agreement, through the research project GEONUM FCT-ANR/MAT-NAN/0122/2012.<span class="hlt">Numerical</span> tools turn to be very important for scenario evaluations of hazardous phenomena such as tsunami. Nevertheless, the predictions highly</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1422924-extended-lagrangian-excited-state-molecular-dynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1422924-extended-lagrangian-excited-state-molecular-dynamics"><span>Extended <span class="hlt">Lagrangian</span> Excited State Molecular Dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei; ...</p> <p>2018-01-09</p> <p>In this work, 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 formore » 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. In conclusion, the XL-ESMD approach is expected to enable <span class="hlt">numerically</span> 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).« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1422924-extended-lagrangian-excited-state-molecular-dynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1422924-extended-lagrangian-excited-state-molecular-dynamics"><span>Extended <span class="hlt">Lagrangian</span> Excited State 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>Bjorgaard, Josiah August; Sheppard, Daniel Glen; Tretiak, Sergei</p> <p></p> <p>In this work, 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 formore » 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. In conclusion, the XL-ESMD approach is expected to enable <span class="hlt">numerically</span> 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).« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AdAtS..34..482L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AdAtS..34..482L"><span><span class="hlt">Numerical</span> simulation of the rapid intensification of Hurricane Katrina (2005): Sensitivity to boundary layer parameterization <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Jianjun; Zhang, Feimin; Pu, Zhaoxia</p> <p>2017-04-01</p> <p>Accurate forecasting of the intensity changes of hurricanes is an important yet challenging problem in <span class="hlt">numerical</span> weather prediction. The rapid intensification of Hurricane Katrina (2005) before its landfall in the southern US is studied with the Advanced Research version of the WRF (Weather Research and Forecasting) model. The sensitivity of <span class="hlt">numerical</span> simulations to two popular planetary boundary layer (PBL) <span class="hlt">schemes</span>, the Mellor-Yamada-Janjic (MYJ) and the Yonsei University (YSU) <span class="hlt">schemes</span>, is investigated. It is found that, compared with the YSU simulation, the simulation with the MYJ <span class="hlt">scheme</span> produces better track and intensity evolution, better vortex structure, and more accurate landfall time and location. Large discrepancies (e.g., over 10 hPa in simulated minimum sea level pressure) are found between the two simulations during the rapid intensification period. Further diagnosis indicates that stronger surface fluxes and vertical mixing in the PBL from the simulation with the MYJ <span class="hlt">scheme</span> lead to enhanced air-sea interaction, which helps generate more realistic simulations of the rapid intensification process. Overall, the results from this study suggest that improved representation of surface fluxes and vertical mixing in the PBL is essential for accurate prediction of hurricane intensity changes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018ApJ...854....5J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018ApJ...854....5J"><span>A New <span class="hlt">Numerical</span> <span class="hlt">Scheme</span> for Cosmic-Ray Transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jiang, Yan-Fei; Oh, S. Peng</p> <p>2018-02-01</p> <p><span class="hlt">Numerical</span> solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful <span class="hlt">numerical</span> instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new <span class="hlt">numerical</span> algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new <span class="hlt">scheme</span> with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1324262-second-order-upwind-lagrangian-particle-method-euler-equations','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1324262-second-order-upwind-lagrangian-particle-method-euler-equations"><span>Second order upwind <span class="hlt">Lagrangian</span> particle method for Euler equations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin</p> <p>2016-06-01</p> <p>A new second order upwind <span class="hlt">Lagrangian</span> particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with <span class="hlt">Lagrangian</span> particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, <span class="hlt">numerical</span> verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1324262','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1324262"><span>Second order upwind <span class="hlt">Lagrangian</span> particle method for Euler equations</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>Samulyak, Roman; Chen, Hsin -Chiang; Yu, Kwangmin</p> <p></p> <p>A new second order upwind <span class="hlt">Lagrangian</span> particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with <span class="hlt">Lagrangian</span> particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and longmore » term stability, and (c) accurate resolution of states at free interfaces. In conclusion, <span class="hlt">numerical</span> verification tests demonstrating the convergence order for fixed domain and free surface problems are presented.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005JHEP...03..011L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005JHEP...03..011L"><span>BRST theory without Hamiltonian and <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>Lyakhovich, S. L.; Sharapov, A. A.</p> <p>2005-03-01</p> <p>We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure or action principle is supposed to exist. For such a generic gauge system we construct a consistent BRST formulation, which includes the conventional BV <span class="hlt">Lagrangian</span> and BFV Hamiltonian <span class="hlt">schemes</span> as particular cases. If the original manifold carries a weak Poisson structure (a bivector field giving rise to a Poisson bracket on the space of physical observables) the generic gauge system is shown to admit deformation quantization by means of the Kontsevich formality theorem. A sigma-model interpretation of this quantization algorithm is briefly discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009PhDT.......192W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009PhDT.......192W"><span>Dynamics of Multibody Systems Near <span class="hlt">Lagrangian</span> Points</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wong, Brian</p> <p></p> <p>This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the <span class="hlt">Lagrangian</span> points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the <span class="hlt">Lagrangian</span> method. The flexible body dynamics of the tethered and truss connected systems are examined using <span class="hlt">numerical</span> simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the <span class="hlt">Lagrangian</span> points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid <span class="hlt">Lagrangian</span> point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. <span class="hlt">Numerical</span> simulations are used to study the long term</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DFD.H8002C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFD.H8002C"><span><span class="hlt">Lagrangian</span> chaos in three- dimensional steady 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>2016-11-01</p> <p>Natural convection plays a key role in fluid dynamics owing to its ubiquitous presence in nature and industry. Buoyancy-driven flows are prototypical systems in the study of thermal instabilities and pattern formation. The differentially heated cavity problem has been widely studied for the investigation of buoyancy-induced oscillatory flow. However, far less attention has been devoted to the three-dimensional <span class="hlt">Lagrangian</span> transport properties in such flows. This study seeks to address this by investigating <span class="hlt">Lagrangian</span> transport in the steady flow inside a cubic cavity differentially-heated from the side. The theoretical and <span class="hlt">numerical</span> analysis expands on previously reported similarities between the current flow and lid-driven flows. The <span class="hlt">Lagrangian</span> dynamics are controlled by the Péclet number (Pe) and the Prandtl number (Pr). Pe controls the behaviour qualitatively in that growing Pe progressively perturbs the integable state (Pe =0), thus paving the way to chaotic dynamics. Pr plays an entirely quantitative role in that Pr<1 and Pr>1 amplifies and diminishes, respectively, the perturbative effect of non-zero Pe. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).</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('https://www.osti.gov/biblio/22667245-improved-performances-subsonic-flows-sph-scheme-gradients-estimated-using-integral-approach','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22667245-improved-performances-subsonic-flows-sph-scheme-gradients-estimated-using-integral-approach"><span>IMPROVED PERFORMANCES IN SUBSONIC FLOWS OF AN SPH <span class="hlt">SCHEME</span> WITH GRADIENTS ESTIMATED USING AN INTEGRAL APPROACH</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>Valdarnini, R., E-mail: valda@sissa.it</p> <p></p> <p>In this paper, we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically investigate the code behavior with subsonic flows, where it is well known that zeroth-order inconsistencies present in standard SPH make it particularly problematic to correctly model the fluid dynamics. In particular, we consider the Gresho–Chan vortex problem, the growth of Kelvin–Helmholtz instabilities, the statistics of driven subsonic turbulence and the cold Keplerian disk problem. We compare simulation results for the different tests with those obtained,more » for the same initial conditions, using standard SPH. We also compare the results with the corresponding ones obtained previously with other <span class="hlt">numerical</span> methods, such as codes based on a moving-mesh <span class="hlt">scheme</span> or Godunov-type <span class="hlt">Lagrangian</span> meshless methods. We quantify code performances by introducing error norms and spectral properties of the particle distribution, in a way similar to what was done in other works. We find that the new SPH formulation exhibits strongly reduced gradient errors and outperforms standard SPH in all of the tests considered. In fact, in terms of accuracy, we find good agreement between the simulation results of the new <span class="hlt">scheme</span> and those produced using other recently proposed <span class="hlt">numerical</span> <span class="hlt">schemes</span>. These findings suggest that the proposed method can be successfully applied for many astrophysical problems in which the presence of subsonic flows previously limited the use of SPH, with the new <span class="hlt">scheme</span> now being competitive in these regimes with other <span class="hlt">numerical</span> methods.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1991JCoPh..97....1B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1991JCoPh..97....1B"><span>A <span class="hlt">Numerical</span> <span class="hlt">Scheme</span> for the Solution of the Space Charge Problem on a Multiply Connected Region</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Budd, C. J.; Wheeler, A. A.</p> <p>1991-11-01</p> <p>In this paper we extend the work of Budd and Wheeler ( Proc. R. Soc. London A, 417, 389, 1988) , who described a new <span class="hlt">numerical</span> <span class="hlt">scheme</span> for the solution of the space charge equation on a simple connected domain, to multiply connected regions. The space charge equation, ▿ · ( Δ overlineϕ ▽ overlineϕ) = 0 , is a third-order nonlinear partial differential equation for the electric potential overlineϕ which models the electric field in the vicinity of a coronating conductor. Budd and Wheeler described a new way of analysing this equation by constructing an orthogonal coordinate system ( overlineϕ, overlineψ) and recasting the equation in terms of x, y, and ▽ overlineϕ as functions of ( overlineϕ, overlineψ). This transformation is singular on multiply connected regions and in this paper we show how this may be overcome to provide an efficient <span class="hlt">numerical</span> <span class="hlt">scheme</span> for the solution of the space charge equation. This <span class="hlt">scheme</span> also provides a new method for the solution of Laplaces equation and the calculation of orthogonal meshes on multiply connected regions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22622245-one-dimensional-lagrangian-implicit-hydrodynamic-algorithm-inertial-confinement-fusion-applications','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22622245-one-dimensional-lagrangian-implicit-hydrodynamic-algorithm-inertial-confinement-fusion-applications"><span>One-dimensional <span class="hlt">Lagrangian</span> implicit hydrodynamic algorithm for Inertial Confinement Fusion applications</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>Ramis, Rafael, E-mail: rafael.ramis@upm.es</p> <p></p> <p>A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The <span class="hlt">scheme</span> uses a fully conservative <span class="hlt">Lagrangian</span> formulation in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity formulation. The space discretized equations are advanced in time using an implicit algorithm. The method includes several <span class="hlt">numerical</span> parameters that can be adjusted locally. In regions with low Courant–Friedrichs–Lewy (CFL) number, where stability is not an issue, they can be adjusted tomore » optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser–matter interaction, where liquid–vapor phase transitions occur.« less</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 Eulerian-<span class="hlt">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 Eulerian-<span class="hlt">Lagrangian</span> computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated <span class="hlt">numerical</span> simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (Eulerian) 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 <span class="hlt">numerical</span> 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 Eulerian-<span class="hlt">Lagrangian</span> method is effective and reliable.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JCoPh.255..266C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JCoPh.255..266C"><span><span class="hlt">Numerical</span> investigation of a modified family of centered <span class="hlt">schemes</span> applied to multiphase equations with nonconservative sources</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Crochet, M. W.; Gonthier, K. A.</p> <p>2013-12-01</p> <p>Systems of hyperbolic partial differential equations are frequently used to model the flow of multiphase mixtures. These equations often contain sources, referred to as nozzling terms, that cannot be posed in divergence form, and have proven to be particularly challenging in the development of finite-volume methods. Upwind <span class="hlt">schemes</span> have recently shown promise in properly resolving the steady wave solution of the associated multiphase Riemann problem. However, these methods require a full characteristic decomposition of the system eigenstructure, which may be either unavailable or computationally expensive. Central <span class="hlt">schemes</span>, such as the Kurganov-Tadmor (KT) family of methods, require minimal characteristic information, which makes them easily applicable to systems with an arbitrary number of phases. However, the proper implementation of nozzling terms in these <span class="hlt">schemes</span> has been mathematically ambiguous. The primary objectives of this work are twofold: first, an extension of the KT family of <span class="hlt">schemes</span> is proposed that formally accounts for the nonconservative nozzling sources. This modification results in a semidiscrete form that retains the simplicity of its predecessor and introduces little additional computational expense. Second, this modified method is applied to multiple, but equivalent, forms of the multiphase equations to perform a <span class="hlt">numerical</span> study by solving several one-dimensional test problems. Both ideal and Mie-Grüneisen equations of state are used, with the results compared to an analytical solution. This study demonstrates that the magnitudes of the resulting <span class="hlt">numerical</span> errors are sensitive to the form of the equations considered, and suggests an optimal form to minimize these errors. Finally, a separate modification of the wave propagation speeds used in the KT family is also suggested that can reduce the extent of <span class="hlt">numerical</span> diffusion in multiphase flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900019473','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900019473"><span>On the use of <span class="hlt">Lagrangian</span> variables in descriptions of unsteady boundary-layer separation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Cowley, Stephen J.; Vandommelen, Leon L.; Lam, Shui T.</p> <p>1990-01-01</p> <p>The <span class="hlt">Lagrangian</span> description of unsteady boundary layer separation is reviewed from both analytical and <span class="hlt">numerical</span> perspectives. It is explained in simple terms how particle distortion gives rise to unsteady separation, and why a theory centered on <span class="hlt">Lagrangian</span> coordinates provides the clearest description of this phenomenon. Some of the more recent results for unsteady three dimensional compressible separation are included. The different forms of separation that can arise from symmetries are emphasized. A possible description of separation is also included when the detaching vorticity layer exits the classical boundary layer region, but still remains much closer to the surface than a typical body-lengthscale.</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('http://adsabs.harvard.edu/abs/2015WRR....51..987L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015WRR....51..987L"><span>A faster <span class="hlt">numerical</span> <span class="hlt">scheme</span> for a coupled system modeling soil erosion and sediment transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Le, M.-H.; Cordier, S.; Lucas, C.; Cerdan, O.</p> <p>2015-02-01</p> <p>Overland flow and soil erosion play an essential role in water quality and soil degradation. Such processes, involving the interactions between water flow and the bed sediment, are classically described by a well-established system coupling the shallow water equations and the Hairsine-Rose model. <span class="hlt">Numerical</span> approximation of this coupled system requires advanced methods to preserve some important physical and mathematical properties; in particular, the steady states and the positivity of both water depth and sediment concentration. Recently, finite volume <span class="hlt">schemes</span> based on Roe's solver have been proposed by Heng et al. (2009) and Kim et al. (2013) for one and two-dimensional problems. In their approach, an additional and artificial restriction on the time step is required to guarantee the positivity of sediment concentration. This artificial condition can lead the computation to be costly when dealing with very shallow flow and wet/dry fronts. The main result of this paper is to propose a new and faster <span class="hlt">scheme</span> for which only the CFL condition of the shallow water equations is sufficient to preserve the positivity of sediment concentration. In addition, the <span class="hlt">numerical</span> procedure of the erosion part can be used with any well-balanced and positivity preserving <span class="hlt">scheme</span> of the shallow water equations. The proposed method is tested on classical benchmarks and also on a realistic configuration.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.363..200D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.363..200D"><span>A conservative <span class="hlt">numerical</span> <span class="hlt">scheme</span> for modeling nonlinear acoustic propagation in thermoviscous homogeneous media</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.</p> <p>2018-06-01</p> <p>A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the <span class="hlt">scheme</span> can match the solutions of the Westervelt and Burgers equations <span class="hlt">numerically</span>. Here, high-order <span class="hlt">numerical</span> descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) <span class="hlt">schemes</span> associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.</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('http://adsabs.harvard.edu/abs/2018JCoPh.362....1S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.362....1S"><span><span class="hlt">Lagrangian</span> particle method for compressible fluid dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Samulyak, Roman; Wang, Xingyu; Chen, Hsin-Chiang</p> <p>2018-06-01</p> <p>A new <span class="hlt">Lagrangian</span> particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with <span class="hlt">Lagrangian</span> particles and is suitable for the simulation of complex free surface/multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremal points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free interfaces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order. The method is generalizable to coupled hyperbolic-elliptic systems. <span class="hlt">Numerical</span> verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.</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/2011APS..DPPGP9002C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..DPPGP9002C"><span>Asymptotic-preserving <span class="hlt">Lagrangian</span> approach for modeling anisotropic transport in magnetized plasmas</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</p> <p>2011-10-01</p> <p>Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy introduced by the presence of the magnetic field (χ∥ /χ⊥ ~1010 in fusion plasmas). Recently, a novel <span class="hlt">Lagrangian</span> method has been proposed to solve the local and non-local purely parallel transport equation in general 3D magnetic fields. The approach avoids <span class="hlt">numerical</span> pollution (in fact, it respects transport barriers -flux surfaces- exactly by construction), is inherently positivity-preserving, and is scalable algorithmically (i.e., work per degree-of-freedom is grid-independent). In this poster, we discuss the extension of the <span class="hlt">Lagrangian</span> approach to include perpendicular transport and sources. We present an asymptotic-preserving <span class="hlt">numerical</span> formulation that ensures a consistent <span class="hlt">numerical</span> discretization temporally and spatially for arbitrary χ∥ /χ⊥ ratios. This is of importance because parallel and perpendicular transport terms in the transport equation may become comparable in regions of the plasma (e.g., at incipient islands), while remaining disparate elsewhere. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry. D. del-Castillo-Negrete, L. Chacón, PRL, 106, 195004 (2011); DPP11 invited talk by del-Castillo-Negrete.</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 Eulerian-<span class="hlt">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 Eulerian-<span class="hlt">Lagrangian</span> large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main <span class="hlt">numerical</span> novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between Eulerian 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 Eulerian 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('http://adsabs.harvard.edu/abs/2014JPhCS.572a2055B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JPhCS.572a2055B"><span><span class="hlt">Numerical</span> modelling of physical processes in a ballistic laboratory setup with a tapered adapter and plastic piston used for obtaining high muzzle velocities</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bykov, N. V.</p> <p>2014-12-01</p> <p><span class="hlt">Numerical</span> modelling of a ballistic setup with a tapered adapter and plastic piston is considered. The processes in the firing chamber are described within the framework of quasi- one-dimensional gas dynamics and a geometrical law of propellant burn by means of <span class="hlt">Lagrangian</span> mass coordinates. The deformable piston is considered to be an ideal liquid with specific equations of state. The <span class="hlt">numerical</span> solution is obtained by means of a modified explicit von Neumann <span class="hlt">scheme</span>. The calculation results given show that the ballistic setup with a tapered adapter and plastic piston produces increased shell muzzle velocities by a factor of more than 1.5-2.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DPPN11052C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DPPN11052C"><span>Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary <span class="hlt">Lagrangian</span>-Eulerian Code</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cornille, Brian; White, Dan</p> <p>2017-10-01</p> <p>We will present methods formulated for the Eulerian advection stage of an arbitrary <span class="hlt">Lagrangian</span>-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a <span class="hlt">Lagrangian</span> formulation of the system. When this <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">numerical</span> 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.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23679366','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23679366"><span><span class="hlt">Lagrangian</span> single-particle turbulent statistics through the Hilbert-Huang transform.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Huang, Yongxiang; Biferale, Luca; Calzavarini, Enrico; Sun, Chao; Toschi, Federico</p> <p>2013-04-01</p> <p>The Hilbert-Huang transform is applied to analyze single-particle <span class="hlt">Lagrangian</span> velocity data from <span class="hlt">numerical</span> simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions C(i)(t) and of their instantaneous frequency ω(i)(t). On the basis of this decomposition we define the ω-conditioned statistical moments of the C(i) modes, named q-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the <span class="hlt">Lagrangian</span> structure function exponents which are consistent with the multifractal prediction in the <span class="hlt">Lagrangian</span> frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/862058','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/862058"><span>Chiral <span class="hlt">Lagrangian</span> with Heavy Quark-Diquark Symmetry</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>Jie Hu; Thomas Mehen</p> <p>2005-11-29</p> <p>We construct a chiral <span class="hlt">Lagrangian</span> for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading O(1/m{sub Q}) symmetry violating operators. The theory is used to predict the electromagnetic decay width of the J=3/2 member of the ground state doubly heavy baryon doublet. <span class="hlt">Numerical</span> estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1361154-gaussian-streaming-model-convolution-lagrangian-effective-field-theory','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1361154-gaussian-streaming-model-convolution-lagrangian-effective-field-theory"><span>The Gaussian streaming model and convolution <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; Castorina, Emanuele; White, Martin</p> <p>2016-12-05</p> <p>We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of <span class="hlt">Lagrangian</span> perturbation theory, effective field theory (EFT) and a generalized <span class="hlt">Lagrangian</span> bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing <span class="hlt">scheme</span>, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22679373-gaussian-streaming-model-convolution-lagrangian-effective-field-theory','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22679373-gaussian-streaming-model-convolution-lagrangian-effective-field-theory"><span>The Gaussian streaming model and convolution <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; Castorina, Emanuele; White, Martin, E-mail: zvlah@stanford.edu, E-mail: ecastorina@berkeley.edu, E-mail: mwhite@berkeley.edu</p> <p></p> <p>We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of <span class="hlt">Lagrangian</span> perturbation theory, effective field theory (EFT) and a generalized <span class="hlt">Lagrangian</span> bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM tomore » a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing <span class="hlt">scheme</span>, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MNRAS.466.3387H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MNRAS.466.3387H"><span>Anisotropic diffusion in mesh-free <span class="hlt">numerical</span> magnetohydrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hopkins, Philip F.</p> <p>2017-04-01</p> <p>We extend recently developed mesh-free <span class="hlt">Lagrangian</span> methods for <span class="hlt">numerical</span> magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent 'eddy diffusion'. We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov <span class="hlt">schemes</span> (MFM/MFV). We show that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new <span class="hlt">scheme</span> for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010OcSci...6..913J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010OcSci...6..913J"><span>A <span class="hlt">numerical</span> <span class="hlt">scheme</span> to calculate temperature and salinity dependent air-water transfer velocities for any gas</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Johnson, M. T.</p> <p>2010-10-01</p> <p>The ocean-atmosphere flux of a gas can be calculated from its measured or estimated concentration gradient across the air-sea interface and the transfer velocity (a term representing the conductivity of the layers either side of the interface with respect to the gas of interest). Traditionally the transfer velocity has been estimated from empirical relationships with wind speed, and then scaled by the Schmidt number of the gas being transferred. Complex, physically based models of transfer velocity (based on more physical forcings than wind speed alone), such as the NOAA COARE algorithm, have more recently been applied to well-studied gases such as carbon dioxide and DMS (although many studies still use the simpler approach for these gases), but there is a lack of validation of such <span class="hlt">schemes</span> for other, more poorly studied gases. The aim of this paper is to provide a flexible <span class="hlt">numerical</span> <span class="hlt">scheme</span> which will allow the estimation of transfer velocity for any gas as a function of wind speed, temperature and salinity, given data on the solubility and liquid molar volume of the particular gas. New and existing parameterizations (including a novel empirical parameterization of the salinity-dependence of Henry's law solubility) are brought together into a <span class="hlt">scheme</span> implemented as a modular, extensible program in the R computing environment which is available in the supplementary online material accompanying this paper; along with input files containing solubility and structural data for ~90 gases of general interest, enabling the calculation of their total transfer velocities and component parameters. Comparison of the <span class="hlt">scheme</span> presented here with alternative <span class="hlt">schemes</span> and methods for calculating air-sea flux parameters shows good agreement in general. It is intended that the various components of this <span class="hlt">numerical</span> <span class="hlt">scheme</span> should be applied only in the absence of experimental data providing robust values for parameters for a particular gas of interest.</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</span>-Eulerian 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</span>-Eulerian (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. <span class="hlt">Numerical</span> examples are presented which demonstrate the accuracy and efficiency of the method.« less</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 <span class="hlt">numerical</span> model for predicting pollutant and sediment transport using an Eulerian-<span class="hlt">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 coded <span class="hlt">Lagrangian</span> marker particle in Eulerian 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. <span class="hlt">Numerical</span> 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('http://adsabs.harvard.edu/abs/2018APhy...64....1G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018APhy...64....1G"><span>Hybrid <span class="hlt">Numerical</span>-Analytical <span class="hlt">Scheme</span> for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.</p> <p>2018-01-01</p> <p><span class="hlt">Numerical</span> simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid <span class="hlt">numerical</span>-analytic approaches are being developed based on the conjugation of a <span class="hlt">numerical</span> solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational <span class="hlt">scheme</span> that allows realization of such a conjugation using a standard software. The latter is used to construct a set of <span class="hlt">numerical</span> solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid <span class="hlt">scheme</span> can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.</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_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('http://hdl.handle.net/2060/19960016617','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960016617"><span><span class="hlt">Numerical</span> Investigation of Two-Phase Flows With Charged Droplets in Electrostatic Field</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kim, Sang-Wook</p> <p>1996-01-01</p> <p>A <span class="hlt">numerical</span> method to solve two-phase turbulent flows with charged droplets in an electrostatic field is presented. The ensemble-averaged Navier-Stokes equations and the electrostatic potential equation are solved using a finite volume method. The transitional turbulence field is described using multiple-time-scale turbulence equations. The equations of motion of droplets are solved using a <span class="hlt">Lagrangian</span> particle tracking <span class="hlt">scheme</span>, and the inter-phase momentum exchange is described by the Particle-In-Cell <span class="hlt">scheme</span>. The electrostatic force caused by an applied electrical potential is calculated using the electrostatic field obtained by solving a Laplacian equation and the force exerted by charged droplets is calculated using the Coulombic force equation. The method is applied to solve electro-hydrodynamic sprays. The calculated droplet velocity distributions for droplet dispersions occurring in a stagnant surrounding are in good agreement with the measured data. For droplet dispersions occurring in a two-phase flow, the droplet trajectories are influenced by aerodynamic forces, the Coulombic force, and the applied electrostatic potential field.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950023716&hterms=comparative+study&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dcomparative%2Bstudy','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950023716&hterms=comparative+study&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dcomparative%2Bstudy"><span>Comparative study of <span class="hlt">numerical</span> <span class="hlt">schemes</span> of TVD3, UNO3-ACM and optimized compact <span class="hlt">scheme</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lee, Duck-Joo; Hwang, Chang-Jeon; Ko, Duck-Kon; Kim, Jae-Wook</p> <p>1995-01-01</p> <p>Three different <span class="hlt">schemes</span> are employed to solve the benchmark problem. The first one is a conventional TVD-MUSCL (Monotone Upwind <span class="hlt">Schemes</span> for Conservation Laws) <span class="hlt">scheme</span>. The second <span class="hlt">scheme</span> is a UNO3-ACM (Uniformly Non-Oscillatory Artificial Compression Method) <span class="hlt">scheme</span>. The third <span class="hlt">scheme</span> is an optimized compact finite difference <span class="hlt">scheme</span> modified by us: the 4th order Runge Kutta time stepping, the 4th order pentadiagonal compact spatial discretization with the maximum resolution characteristics. The problems of category 1 are solved by using the second (UNO3-ACM) and third (Optimized Compact) <span class="hlt">schemes</span>. The problems of category 2 are solved by using the first (TVD3) and second (UNO3-ACM) <span class="hlt">schemes</span>. The problem of category 5 is solved by using the first (TVD3) <span class="hlt">scheme</span>. It can be concluded from the present calculations that the Optimized Compact <span class="hlt">scheme</span> and the UN03-ACM show good resolutions for category 1 and category 2 respectively.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CMMPh..58..274S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CMMPh..58..274S"><span>High-Order Multioperator Compact <span class="hlt">Schemes</span> for <span class="hlt">Numerical</span> Simulation of Unsteady Subsonic Airfoil Flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Savel'ev, A. D.</p> <p>2018-02-01</p> <p>On the basis of high-order <span class="hlt">schemes</span>, the viscous gas flow over the NACA2212 airfoil is <span class="hlt">numerically</span> simulated at a free-stream Mach number of 0.3 and Reynolds numbers ranging from 103 to 107. Flow regimes sequentially varying due to variations in the free-stream viscosity are considered. Vortex structures developing on the airfoil surface are investigated, and a physical interpretation of this phenomenon is given.</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 Eulerian-<span class="hlt">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 Eulerian-<span class="hlt">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. <span class="hlt">Numerical</span> examples illustrating these methods are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/5455999-lagrangian-formulation-penny-shaped-perkins-kern-geometry-models','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/5455999-lagrangian-formulation-penny-shaped-perkins-kern-geometry-models"><span><span class="hlt">Lagrangian</span> formulation for penny-shaped and Perkins-Kern geometry models</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.S.</p> <p>1989-09-01</p> <p>This paper discusses basic theories for vertical penny-shaped and Perkins-Kern (PK) geometry models developed with a <span class="hlt">Lagrangian</span> formulation combined with a virtual-work analysis. The <span class="hlt">Lagrangian</span> formulation yields a pair of nonlinear equations in R/sub f/ or L/sub f/ and b/sub f/, the fracture radius or length and half-width. By introduction of a virtual-work analysis, a simple equation is obtained that can be solved <span class="hlt">numerically</span>. This equation is written in a form that can be used to determine fracture geometry when the fluid-loss coefficient of the fracturing fluid is known. Also, this equation, coupled with a material-balance equation after shut-in, canmore » be used to analyze pressure-decline data after shut-in to determine the effective fluid-loss coefficient and fracture geometry.« less</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 code 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 <span class="hlt">scheme</span> 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('https://ntrs.nasa.gov/search.jsp?R=19930040954&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=19930040954&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian"><span>Computing 3-D steady supersonic flow via a new <span class="hlt">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>Loh, C. Y.; Liou, M.-S.</p> <p>1993-01-01</p> <p>The new <span class="hlt">Lagrangian</span> method introduced by Loh and Hui (1990) is extended for 3-D steady supersonic flow computation. Details of the conservation form, the implementation of the local Riemann solver, and the Godunov and the high resolution TVD <span class="hlt">schemes</span> are presented. The new approach is robust yet accurate, capable of handling complicated geometry and reactions between discontinuous waves. It keeps all the advantages claimed in the 2-D method of Loh and Hui, e.g., crisp resolution for a slip surface (contact discontinuity) and automatic grid generation along the stream.</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 <span class="hlt">numerical</span> 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 Eulerian-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('http://adsabs.harvard.edu/abs/2014HESS...18.2503C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014HESS...18.2503C"><span>Kalman filters for assimilating near-surface observations into the Richards equation - Part 1: Retrieving state profiles with linear and nonlinear <span class="hlt">numerical</span> <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chirico, G. B.; Medina, H.; Romano, N.</p> <p>2014-07-01</p> <p>This paper examines the potential of different algorithms, based on the Kalman filtering approach, for assimilating near-surface observations into a one-dimensional Richards equation governing soil water flow in soil. Our specific objectives are: (i) to compare the efficiency of different Kalman filter algorithms in retrieving matric pressure head profiles when they are implemented with different <span class="hlt">numerical</span> <span class="hlt">schemes</span> of the Richards equation; (ii) to evaluate the performance of these algorithms when nonlinearities arise from the nonlinearity of the observation equation, i.e. when surface soil water content observations are assimilated to retrieve matric pressure head values. The study is based on a synthetic simulation of an evaporation process from a homogeneous soil column. Our first objective is achieved by implementing a Standard Kalman Filter (SKF) algorithm with both an explicit finite difference <span class="hlt">scheme</span> (EX) and a Crank-Nicolson (CN) linear finite difference <span class="hlt">scheme</span> of the Richards equation. The Unscented (UKF) and Ensemble Kalman Filters (EnKF) are applied to handle the nonlinearity of a backward Euler finite difference <span class="hlt">scheme</span>. To accomplish the second objective, an analogous framework is applied, with the exception of replacing SKF with the Extended Kalman Filter (EKF) in combination with a CN <span class="hlt">numerical</span> <span class="hlt">scheme</span>, so as to handle the nonlinearity of the observation equation. While the EX <span class="hlt">scheme</span> is computationally too inefficient to be implemented in an operational assimilation <span class="hlt">scheme</span>, the retrieval algorithm implemented with a CN <span class="hlt">scheme</span> is found to be computationally more feasible and accurate than those implemented with the backward Euler <span class="hlt">scheme</span>, at least for the examined one-dimensional problem. The UKF appears to be as feasible as the EnKF when one has to handle nonlinear <span class="hlt">numerical</span> <span class="hlt">schemes</span> or additional nonlinearities arising from the observation equation, at least for systems of small dimensionality as the one examined in this study.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CompM..55..903N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CompM..55..903N"><span><span class="hlt">Numerically</span> stable formulas for a particle-based explicit exponential integrator</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</p> <p>2015-05-01</p> <p><span class="hlt">Numerically</span> stable formulas are presented for the closed-form analytical solution of the X-IVAS <span class="hlt">scheme</span> in 3D. This <span class="hlt">scheme</span> is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this <span class="hlt">scheme</span> involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (<span class="hlt">Lagrangian</span>-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS <span class="hlt">scheme</span>. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DFD.A3005J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DFD.A3005J"><span><span class="hlt">Numerical</span> Simulation of Shock Interaction with Deformable Particles Using a Constrained Interface Reinitialization <span class="hlt">Scheme</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jackson, Thomas L.; Sridharan, Prashanth; Zhang, Ju; Balachandar, S.</p> <p>2015-11-01</p> <p>In this work we present axisymmetric <span class="hlt">numerical</span> simulations of shock propagating in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. The <span class="hlt">numerical</span> method is a finite-volume based solver on a Cartesian grid, which allows for multi-material interfaces and shocks. To preserve particle mass and volume, a novel constraint reinitialization <span class="hlt">scheme</span> is introduced. We compute the unsteady drag coefficient as a function of post-shock pressure, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. Using this information, we also present a simplified point-particle force model that can be used for mesoscale simulations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1439449-lagrangian-particle-method-compressible-fluid-dynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1439449-lagrangian-particle-method-compressible-fluid-dynamics"><span><span class="hlt">Lagrangian</span> particle method for compressible fluid 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>Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang</p> <p></p> <p>A new <span class="hlt">Lagrangian</span> particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with <span class="hlt">Lagrangian</span> particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, <span class="hlt">numerical</span> verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1439449-lagrangian-particle-method-compressible-fluid-dynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1439449-lagrangian-particle-method-compressible-fluid-dynamics"><span><span class="hlt">Lagrangian</span> particle method for compressible fluid dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Samulyak, Roman; Wang, Xingyu; Chen, Hsin -Chiang</p> <p>2018-02-09</p> <p>A new <span class="hlt">Lagrangian</span> particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with <span class="hlt">Lagrangian</span> particles and is suitable for the simulation of complex free surface / multi-phase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) a second-order particle-based algorithm that reduces to the first-order upwind method at local extremalmore » points, providing accuracy and long term stability, and (c) more accurate resolution of entropy discontinuities and states at free inter-faces. While the method is consistent and convergent to a prescribed order, the conservation of momentum and energy is not exact and depends on the convergence order . The method is generalizable to coupled hyperbolic-elliptic systems. As a result, <span class="hlt">numerical</span> verification tests demonstrating the convergence order are presented as well as examples of complex multiphase flows.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/6941008','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/6941008"><span>First order comparison of <span class="hlt">numerical</span> calculation and two different turtle input <span class="hlt">schemes</span> to represent a SLC defocusing magnet</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>Jaeger, J.</p> <p>1983-07-14</p> <p>Correcting the dispersion function in the SLC north arc it turned out that backleg-windings (BLW) acting horizontally as well as BLW acting vertically have to be used. In the latter case the question arose what is the best representation of a defocusing magnet with excited BLW acting in the vertical plane for the computer code TURTLE. Two different <span class="hlt">schemes</span>, the 14.-<span class="hlt">scheme</span> and the 20.-<span class="hlt">scheme</span> were studied and the TURTLE output for one ray through such a magnet compared with the <span class="hlt">numerical</span> solution of the equation of motion; only terms of first order have been taken into account.</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://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/2013JSP...153..801L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JSP...153..801L"><span><span class="hlt">Numerical</span> Solution of Dyson Brownian Motion and a Sampling <span class="hlt">Scheme</span> for Invariant Matrix Ensembles</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Li, Xingjie Helen; Menon, Govind</p> <p>2013-12-01</p> <p>The Dyson Brownian Motion (DBM) describes the stochastic evolution of N points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler <span class="hlt">scheme</span> to <span class="hlt">numerically</span> solve the Dyson Brownian motion and sample the equilibrium measure for non-quadratic potentials. The Coulomb repulsion is too singular for the SDE to satisfy the hypotheses of rigorous convergence proofs for tamed Euler <span class="hlt">schemes</span> (Hutzenthaler et al. in Ann. Appl. Probab. 22(4):1611-1641, 2012). Nevertheless, in practice the <span class="hlt">scheme</span> is observed to be stable for time steps of O(1/ N 2) and to relax exponentially fast to the equilibrium measure with a rate constant of O(1) independent of N. Further, this convergence rate appears to improve with N in accordance with O(1/ N) relaxation of local statistics of the Dyson Brownian motion. This allows us to use the Dyson Brownian motion to sample N× N Hermitian matrices from the invariant ensembles. The computational cost of generating M independent samples is O( MN 4) with a naive <span class="hlt">scheme</span>, and O( MN 3log N) when a fast multipole method is used to evaluate the Coulomb interaction.</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> </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.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><span class="hlt">Numerical</span> methods for the weakly compressible Generalized Langevin Model in Eulerian 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 <span class="hlt">numerical</span> 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 Eulerian reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a Eulerian-frame <span class="hlt">numerical</span> flow solver. GLM in a Eulerian 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 <span class="hlt">numerical</span> solution of GLMEF requires special considerations. In this paper we investigate different <span class="hlt">numerical</span> 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 <span class="hlt">scheme</span>, adapted from a <span class="hlt">scheme</span> originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than <span class="hlt">schemes</span> 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/2016SoPh..291.3583G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016SoPh..291.3583G"><span>A Fixed-point <span class="hlt">Scheme</span> for the <span class="hlt">Numerical</span> Construction of Magnetohydrostatic Atmospheres in Three Dimensions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gilchrist, S. A.; Braun, D. C.; Barnes, G.</p> <p>2016-12-01</p> <p>Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. <span class="hlt">Numerical</span> approaches, too, are often limited in scope and have tended to focus on the two-dimensional problem. In this article we develop a <span class="hlt">numerical</span> method for solving the nonlinear magnetohydrostatic equations in three dimensions. Our method is a fixed-point iteration <span class="hlt">scheme</span> that extends the method of Grad and Rubin ( Proc. 2nd Int. Conf. on Peaceful Uses of Atomic Energy 31, 190, 1958) to include a finite gravity force. We apply the method to a test case to demonstrate the method in general and our implementation in code in particular.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016BoLMe.160..269R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016BoLMe.160..269R"><span>A New Framework to Compare Mass-Flux <span class="hlt">Schemes</span> Within the AROME <span class="hlt">Numerical</span> Weather Prediction Model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Riette, Sébastien; Lac, Christine</p> <p>2016-08-01</p> <p>In the Application of Research to Operations at Mesoscale (AROME) <span class="hlt">numerical</span> weather forecast model used in operations at Météo-France, five mass-flux <span class="hlt">schemes</span> are available to parametrize shallow convection at kilometre resolution. All but one are based on the eddy-diffusivity-mass-flux approach, and differ in entrainment/detrainment, the updraft vertical velocity equation and the closure assumption. The fifth is based on a more classical mass-flux approach. Screen-level scores obtained with these <span class="hlt">schemes</span> show few discrepancies and are not sufficient to highlight behaviour differences. Here, we describe and use a new experimental framework, able to compare and discriminate among different <span class="hlt">schemes</span>. For a year, daily forecast experiments were conducted over small domains centred on the five French metropolitan radio-sounding locations. Cloud base, planetary boundary-layer height and normalized vertical profiles of specific humidity, potential temperature, wind speed and cloud condensate were compared with observations, and with each other. The framework allowed the behaviour of the different <span class="hlt">schemes</span> in and above the boundary layer to be characterized. In particular, the impact of the entrainment/detrainment formulation, closure assumption and cloud <span class="hlt">scheme</span> were clearly visible. Differences mainly concerned the transport intensity thus allowing <span class="hlt">schemes</span> to be separated into two groups, with stronger or weaker updrafts. In the AROME model (with all interactions and the possible existence of compensating errors), evaluation diagnostics gave the advantage to the first group.</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://hdl.handle.net/2060/19930017851','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930017851"><span>Parallel solution of high-order <span class="hlt">numerical</span> <span class="hlt">schemes</span> for solving incompressible flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Milner, Edward J.; Lin, Avi; Liou, May-Fun; Blech, Richard A.</p> <p>1993-01-01</p> <p>A new parallel <span class="hlt">numerical</span> <span class="hlt">scheme</span> for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790021668','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790021668"><span>Research on an augmented <span class="hlt">Lagrangian</span> penalty function algorithm for nonlinear programming</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Frair, L.</p> <p>1978-01-01</p> <p>The augmented <span class="hlt">Lagrangian</span> (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. <span class="hlt">Numerical</span> experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920016571&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=19920016571&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing"><span>A new <span class="hlt">Lagrangian</span> method for real gases at supersonic speed</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.; Liou, Meng-Sing</p> <p>1992-01-01</p> <p>With the renewed interest in high speed flights, the real gas effect is of theoretical as well as practical importance. In the past decade, upwind splittings or Godunov-type Riemann solutions have received tremendous attention and as a result significant progress has been made both in the ideal and non-ideal gas. In this paper, we propose a new approach that is formulated using the <span class="hlt">Lagrangian</span> description, for the calculation of supersonic/hypersonic real gas inviscid flows. This new formulation avoids the grid generation step which is automatically obtained as the solution procedure marches in the 'time-like' direction. As a result, no remapping is required and the accuracy is faithfully maintained in the <span class="hlt">Lagrangian</span> level. In this paper, we give <span class="hlt">numerical</span> results for a variety of real gas problems consisting of essential elements in high speed flows, such as shock waves, expansion waves, slip surfaces and their interactions. Finally, calculations for flows in a generic inlet and nozzle are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1361589','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1361589"><span>ALE3D: An Arbitrary <span class="hlt">Lagrangian</span>-Eulerian Multi-Physics Code</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>Noble, Charles R.; Anderson, Andrew T.; Barton, Nathan R.</p> <p></p> <p>ALE3D is a multi-physics <span class="hlt">numerical</span> simulation software tool utilizing arbitrary-<span class="hlt">Lagrangian</span>- 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.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20070022276','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20070022276"><span>An Improved Transformation and Optimized Sampling <span class="hlt">Scheme</span> for the <span class="hlt">Numerical</span> Evaluation of Singular and Near-Singular Potentials</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Khayat, Michael A.; Wilton, Donald R.; Fink, Patrick W.</p> <p>2007-01-01</p> <p>Simple and efficient <span class="hlt">numerical</span> procedures using singularity cancellation methods are presented for evaluating singular and near-singular potential integrals. Four different transformations are compared and the advantages of the Radial-angular transform are demonstrated. A method is then described for optimizing this integration <span class="hlt">scheme</span>.</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/19658812','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19658812"><span><span class="hlt">Lagrangian</span>-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Pietarila Graham, Jonathan; Mininni, Pablo D; Pouquet, Annick</p> <p>2009-07-01</p> <p>We demonstrate that, for the case of quasiequipartition between the velocity and the magnetic field, the <span class="hlt">Lagrangian</span>-averaged magnetohydrodynamics (LAMHD) alpha model reproduces well both the large-scale and the small-scale properties of turbulent flows; in particular, it displays no increased (superfilter) bottleneck effect with its ensuing enhanced energy spectrum at the onset of the subfilter scales. This is in contrast to the case of the neutral fluid in which the <span class="hlt">Lagrangian</span>-averaged Navier-Stokes alpha model is somewhat limited in its applications because of the formation of spatial regions with no internal degrees of freedom and subsequent contamination of superfilter-scale spectral properties. We argue that, as the Lorentz force breaks the conservation of circulation and enables spectrally nonlocal energy transfer (associated with Alfvén waves), it is responsible for the absence of a viscous bottleneck in magnetohydrodynamics (MHD), as compared to the fluid case. As LAMHD preserves Alfvén waves and the circulation properties of MHD, there is also no (superfilter) bottleneck found in LAMHD, making this method capable of large reductions in required <span class="hlt">numerical</span> degrees of freedom; specifically, we find a reduction factor of approximately 200 when compared to a direct <span class="hlt">numerical</span> simulation on a large grid of 1536;{3} points at the same Reynolds number.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29581453','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29581453"><span>Extracting quasi-steady <span class="hlt">Lagrangian</span> transport patterns from the ocean circulation: An application to the Gulf of Mexico.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Duran, R; Beron-Vera, F J; Olascoaga, M J</p> <p>2018-03-26</p> <p>We construct a climatology of <span class="hlt">Lagrangian</span> coherent structures (LCSs)-the concealed skeleton that shapes transport-with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as time-mean Cauchy-Green strain tensorlines of the climatological velocity, the climatological LCSs (cLCSs) unveil recurrent <span class="hlt">Lagrangian</span> circulation patterns. The cLCSs strongly constrain the ensemble-mean <span class="hlt">Lagrangian</span> circulation of the instantaneous model velocity, showing that a climatological velocity can preserve meaningful transport information. The quasi-steady transport patterns revealed by the cLCSs agree well with aspects of the GoM circulation described in several previous observational and <span class="hlt">numerical</span> studies. For example, the cLCSs identify regions of persistent isolation, and suggest that coastal regions previously identified as high-risk for pollution impact are regions of maximal attraction. We also show that cLCSs are remarkably accurate at identifying transport patterns observed during the Deepwater Horizon and Ixtoc oil spills, and during the Grand <span class="hlt">LAgrangian</span> Deployment (GLAD) experiment. Thus it is shown that computing cLCSs is an efficient and meaningful way of synthesizing vast amounts of <span class="hlt">Lagrangian</span> information. The cLCS method confirms previous GoM studies, and contributes to our understanding by revealing the persistent nature of the dynamics and kinematics treated therein.</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> computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of <span class="hlt">Lagrangian</span> and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. <span class="hlt">Numerical</span> results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature. © Springer-Verlag 2011</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> the purpose of computation, thanks to the equivalence of the Laplace-Beltrami operator in the two representations. The coupled partial differential equations (PDEs) are solved with an iterative procedure to reach a steady state, which delivers desired solvent-solute interface and electrostatic potential for problems of interest. These quantities are utilized to evaluate the solvation free energies and protein-protein binding affinities. A number of computational methods and algorithms are described for the interconversion of <span class="hlt">Lagrangian</span> and Eulerian representations, and for the solution of the coupled PDE system. The proposed approaches have been extensively validated. We also verify that the mean curvature flow indeed gives rise to the minimal molecular surface (MMS) and the proposed variational procedure indeed offers minimal total free energy. Solvation analysis and applications are considered for a set of 17 small compounds and a set of 23 proteins. The salt effect on protein-protein binding affinity is investigated with two protein complexes by using the present model. <span class="hlt">Numerical</span> results are compared to the experimental measurements and to those obtained by using other theoretical methods in the literature. PMID:21279359</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/2016APS..DFDD17004D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDD17004D"><span><span class="hlt">Lagrangian</span> analysis of premixed turbulent combustion in hydrogen-air flames</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter</p> <p>2016-11-01</p> <p><span class="hlt">Lagrangian</span> analysis has long been a tool used to analyze non-reacting turbulent flows, and has recently gained attention in the reacting flow and combustion communities. The approach itself allows one to separate local molecular effects, such as those due to reactions or diffusion, from turbulent advective effects along fluid pathlines, or trajectories. Accurate calculation of these trajectories can, however, be rather difficult due to the chaotic nature of turbulent flows and the added complexity of reactions. In order to determine resolution requirements and verify the <span class="hlt">numerical</span> algorithm, extensive tests are described in this talk for prescribed steady, unsteady, and chaotic flows, as well as for direct <span class="hlt">numerical</span> simulations (DNS) of non-reacting homogeneous isotropic turbulence. The <span class="hlt">Lagrangian</span> analysis is then applied to DNS of premixed hydrogen-air flames at two different turbulence intensities for both single- and multi-step chemical mechanisms. Non-monotonic temperature and fuel-mass fraction evolutions are found to exist along trajectories passing through the flame brush. Such non-monotonicity is shown to be due to molecular diffusion resulting from large spatial gradients created by turbulent advection. This work was supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-14-1-0273, and the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) under a Frontier project award.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20070003485&hterms=levels+law&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DA%2Blevels%2Blaw','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20070003485&hterms=levels+law&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3DA%2Blevels%2Blaw"><span><span class="hlt">Numerical</span> <span class="hlt">Schemes</span> for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Barth, Timothy J.; Sethian, James A.</p> <p>2006-01-01</p> <p>Borrowing from techniques developed for conservation law equations, we have developed both monotone and higher order accurate <span class="hlt">numerical</span> <span class="hlt">schemes</span> which discretize the Hamilton-Jacobi and level set equations on triangulated domains. The use of unstructured meshes containing triangles (2D) and tetrahedra (3D) easily accommodates mesh adaptation to resolve disparate level set feature scales with a minimal number of solution unknowns. The minisymposium talk will discuss these algorithmic developments and present sample calculations using our adaptive triangulation algorithm applied to various moving interface problems such as etching, deposition, and curvature flow.</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> </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://hdl.handle.net/2060/19930017902','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930017902"><span>Positivity-preserving <span class="hlt">numerical</span> <span class="hlt">schemes</span> for multidimensional advection</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Leonard, B. P.; Macvean, M. K.; Lock, A. P.</p> <p>1993-01-01</p> <p>This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomial interpolation algorithm (UTOPIA). Particular attention is paid to the problem of flow-to-grid angle-dependent, anisotropic distortion typical of one-dimensional <span class="hlt">schemes</span> used component-wise. The third-order multidimensional <span class="hlt">scheme</span> automatically includes certain cross-difference terms that guarantee good isotropy (and stability). However, above first-order, polynomial-based advection <span class="hlt">schemes</span> do not preserve positivity (the multidimensional analogue of monotonicity). For this reason, a multidimensional generalization of the first author's universal flux-limiter is sought. This is a very challenging problem. A simple flux-limiter can be found; but this introduces strong anisotropic distortion. A more sophisticated technique, limiting part of the flux and then restoring the isotropy-maintaining cross-terms afterwards, gives more satisfactory results. Test cases are confined to two dimensions; three-dimensional extensions are briefly discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26871161','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26871161"><span>Structure of sheared and rotating turbulence: Multiscale statistics of <span class="hlt">Lagrangian</span> and Eulerian accelerations and passive scalar dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie</p> <p>2016-01-01</p> <p>The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct <span class="hlt">numerical</span> simulation results. The statistical properties of <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its <span class="hlt">Lagrangian</span> counterpart is only due to gradient production and viscous dissipation.</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 <span class="hlt">numerical</span> 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 Eulerian-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/2016APS..DFDA34001M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDA34001M"><span>Analysis of <span class="hlt">Lagrangian</span> stretching in turbulent channel flow using a database task-parallel particle tracking approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Meneveau, Charles; Johnson, Perry; Hamilton, Stephen; Burns, Randal</p> <p>2016-11-01</p> <p>An intrinsic property of turbulent flows is the exponential deformation of fluid elements along <span class="hlt">Lagrangian</span> paths. The production of enstrophy by vorticity stretching follows from a similar mechanism in the <span class="hlt">Lagrangian</span> view, though the alignment statistics differ and viscosity prevents unbounded growth. In this paper, the stretching properties of fluid elements and vorticity along <span class="hlt">Lagrangian</span> paths are studied in a channel flow at Reτ = 1000 and compared with prior, known results from isotropic turbulence. To track <span class="hlt">Lagrangian</span> paths in a public database containing Direct <span class="hlt">Numerical</span> Simulation (DNS) results, the task-parallel approach previously employed in the isotropic database is extended to the case of flow in a bounded domain. It is shown that above 100 viscous units from the wall, stretching statistics are equal to their isotropic values, in support of the local isotropy hypothesis. Normalized by dissipation rate, the stretching in the buffer layer and below is less efficient due to less favorable alignment statistics. The Cramér function characterizing cumulative <span class="hlt">Lagrangian</span> stretching statistics shows that overall the channel flow has about half of the stretching per unit dissipation compared with isotropic turbulence. Supported by a National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1232825, and by National Science Foundation Grants CBET-1507469, ACI-1261715, OCI-1244820 and by JHU IDIES.</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 Eulerian/<span class="hlt">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 Eulerian/<span class="hlt">Lagrangian</span> approach to calculating helicopter rotor flows with concentrated vortices is described. The method computes a general evolving vorticity distribution without any significant <span class="hlt">numerical</span> 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('http://adsabs.harvard.edu/abs/2011AcNum..20..569W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AcNum..20..569W"><span>Variationally consistent discretization <span class="hlt">schemes</span> and <span class="hlt">numerical</span> algorithms for contact problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wohlmuth, Barbara</p> <p></p> <p>We consider variationally consistent discretization <span class="hlt">schemes</span> for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration <span class="hlt">schemes</span>. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. <span class="hlt">Numerical</span> results in two and three dimensions illustrate the wide range of</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.358....1M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.358....1M"><span>Spatial eigensolution analysis of energy-stable flux reconstruction <span class="hlt">schemes</span> and influence of the <span class="hlt">numerical</span> flux on accuracy and robustness</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mengaldo, Gianmarco; De Grazia, Daniele; Moura, Rodrigo C.; Sherwin, Spencer J.</p> <p>2018-04-01</p> <p>This study focuses on the dispersion and diffusion characteristics of high-order energy-stable flux reconstruction (ESFR) <span class="hlt">schemes</span> via the spatial eigensolution analysis framework proposed in [1]. The analysis is performed for five ESFR <span class="hlt">schemes</span>, where the parameter 'c' dictating the properties of the specific <span class="hlt">scheme</span> recovered is chosen such that it spans the entire class of ESFR methods, also referred to as VCJH <span class="hlt">schemes</span>, proposed in [2]. In particular, we used five values of 'c', two that correspond to its lower and upper bounds and the others that identify three <span class="hlt">schemes</span> that are linked to common high-order methods, namely the ESFR recovering two versions of discontinuous Galerkin methods and one recovering the spectral difference <span class="hlt">scheme</span>. The performance of each <span class="hlt">scheme</span> is assessed when using different <span class="hlt">numerical</span> intercell fluxes (e.g. different levels of upwinding), ranging from "under-" to "over-upwinding". In contrast to the more common temporal analysis, the spatial eigensolution analysis framework adopted here allows one to grasp crucial insights into the diffusion and dispersion properties of FR <span class="hlt">schemes</span> for problems involving non-periodic boundary conditions, typically found in open-flow problems, including turbulence, unsteady aerodynamics and aeroacoustics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4375614','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4375614"><span>On the error propagation of semi-Lagrange and Fourier methods for advection problems☆</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Einkemmer, Lukas; Ostermann, Alexander</p> <p>2015-01-01</p> <p>In this paper we study the error propagation of <span class="hlt">numerical</span> <span class="hlt">schemes</span> for the advection equation in the case where high precision is desired. The <span class="hlt">numerical</span> methods considered are based on the fast Fourier transform, polynomial interpolation (semi-<span class="hlt">Lagrangian</span> methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-<span class="hlt">Lagrangian</span> approach (which is conservative and has to store more than a single value per cell). We demonstrate, by carrying out <span class="hlt">numerical</span> experiments, that the worst case error estimates given in the literature provide a good explanation for the error propagation of the interpolation-based semi-<span class="hlt">Lagrangian</span> methods. For the discontinuous Galerkin semi-<span class="hlt">Lagrangian</span> method, however, we find that the characteristic property of semi-<span class="hlt">Lagrangian</span> error estimates (namely the fact that the error increases proportionally to the number of time steps) is not observed. We provide an explanation for this behavior and conduct <span class="hlt">numerical</span> simulations that corroborate the different qualitative features of the error in the two respective types of semi-<span class="hlt">Lagrangian</span> methods. The method based on the fast Fourier transform is exact but, due to round-off errors, susceptible to a linear increase of the error in the number of time steps. We show how to modify the Cooley–Tukey algorithm in order to obtain an error growth that is proportional to the square root of the number of time steps. Finally, we show, for a simple model, that our conclusions hold true if the advection solver is used as part of a splitting <span class="hlt">scheme</span>. PMID:25844018</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://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 Eulerian 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/2017EGUGA..19..688R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19..688R"><span>Sensitivity Analysis of a <span class="hlt">Lagrangian</span> Sea Ice Model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rabatel, Matthias; Rampal, Pierre; Bertino, Laurent; Carrassi, Alberto; Jones, Christopher K. R. T.</p> <p>2017-04-01</p> <p>Large changes in the Arctic sea ice have been observed in the last decades in terms of the ice thickness, extension and drift. Understanding the mechanisms behind these changes is of paramount importance to enhance our modeling and forecasting capabilities. For 40 years, models have been developed to describe the non-linear dynamical response of the sea ice to a number of external and internal factors. Nevertheless, there still exists large deviations between predictions and observations. There are related to incorrect descriptions of the sea ice response and/or to the uncertainties about the different sources of information: parameters, initial and boundary conditions and external forcing. Data assimilation (DA) methods are used to combine observations with models, and there is nowadays an increasing interest of DA for sea-ice models and observations. We consider here the state-of-the art sea-ice model, neXtSIM te{Rampal2016a}, which is based on a time-varying <span class="hlt">Lagrangian</span> mesh and makes use of the Elasto-Brittle rheology. Our ultimate goal is designing appropriate DA <span class="hlt">scheme</span> for such a modelling facility. This contribution reports about the first milestone along this line: a sensitivity analysis in order to quantify forecast error to guide model development and to set basis for further <span class="hlt">Lagrangian</span> DA methods. Specific features of the sea-ice dynamics in relation to the wind are thus analysed. Virtual buoys are deployed across the Arctic domain and their trajectories of motion are analysed. The simulated trajectories are also compared to real buoys trajectories observed. The model response is also compared with that one from a model version not including internal forcing to highlight the role of the rheology. Conclusions and perspectives for the general DA implementation are also discussed. \\bibitem{Rampal2016a} P. Rampal, S. Bouillon, E. Ólason, and M. Morlighem. ne{X}t{SIM}: a new {<span class="hlt">L}agrangian</span> sea ice model. The Cryosphere, 10 (3): 1055-1073, 2016.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvA..94e2122S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvA..94e2122S"><span>Generalized continuity equations from two-field Schrödinger <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>Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.</p> <p>2016-11-01</p> <p>A variational <span class="hlt">scheme</span> for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a <span class="hlt">Lagrangian</span> which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013APS..DFDG26004V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013APS..DFDG26004V"><span><span class="hlt">Numerical</span> simulations of turbulent jet ignition and combustion</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Validi, Abdoulahad; Irannejad, Abolfazl; Jaberi, Farhad</p> <p>2013-11-01</p> <p>The ignition and combustion of a homogeneous lean hydrogen-air mixture by a turbulent jet flow of hot combustion products injected into a colder gas mixture are studied by a high fidelity <span class="hlt">numerical</span> model. Turbulent jet ignition can be considered as an efficient method for starting and controlling the reaction in homogeneously charged combustion systems used in advanced internal combustion and gas turbine engines. In this work, we study in details the physics of turbulent jet ignition in a fundamental flow configuration. The flow and combustion are modeled with the hybrid large eddy simulation/filtered mass density function (LES/FMDF) approach, in which the filtered form the compressible Navier-Stokes equations are solved with a high-order finite difference <span class="hlt">scheme</span> for the turbulent velocity and the FMDF transport equations are solved with a <span class="hlt">Lagrangian</span> stochastic method to obtain the scalar (temperature and species mass fractions) field. The hydrogen oxidation is described by a detailed reaction mechanism with 37 elementary reactions and 9 species.</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('http://adsabs.harvard.edu/abs/2018IJMPC..2950013D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018IJMPC..2950013D"><span>A <span class="hlt">Lagrangian</span> model for the age of tracer in surface water</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ding, Yu; Liu, Haifei; Yi, Yujun</p> <p></p> <p>The age of tracer is a spatio-temporal scale, indicating the transition time of solute particles, which is helpful to monitor and manage the pollutant leakage accidents. In this study, an effective <span class="hlt">Lagrangian</span> model for the age of tracer is developed based on the lattice Boltzmann method in D2Q5 lattices. A tracer age problem in an asymmetrical circular reservoir is then employed as a benchmark test to verify this method. Then it is applied to computing the age of tracers under two different reservoir operation <span class="hlt">schemes</span> in the Danjiangkou Reservoir, the drinking water source for the Middle Route of South-to-North Water Transfer Project.</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 Eulerian-<span class="hlt">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 <span class="hlt">numerical</span> model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and <span class="hlt">Lagrangian</span> paradigms will be used to assess the relevance of <span class="hlt">Lagrangian</span>-Eulerian 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 <span class="hlt">scheme</span> 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 Eulerian 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 Eulerian-<span class="hlt">Lagrangian</span> formulation and the resolution of the mesh used in the Eulerian 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('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 Eulerian calculations for fluids. Because of different <span class="hlt">numerical</span> representations of the materials, additional <span class="hlt">numerical</span> <span class="hlt">schemes</span> are needed to ensure continuity of the materials. New applications of the method to compute fluid motions have revealed <span class="hlt">numerical</span> 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 Eulerian 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 <span class="hlt">numerical</span> <span class="hlt">scheme</span> can be efficiently built based on the dual domain material point method. In this talk, the theoretical foundation of the method will be introduced. <span class="hlt">Numerical</span> examples will be shown. Work sponsored by the next generation code project of LANL.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19760013328','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19760013328"><span>A <span class="hlt">numerical</span> <span class="hlt">scheme</span> to solve unstable boundary value problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kalnay Derivas, E.</p> <p>1975-01-01</p> <p>A new iterative <span class="hlt">scheme</span> for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than <span class="hlt">schemes</span> based in forward time integrations (false transient <span class="hlt">schemes</span>). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative <span class="hlt">schemes</span> fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.</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 Eulerian <span class="hlt">schemes</span>. 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..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 <span class="hlt">numerical</span> simulations, mesoscale vortices feature prominently as collectively rotating regions that remain visibly coherent. Prior studies on transport from ocean vortices typically rely on Eulerian identification methods, in which vortices are identified by selecting closed contours of Eulerian 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 Eulerian contours, revealing significant discrepancies between the advection of the contour's material interior and the evolution of the Eulerian field contour. This work investigates the global mass and tracer transport associated with materially coherent surface ocean vortices. Further, it addresses differences between Eulerian 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 <span class="hlt">numerical</span> 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 Eulerian vortex methods are poorly suited to answer questions of mass and tracer transport.</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('http://adsabs.harvard.edu/abs/2009JCoAM.223.1058V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009JCoAM.223.1058V"><span>Given a one-step <span class="hlt">numerical</span> <span class="hlt">scheme</span>, on which ordinary differential equations is it exact?</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Villatoro, Francisco R.</p> <p>2009-01-01</p> <p>A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given <span class="hlt">numerical</span> <span class="hlt">scheme</span> is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26575565','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26575565"><span>Extended <span class="hlt">Lagrangian</span> formulation of charge-constrained tight-binding 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>Cawkwell, M J; Coe, J D; Yadav, S K; Liu, X-Y; Niklasson, A M N</p> <p>2015-06-09</p> <p>The extended <span class="hlt">Lagrangian</span> Born-Oppenheimer molecular dynamics formalism [Niklasson, Phys. Rev. Lett., 2008, 100, 123004] has been applied to a tight-binding model under the constraint of local charge neutrality to yield microcanonical trajectories with both precise, long-term energy conservation and a reduced number of self-consistent field optimizations at each time step. The extended <span class="hlt">Lagrangian</span> molecular dynamics formalism restores time reversal symmetry in the propagation of the electronic degrees of freedom, and it enables the efficient and accurate self-consistent optimization of the chemical potential and atomwise potential energy shifts in the on-site elements of the tight-binding Hamiltonian that are required when enforcing local charge neutrality. These capabilities are illustrated with microcanonical molecular dynamics simulations of a small metallic cluster using an sd-valent tight-binding model for titanium. The effects of weak dissipation on the propagation of the auxiliary degrees of freedom for the chemical potential and on-site Hamiltonian matrix elements that is used to counteract the accumulation of <span class="hlt">numerical</span> noise during trajectories was also investigated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000056868','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000056868"><span>Implicit Space-Time Conservation Element and Solution Element <span class="hlt">Schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chang, Sin-Chung; Himansu, Ananda; Wang, Xiao-Yen</p> <p>1999-01-01</p> <p>Artificial <span class="hlt">numerical</span> dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional <span class="hlt">numerical</span> <span class="hlt">schemes</span> can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit <span class="hlt">numerical</span> <span class="hlt">schemes</span> such that artificial <span class="hlt">numerical</span> dissipation will not overwhelm physical dissipation. Specifically, these <span class="hlt">schemes</span> have the property that <span class="hlt">numerical</span> dissipation vanishes when the physical viscosity goes to zero. These new <span class="hlt">schemes</span> therefore accurately model the physical dissipation even when it is extremely small. The new <span class="hlt">schemes</span> presented are two highly accurate implicit solvers for a convection-diffusion equation. The two <span class="hlt">schemes</span> become identical in the pure convection case, and in the pure diffusion case. The implicit <span class="hlt">schemes</span> are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the <span class="hlt">schemes</span> are analysed, and some <span class="hlt">numerical</span> results are presented. It is shown that, in the inviscid case, the new <span class="hlt">schemes</span> become explicit and their amplification factors are identical to those of the Leapfrog <span class="hlt">scheme</span>. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson <span class="hlt">scheme</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/332728','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/332728"><span>Elimination of artificial grid distortion and hourglass-type motions by means of <span class="hlt">Lagrangian</span> subzonal masses and pressures</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>Caramana, E.J.; Shashkov, M.J.</p> <p>1997-12-31</p> <p>The bane of <span class="hlt">Lagrangian</span> hydrodynamics calculations is premature breakdown of the grid topology that results in severe degradation of accuracy and run termination often long before the assumption of <span class="hlt">Lagrangian</span> zonal mass ceased to be valid. At short spatial grid scales this is usually referred to by the terms hourglass mode or keystone motion associated in particular with underconstrained grids such as quadrilaterals and hexahedrons in two and three dimensions, respectively. At longer spatial scales relative to the grid spacing there is what is referred to ubiquitously as spurious vorticity, or the long-thin zone problem. In both cases the resultmore » is anomalous grid distortion and tangling that has nothing to do with the actual solution, as would be the case for turbulent flow. In this work the authors show how such motions can be eliminated by the proper use of subzonal <span class="hlt">Lagrangian</span> masses, and associated densities and pressures. These subzonal masses arise in a natural way from the fact that they require the mass associated with the nodal grid point to be constant in time. This is addition to the usual assumption of constant, <span class="hlt">Lagrangian</span> zonal mass in staggered grid hydrodynamics <span class="hlt">scheme</span>. The authors show that with proper discretization of subzonal forces resulting from subzonal pressures, hourglass motion and spurious vorticity can be eliminated for a very large range of problems. Finally the authors are presenting results of calculations of many test problems.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MS%26E..263d2110D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MS%26E..263d2110D"><span>A <span class="hlt">numerical</span> <span class="hlt">scheme</span> for singularly perturbed reaction-diffusion problems with a negative shift via numerov method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.</p> <p>2017-11-01</p> <p>In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted <span class="hlt">numerical</span> method using Numerov finite difference <span class="hlt">scheme</span>, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.339...68G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.339...68G"><span><span class="hlt">Lagrangian</span> transported MDF methods for compressible high speed flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gerlinger, Peter</p> <p>2017-06-01</p> <p>This paper deals with the application of thermochemical <span class="hlt">Lagrangian</span> MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged Navier-Stokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures <span class="hlt">numerical</span> stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/<span class="hlt">Lagrangian</span> particle solver (PS).</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 Eulerian and <span class="hlt">Lagrangian</span> components separately. The approach is shown to feature bounded <span class="hlt">numerical</span> 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('http://hdl.handle.net/2060/19950011695','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950011695"><span>Floating shock fitting via <span class="hlt">Lagrangian</span> adaptive meshes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Vanrosendale, John</p> <p>1994-01-01</p> <p>In recent works we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe <span class="hlt">scheme</span> discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting <span class="hlt">Lagrangian</span> Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ascl.soft09005G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ascl.soft09005G"><span>HARM: A <span class="hlt">Numerical</span> <span class="hlt">Scheme</span> for General Relativistic Magnetohydrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gammie, Charles, F.; McKinney, Jonathan C.; Tóth, Gábor</p> <p>2012-09-01</p> <p>HARM uses a conservative, shock-capturing <span class="hlt">scheme</span> for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer <span class="hlt">scheme</span>. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. On smooth flows HARM converges at second order.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19780036071&hterms=solve&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsolve','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19780036071&hterms=solve&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsolve"><span>A <span class="hlt">numerical</span> <span class="hlt">scheme</span> to solve unstable boundary value problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kalnay-Rivas, E.</p> <p>1977-01-01</p> <p>The considered <span class="hlt">scheme</span> makes it possible to determine an unstable steady state solution in cases in which, because of lack of symmetry, such a solution cannot be obtained analytically, and other time integration or relaxation <span class="hlt">schemes</span>, because of instability, fail to converge. The iterative solution of a single complex equation is discussed and a nonlinear system of equations is considered. Described applications of the <span class="hlt">scheme</span> are related to a steady state solution with shear instability, an unstable nonlinear Ekman boundary layer, and the steady state solution of a baroclinic atmosphere with asymmetric forcing. The <span class="hlt">scheme</span> makes use of forward and backward time integrations of the original spatial differential operators and of an approximation of the adjoint operators. Only two computations of the time derivative per iteration are required.</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 Eulerian 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('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.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 <span class="hlt">numerical</span> methods such as <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> techniques needed to embody those solvers in code.</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 <span class="hlt">numerical</span> methods such as <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> techniques needed to embody those solvers in code. PMID:29045443</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhFl...28h5103W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhFl...28h5103W"><span>Mixing model with multi-particle interactions for <span class="hlt">Lagrangian</span> simulations of turbulent mixing</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Watanabe, T.; Nagata, K.</p> <p>2016-08-01</p> <p>We report on the <span class="hlt">numerical</span> study of the mixing volume model (MVM) for molecular diffusion in <span class="hlt">Lagrangian</span> simulations of turbulent mixing problems. The MVM is based on the multi-particle interaction in a finite volume (mixing volume). A priori test of the MVM, based on the direct <span class="hlt">numerical</span> simulations of planar jets, is conducted in the turbulent region and the interfacial layer between the turbulent and non-turbulent fluids. The results show that the MVM predicts well the mean effects of the molecular diffusion under various <span class="hlt">numerical</span> and flow parameters. The number of the mixing particles should be large for predicting a value of the molecular diffusion term positively correlated to the exact value. The size of the mixing volume relative to the Kolmogorov scale η is important in the performance of the MVM. The scalar transfer across the turbulent/non-turbulent interface is well captured by the MVM especially with the small mixing volume. Furthermore, the MVM with multiple mixing particles is tested in the hybrid implicit large-eddy-simulation/<span class="hlt">Lagrangian</span>-particle-simulation (LES-LPS) of the planar jet with the characteristic length of the mixing volume of O(100η). Despite the large mixing volume, the MVM works well and decays the scalar variance in a rate close to the reference LES. The statistics in the LPS are very robust to the number of the particles used in the simulations and the computational grid size of the LES. Both in the turbulent core region and the intermittent region, the LPS predicts a scalar field well correlated to the LES.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcMod.120....1C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcMod.120....1C"><span>Comparison of in situ microstructure measurements to different turbulence closure <span class="hlt">schemes</span> in a 3-D <span class="hlt">numerical</span> ocean circulation model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Costa, Andrea; Doglioli, Andrea M.; Marsaleix, Patrick; Petrenko, Anne A.</p> <p>2017-12-01</p> <p>In situ measurements of kinetic energy dissipation rate ε and estimates of eddy viscosity KZ from the Gulf of Lion (NW Mediterranean Sea) are used to assess the ability of k - ɛ and k - ℓ closure <span class="hlt">schemes</span> to predict microscale turbulence in a 3-D <span class="hlt">numerical</span> ocean circulation model. Two different surface boundary conditions are considered in order to investigate their influence on each closure <span class="hlt">schemes</span>' performance. The effect of two types of stability functions and optical <span class="hlt">schemes</span> on the k - ɛ <span class="hlt">scheme</span> is also explored. Overall, the 3-D model predictions are much closer to the in situ data in the surface mixed layer as opposed to below it. Above the mixed layer depth, we identify one model's configuration that outperforms all the other ones. Such a configuration employs a k - ɛ <span class="hlt">scheme</span> with Canuto A stability functions, surface boundary conditions parameterizing wave breaking and an appropriate photosynthetically available radiation attenuation length. Below the mixed layer depth, reliability is limited by the model's resolution and the specification of a hard threshold on the minimum turbulent kinetic energy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.753c2004B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.753c2004B"><span>3D <span class="hlt">Lagrangian</span> VPM: simulations of the near-wake of an actuator disc and horizontal axis wind turbine</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Berdowski, T.; Ferreira, C.; Walther, J.</p> <p>2016-09-01</p> <p>The application of a 3-dimensional <span class="hlt">Lagrangian</span> vortex particle method has been assessed for modelling the near-wake of an axisymmetrical actuator disc and 3-bladed horizontal axis wind turbine with prescribed circulation from the MEXICO (Model EXperiments In COntrolled conditions) experiment. The method was developed in the framework of the open- source Parallel Particle-Mesh library for handling the efficient data-parallelism on a CPU (Central Processing Unit) cluster, and utilized a O(N log N)-type fast multipole method for computational acceleration. Simulations with the actuator disc resulted in a wake expansion, velocity deficit profile, and induction factor that showed a close agreement with theoretical, <span class="hlt">numerical</span>, and experimental results from literature. Also the shear layer expansion was present; the Kelvin-Helmholtz instability in the shear layer was triggered due to the round-off limitations of a <span class="hlt">numerical</span> method, but this instability was delayed to beyond 1 diameter downstream due to the particle smoothing. Simulations with the 3-bladed turbine demonstrated that a purely 3-dimensional flow representation is challenging to model with particles. The manifestation of local complex flow structures of highly stretched vortices made the simulation unstable, but this was successfully counteracted by the application of a particle strength exchange <span class="hlt">scheme</span>. The axial and radial velocity profile over the near wake have been compared to that of the original MEXICO experiment, which showed close agreement between results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CMaPh.351..689B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CMaPh.351..689B"><span>A Constructive Approach to Regularity of <span class="hlt">Lagrangian</span> Trajectories for Incompressible Euler Flow in a Bounded Domain</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Besse, Nicolas; Frisch, Uriel</p> <p>2017-04-01</p> <p>The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved <span class="hlt">numerical</span> exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's <span class="hlt">Lagrangian</span> formulation of the Euler equations and second, by taking advantage of analyticity results of the <span class="hlt">Lagrangian</span> trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the <span class="hlt">Lagrangian</span> map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the <span class="hlt">Lagrangian</span> flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the <span class="hlt">Lagrangian</span> trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-<span class="hlt">Lagrangian</span> method.</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 codes 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 codes that have and continue to emerge, and the challenges of the coming age of petascale computing.</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('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 codes 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/2002iaf..confE..45B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002iaf..confE..45B"><span>Orbital Maneuvers for Spacecrafts Travelling to/from the <span class="hlt">Lagrangian</span> Points</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bertachini, A.</p> <p></p> <p>The well-known <span class="hlt">Lagrangian</span> points that appear in the planar restricted three-body problem (Szebehely, 1967) are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L1, L2 and L3) are always unstable and the triangular points (L4 and L5) are stable in the present case studied (Sun-Earth system). They are all very good points to locate a space-station, since they require a small amount of V (and fuel), the control to be used for station-keeping. The triangular points are specially good for this purpose, since they are stable equilibrium points. In this paper, the planar restricted three-body problem is regularized (using Lemaître regularization) and combined with <span class="hlt">numerical</span> integration and gradient methods to solve the two point boundary value problem (the Lambert's three-body problem). This combination is applied to the search of families of transfer orbits between the <span class="hlt">Lagrangian</span> points and the Earth, in the Sun-Earth system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude and direction of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the <span class="hlt">Lagrangian</span> point and the second one when arriving/living at the Earth. This paper is a continuation of two previous papers that studied transfers in the Earth-Moon system: Broucke (1979), that studied transfer orbits between the <span class="hlt">Lagrangian</span> points and the Moon and Prado (1996), that studied transfer orbits between the <span class="hlt">Lagrangian</span> points and the Earth. So, the equations of motion are: whereis the pseudo-potential given by: To solve the TPBVP in the regularized variables the following steps are used: i) Guess a initial velocity Vi, so together with the initial prescribed position ri the complete initial state is known; ii</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA568415','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA568415"><span><span class="hlt">Numerical</span> <span class="hlt">Schemes</span> and Computational Studies for Dynamically Orthogonal Equations (Multidisciplinary Simulation, Estimation, and Assimilation Systems: Reports in Ocean Science and Engineering)</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2011-08-01</p> <p>heat transfers [49, 52]. However, the DO method has not yet been applied to Boussinesq flows, and the <span class="hlt">numerical</span> challenges of the DO decomposition for...used a PCE <span class="hlt">scheme</span> to study mixing in a two-dimensional (2D) microchannel and improved the efficiency of their solution <span class="hlt">scheme</span> by decoupling the...to several Navier-Stokes flows and their stochastic dynamics has been studied, including mean-mode and mode-mode energy transfers for 2D flows and</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..1817883E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..1817883E"><span><span class="hlt">Numerical</span> simulation of flood inundation using a well-balanced kinetic <span class="hlt">scheme</span> for the shallow water equations with bulk recharge and discharge</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ersoy, Mehmet; Lakkis, Omar; Townsend, Philip</p> <p>2016-04-01</p> <p>The flow of water in rivers and oceans can, under general assumptions, be efficiently modelled using Saint-Venant's shallow water system of equations (SWE). SWE is a hyperbolic system of conservation laws (HSCL) which can be derived from a starting point of incompressible Navier-Stokes. A common difficulty in the <span class="hlt">numerical</span> simulation of HSCLs is the conservation of physical entropy. Work by Audusse, Bristeau, Perthame (2000) and Perthame, Simeoni (2001), proposed <span class="hlt">numerical</span> SWE solvers known as kinetic <span class="hlt">schemes</span> (KSs), which can be shown to have desirable entropy-consistent properties, and are thus called well-balanced <span class="hlt">schemes</span>. A KS is derived from kinetic equations that can be integrated into the SWE. In flood risk assessment models the SWE must be coupled with other equations describing interacting meteorological and hydrogeological phenomena such as rain and groundwater flows. The SWE must therefore be appropriately modified to accommodate source and sink terms, so kinetic <span class="hlt">schemes</span> are no longer valid. While modifications of SWE in this direction have been recently proposed, e.g., Delestre (2010), we depart from the extant literature by proposing a novel model that is "entropy-consistent" and naturally extends the SWE by respecting its kinetic formulation connections. This allows us to derive a system of partial differential equations modelling flow of a one-dimensional river with both a precipitation term and a groundwater flow model to account for potential infiltration and recharge. We exhibit <span class="hlt">numerical</span> simulations of the corresponding kinetic <span class="hlt">schemes</span>. These simulations can be applied to both real world flood prediction and the tackling of wider issues on how climate and societal change are affecting flood risk.</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/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 <span class="hlt">numerically</span> 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 <span class="hlt">numerical</span> 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 Eulerian 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://adsabs.harvard.edu/abs/2013JOM....65i1164B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JOM....65i1164B"><span><span class="hlt">Numerical</span> Modeling of Inclusion Behavior in Liquid Metal Processing</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bellot, Jean-Pierre; Descotes, Vincent; Jardy, Alain</p> <p>2013-09-01</p> <p>Thermomechanical performance of metallic alloys is directly related to the metal cleanliness that has always been a challenge for metallurgists. During liquid metal processing, particles can grow or decrease in size either by mass transfer with the liquid phase or by agglomeration/fragmentation mechanisms. As a function of <span class="hlt">numerical</span> density of inclusions and of the hydrodynamics of the reactor, different <span class="hlt">numerical</span> modeling approaches are proposed; in the case of an isolated particle, the <span class="hlt">Lagrangian</span> technique coupled with a dissolution model is applied, whereas in the opposite case of large inclusion phase concentration, the population balance equation must be solved. Three examples of <span class="hlt">numerical</span> modeling studies achieved at Institut Jean Lamour are discussed. They illustrate the application of the <span class="hlt">Lagrangian</span> technique (for isolated exogenous inclusion in titanium bath) and the Eulerian technique without or with the aggregation process: for precipitation and growing of inclusions at the solidification front of a Maraging steel, and for endogenous inclusions in the molten steel bath of a gas-stirred ladle, respectively.</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 Eulerian 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 Eulerian current varies approximately in anti-phase over the shelf, and that the latter is <span class="hlt">numerically</span> 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 <span class="hlt">numerical</span> value at the coast on the shallow part of the shelf. Enhancing the effect of bottom friction on the Eulerian 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/2016PhFl...28f1901S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhFl...28f1901S"><span>An unstructured mesh arbitrary <span class="hlt">Lagrangian</span>-Eulerian 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</span>-Eulerian (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 <span class="hlt">scheme</span> 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 <span class="hlt">numerical</span> 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('https://ntrs.nasa.gov/search.jsp?R=19890037912&hterms=projectile+motion&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dprojectile%2Bmotion','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19890037912&hterms=projectile+motion&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dprojectile%2Bmotion"><span><span class="hlt">Numerical</span> simulation of three-dimensional transonic turbulent projectile aerodynamics by TVD <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shiau, Nae-Haur; Hsu, Chen-Chi; Chyu, Wei-Jao</p> <p>1989-01-01</p> <p>The two-dimensional symmetric TVD <span class="hlt">scheme</span> proposed by Yee has been extended to and investigated for three-dimensional thin-layer Navier-Stokes simulation of complex aerodynamic problems. An existing three-dimensional Navier-stokes code based on the beam and warming algorithm is modified to provide an option of using the TVD algorithm and the flow problem considered is a transonic turbulent flow past a projectile with sting at ten-degree angle of attack. <span class="hlt">Numerical</span> experiments conducted for three flow cases, free-stream Mach numbers of 0.91, 0.96 and 1.20 show that the symmetric TVD algorithm can provide surface pressure distribution in excellent agreement with measured data; moreover, the rate of convergence to attain a steady state solution is about two times faster than the original beam and warming algorithm.</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 Eulerian 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 Eulerian 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 Eulerian 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('https://ntrs.nasa.gov/search.jsp?R=19930059665&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=19930059665&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian"><span>Variational data assimilation with a semi-<span class="hlt">Lagrangian</span> semi-implicit global shallow-water equation model and its adjoint</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Li, Y.; Navon, I. M.; Courtier, P.; Gauthier, P.</p> <p>1993-01-01</p> <p>An adjoint model is developed for variational data assimilation using the 2D semi-<span class="hlt">Lagrangian</span> semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-<span class="hlt">Lagrangian</span> <span class="hlt">scheme</span> is preserved during the minimization process, related to the variational data assimilation procedure.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20130011909','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20130011909"><span>Imposing a <span class="hlt">Lagrangian</span> Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.</p> <p>2012-01-01</p> <p>In many astrophysical simulations, both Eulerian and <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the <span class="hlt">Lagrangian</span> entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and <span class="hlt">Lagrangian</span> markers to model fluid structure interactions. These widely varying roles for <span class="hlt">Lagrangian</span> entities are possible because of the highly modular, flexible, and extensible architecture of the <span class="hlt">Lagrangian</span> framework. In this paper, we describe the <span class="hlt">Lagrangian</span> framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the <span class="hlt">Lagrangian</span> entities in fundamentally different ways.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ApJS..201...27D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ApJS..201...27D"><span>Imposing a <span class="hlt">Lagrangian</span> Particle Framework on an Eulerian Hydrodynamics Infrastructure in FLASH</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.</p> <p>2012-08-01</p> <p>In many astrophysical simulations, both Eulerian and <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the <span class="hlt">Lagrangian</span> entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and <span class="hlt">Lagrangian</span> markers to model fluid-structure interactions. These widely varying roles for <span class="hlt">Lagrangian</span> entities are possible because of the highly modular, flexible, and extensible architecture of the <span class="hlt">Lagrangian</span> framework. In this paper, we describe the <span class="hlt">Lagrangian</span> framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the <span class="hlt">Lagrangian</span> entities in fundamentally different ways.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22598910-mixing-model-multi-particle-interactions-lagrangian-simulations-turbulent-mixing','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22598910-mixing-model-multi-particle-interactions-lagrangian-simulations-turbulent-mixing"><span>Mixing model with multi-particle interactions for <span class="hlt">Lagrangian</span> simulations of turbulent mixing</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>Watanabe, T., E-mail: watanabe.tomoaki@c.nagoya-u.jp; Nagata, K.</p> <p></p> <p>We report on the <span class="hlt">numerical</span> study of the mixing volume model (MVM) for molecular diffusion in <span class="hlt">Lagrangian</span> simulations of turbulent mixing problems. The MVM is based on the multi-particle interaction in a finite volume (mixing volume). A priori test of the MVM, based on the direct <span class="hlt">numerical</span> simulations of planar jets, is conducted in the turbulent region and the interfacial layer between the turbulent and non-turbulent fluids. The results show that the MVM predicts well the mean effects of the molecular diffusion under various <span class="hlt">numerical</span> and flow parameters. The number of the mixing particles should be large for predicting amore » value of the molecular diffusion term positively correlated to the exact value. The size of the mixing volume relative to the Kolmogorov scale η is important in the performance of the MVM. The scalar transfer across the turbulent/non-turbulent interface is well captured by the MVM especially with the small mixing volume. Furthermore, the MVM with multiple mixing particles is tested in the hybrid implicit large-eddy-simulation/<span class="hlt">Lagrangian</span>-particle-simulation (LES–LPS) of the planar jet with the characteristic length of the mixing volume of O(100η). Despite the large mixing volume, the MVM works well and decays the scalar variance in a rate close to the reference LES. The statistics in the LPS are very robust to the number of the particles used in the simulations and the computational grid size of the LES. Both in the turbulent core region and the intermittent region, the LPS predicts a scalar field well correlated to the LES.« less</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 Eulerian 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/2016ascl.soft02021T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ascl.soft02021T"><span>COLAcode: COmoving <span class="hlt">Lagrangian</span> Acceleration code</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 code 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 code 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('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('http://adsabs.harvard.edu/abs/2016EnOp...48.2114R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EnOp...48.2114R"><span>A shifted hyperbolic augmented <span class="hlt">Lagrangian</span>-based artificial fish two-swarm algorithm with guaranteed convergence for constrained global optimization</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rocha, Ana Maria A. C.; Costa, M. Fernanda P.; Fernandes, Edite M. G. P.</p> <p>2016-12-01</p> <p>This article presents a shifted hyperbolic penalty function and proposes an augmented <span class="hlt">Lagrangian</span>-based algorithm for non-convex constrained global optimization problems. Convergence to an ?-global minimizer is proved. At each iteration k, the algorithm requires the ?-global minimization of a bound constrained optimization subproblem, where ?. The subproblems are solved by a stochastic population-based metaheuristic that relies on the artificial fish swarm paradigm and a two-swarm strategy. To enhance the speed of convergence, the algorithm invokes the Nelder-Mead local search with a dynamically defined probability. <span class="hlt">Numerical</span> experiments with benchmark functions and engineering design problems are presented. The results show that the proposed shifted hyperbolic augmented <span class="hlt">Lagrangian</span> compares favorably with other deterministic and stochastic penalty-based methods.</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('http://hdl.handle.net/2060/19960049629','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960049629"><span>Atomization simulations using an Eulerian-VOF-<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>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) <span class="hlt">numerical</span> 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://hdl.handle.net/2060/20010027898','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20010027898"><span>Modeling of Convective-Stratiform Precipitation Processes: Sensitivity to Partitioning Methods and <span class="hlt">Numerical</span> Advection <span class="hlt">Schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lang, Steve; Tao, W.-K.; Simpson, J.; Ferrier, B.; Einaudi, Franco (Technical Monitor)</p> <p>2001-01-01</p> <p>Six different convective-stratiform separation techniques, including a new technique that utilizes the ratio of vertical and terminal velocities, are compared and evaluated using two-dimensional <span class="hlt">numerical</span> simulations of a tropical [Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE)] and midlatitude continental [Preliminary Regional Experiment for STORM-Central (PRESTORM)] squall line. The simulations are made using two different <span class="hlt">numerical</span> advection <span class="hlt">schemes</span>: 4th order and positive definite advection. Comparisons are made in terms of rainfall, cloud coverage, mass fluxes, apparent heating and moistening, mean hydrometeor profiles, CFADs (Contoured Frequency with Altitude Diagrams), microphysics, and latent heating retrieval. Overall, it was found that the different separation techniques produced results that qualitatively agreed. However, the quantitative differences were significant. Observational comparisons were unable to conclusively evaluate the performance of the techniques. Latent heating retrieval was shown to be sensitive to the use of separation technique mainly due to the stratiform region for methods that found very little stratiform rain. The midlatitude PRESTORM simulation was found to be nearly invariant with respect to advection type for most quantities while for TOGA COARE fourth order advection produced <span class="hlt">numerous</span> shallow convective cores and positive definite advection fewer cells that were both broader and deeper penetrating above the freezing level.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003EAEJA.....8469M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003EAEJA.....8469M"><span>On the validation of cloud parametrization <span class="hlt">schemes</span> in <span class="hlt">numerical</span> atmospheric models with satellite data from ISCCP</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Meinke, I.</p> <p>2003-04-01</p> <p>A new method is presented to validate cloud parametrization <span class="hlt">schemes</span> in <span class="hlt">numerical</span> atmospheric models with satellite data of scanning radiometers. This method is applied to the regional atmospheric model HRM (High Resolution Regional Model) using satellite data from ISCCP (International Satellite Cloud Climatology Project). Due to the limited reliability of former validations there has been a need for developing a new validation method: Up to now differences between simulated and measured cloud properties are mostly declared as deficiencies of the cloud parametrization <span class="hlt">scheme</span> without further investigation. Other uncertainties connected with the model or with the measurements have not been taken into account. Therefore changes in the cloud parametrization <span class="hlt">scheme</span> based on such kind of validations might not be realistic. The new method estimates uncertainties of the model and the measurements. Criteria for comparisons of simulated and measured data are derived to localize deficiencies in the model. For a better specification of these deficiencies simulated clouds are classified regarding their parametrization. With this classification the localized model deficiencies are allocated to a certain parametrization <span class="hlt">scheme</span>. Applying this method to the regional model HRM the quality of forecasting cloud properties is estimated in detail. The overestimation of simulated clouds in low emissivity heights especially during the night is localized as model deficiency. This is caused by subscale cloudiness. As the simulation of subscale clouds in the regional model HRM is described by a relative humidity parametrization these deficiencies are connected with this parameterization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CQGra..34w7001D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CQGra..34w7001D"><span>A <span class="hlt">numerical</span> relativity <span class="hlt">scheme</span> for cosmological simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Daverio, David; Dirian, Yves; Mitsou, Ermis</p> <p>2017-12-01</p> <p>Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3  +  1 integration <span class="hlt">scheme</span> for general relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this <span class="hlt">scheme</span> is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003ApJ...589..444G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003ApJ...589..444G"><span>HARM: A <span class="hlt">Numerical</span> <span class="hlt">Scheme</span> for General Relativistic Magnetohydrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gammie, Charles F.; McKinney, Jonathan C.; Tóth, Gábor</p> <p>2003-05-01</p> <p>We describe a conservative, shock-capturing <span class="hlt">scheme</span> for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer <span class="hlt">scheme</span>. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AdSR...14..195R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AdSR...14..195R"><span>The HIRLAM fast radiation <span class="hlt">scheme</span> for mesoscale <span class="hlt">numerical</span> weather prediction models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rontu, Laura; Gleeson, Emily; Räisänen, Petri; Pagh Nielsen, Kristian; Savijärvi, Hannu; Hansen Sass, Bent</p> <p>2017-07-01</p> <p>This paper provides an overview of the HLRADIA shortwave (SW) and longwave (LW) broadband radiation <span class="hlt">schemes</span> used in the HIRLAM <span class="hlt">numerical</span> weather prediction (NWP) model and available in the HARMONIE-AROME mesoscale NWP model. The advantage of broadband, over spectral, <span class="hlt">schemes</span> is that they can be called more frequently within the model, without compromising on computational efficiency. In mesoscale models fast interactions between clouds and radiation and the surface and radiation can be of greater importance than accounting for the spectral details of clear-sky radiation; thus calling the routines more frequently can be of greater benefit than the deterioration due to loss of spectral details. Fast but physically based radiation parametrizations are expected to be valuable for high-resolution ensemble forecasting, because as well as the speed of their execution, they may provide realistic physical perturbations. Results from single-column diagnostic experiments based on CIRC benchmark cases and an evaluation of 10 years of radiation output from the FMI operational archive of HIRLAM forecasts indicate that HLRADIA performs sufficiently well with respect to the clear-sky downwelling SW and longwave LW fluxes at the surface. In general, HLRADIA tends to overestimate surface fluxes, with the exception of LW fluxes under cold and dry conditions. The most obvious overestimation of the surface SW flux was seen in the cloudy cases in the 10-year comparison; this bias may be related to using a cloud inhomogeneity correction, which was too large. According to the CIRC comparisons, the outgoing LW and SW fluxes at the top of atmosphere are mostly overestimated by HLRADIA and the net LW flux is underestimated above clouds. The absorption of SW radiation by the atmosphere seems to be underestimated and LW absorption seems to be overestimated. Despite these issues, the overall results are satisfying and work on the improvement of HLRADIA for the use in HARMONIE-AROME NWP system</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/2014EGUGA..16.2707C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..16.2707C"><span>Optimal design of a <span class="hlt">lagrangian</span> observing system for hydrodynamic surveys in coastal areas</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cucco, Andrea; Quattrocchi, Giovanni; Antognarelli, Fabio; Satta, Andrea; Maicu, Francesco; Ferrarin, Christian; Umgiesser, Georg</p> <p>2014-05-01</p> <p>The optimization of ocean observing systems is a pressing need for scientific research. In particular, the improvement of ocean short-term observing networks is achievable by reducing the cost-benefit ratio of the field campaigns and by increasing the quality of measurements. <span class="hlt">Numerical</span> modeling is a powerful tool for determining the appropriateness of a specific observing system and for optimizing the sampling design. This is particularly true when observations are carried out in coastal areas and lagoons where, the use satellites is prohibitive due to the water shallowness. For such areas, <span class="hlt">numerical</span> models are the most efficient tool both to provide a preliminary assess of the local physical environment and to make short -term predictions above its change. In this context, a test case experiment was carried out within an enclosed shallow water areas, the Cabras Lagoon (Sardinia, Italy). The aim of the experiment was to explore the optimal design for a field survey based on the use of coastal <span class="hlt">lagrangian</span> buoys. A three-dimensional hydrodynamic model based on the finite element method (SHYFEM3D, Umgiesser et al., 2004) was implemented to simulate the lagoon water circulation. The model domain extent to the whole Cabras lagoon and to the whole Oristano Gulf, including the surrounding coastal area. Lateral open boundary conditions were provided by the operational ocean model system WMED and only wind forcing, provided by SKIRON atmospheric model (Kallos et al., 1997), was considered as surface boundary conditions. The model was applied to provide a number of ad hoc scenarios and to explore the efficiency of the short-term hydrodynamic survey. A first field campaign was carried out to investigate the <span class="hlt">lagrangian</span> circulation inside the lagoon under the main wind forcing condition (Mistral wind from North-West). The trajectories followed by the <span class="hlt">lagrangian</span> buoys and the estimated <span class="hlt">lagrangian</span> velocities were used to calibrate the model parameters and to validate the</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 Eulerian formalism, we introduce a deterministic particle-based <span class="hlt">numerical</span> 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> <span class="hlt">schemes</span>, 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 Eulerian 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 Eulerian formalism, we introduce a deterministic particle-based <span class="hlt">numerical</span> 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> <span class="hlt">schemes</span>, 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 Eulerian 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/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 code 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 code 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> <span class="hlt">scheme</span> 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('http://adsabs.harvard.edu/abs/2018JCoPh.354..529C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.354..529C"><span>A high order semi-<span class="hlt">Lagrangian</span> discontinuous Galerkin method for Vlasov-Poisson simulations without operator splitting</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cai, Xiaofeng; Guo, Wei; Qiu, Jing-Mei</p> <p>2018-02-01</p> <p>In this paper, we develop a high order semi-<span class="hlt">Lagrangian</span> (SL) discontinuous Galerkin (DG) method for nonlinear Vlasov-Poisson (VP) simulations without operator splitting. In particular, we combine two recently developed novel techniques: one is the high order non-splitting SLDG transport method (Cai et al. (2017) [4]), and the other is the high order characteristics tracing technique proposed in Qiu and Russo (2017) [29]. The proposed method with up to third order accuracy in both space and time is locally mass conservative, free of splitting error, positivity-preserving, stable and robust for large time stepping size. The SLDG VP solver is applied to classic benchmark test problems such as Landau damping and two-stream instabilities for VP simulations. Efficiency and effectiveness of the proposed <span class="hlt">scheme</span> is extensively tested. Tremendous CPU savings are shown by comparisons between the proposed SL DG <span class="hlt">scheme</span> and the classical Runge-Kutta DG method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.365..362C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.365..362C"><span>Semi-<span class="hlt">Lagrangian</span> particle methods for high-dimensional Vlasov-Poisson systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cottet, Georges-Henri</p> <p>2018-07-01</p> <p>This paper deals with the implementation of high order semi-<span class="hlt">Lagrangian</span> particle methods to handle high dimensional Vlasov-Poisson systems. It is based on recent developments in the <span class="hlt">numerical</span> analysis of particle methods and the paper focuses on specific algorithmic features to handle large dimensions. The methods are tested with uniform particle distributions in particular against a recent multi-resolution wavelet based method on a 4D plasma instability case and a 6D gravitational case. Conservation properties, accuracy and computational costs are monitored. The excellent accuracy/cost trade-off shown by the method opens new perspective for accurate simulations of high dimensional kinetic equations by particle methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA109678','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA109678"><span>Three-Dimensional <span class="hlt">Numerical</span> Analyses of Earth Penetration Dynamics</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1979-01-31</p> <p><span class="hlt">Lagrangian</span> formulation based on the HEMP method and has been adapted and validated for treatment of normal-incidence (axisymmetric) impact and...code, is a detailed analysis of the structural response of the EPW. This analysis is generated using a nonlinear dynamic, elastic- plastic finite element...based on the HEMP <span class="hlt">scheme</span>. Thus, the code has the same material modeling capabilities and abilities to track large scale motion found in the WAVE-L code</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013CompM..51..865C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013CompM..51..865C"><span>A two-field modified <span class="hlt">Lagrangian</span> formulation for robust simulations of extrinsic cohesive zone models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cazes, F.; Coret, M.; Combescure, A.</p> <p>2013-06-01</p> <p>This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field <span class="hlt">Lagrangian</span> weak formulation in which cohesive tractions are chosen as the field variables along the crack's path is presented. Unfortunately, this formulation cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading-unloading change of state at the integration points of the cohesive elements. Therefore, a modified <span class="hlt">Lagrangian</span> formulation using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed formulations to simulate fracture accurately and without field oscillations is investigated through three <span class="hlt">numerical</span> test examples.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PApGe.174.1071P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PApGe.174.1071P"><span>On the Quality of Velocity Interpolation <span class="hlt">Schemes</span> for Marker-in-Cell Method and Staggered Grids</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pusok, Adina E.; Kaus, Boris J. P.; Popov, Anton A.</p> <p>2017-03-01</p> <p>The marker-in-cell method is generally considered a flexible and robust method to model the advection of heterogenous non-diffusive properties (i.e., rock type or composition) in geodynamic problems. In this method, <span class="hlt">Lagrangian</span> points carrying compositional information are advected with the ambient velocity field on an Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without considering the divergence of the velocity field at the interpolated locations (i.e., non-conservative). Such interpolation <span class="hlt">schemes</span> can induce non-physical clustering of markers when strong velocity gradients are present (Journal of Computational Physics 166:218-252, 2001) and this may, eventually, result in empty grid cells, a serious <span class="hlt">numerical</span> violation of the marker-in-cell method. To remedy this at low computational costs, Jenny et al. (Journal of Computational Physics 166:218-252, 2001) and Meyer and Jenny (Proceedings in Applied Mathematics and Mechanics 4:466-467, 2004) proposed a simple, conservative velocity interpolation <span class="hlt">scheme</span> for 2-D staggered grid, while Wang et al. (Geochemistry, Geophysics, Geosystems 16(6):2015-2023, 2015) extended the formulation to 3-D finite element methods. Here, we adapt this formulation for 3-D staggered grids (correction interpolation) and we report on the quality of various velocity interpolation methods for 2-D and 3-D staggered grids. We test the interpolation <span class="hlt">schemes</span> in combination with different advection <span class="hlt">schemes</span> on incompressible Stokes problems with strong velocity gradients, which are discretized using a finite difference method. Our results suggest that a conservative formulation reduces the dispersion and clustering of markers, minimizing the need of unphysical marker control in geodynamic models.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20060047741','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20060047741"><span><span class="hlt">Numerical</span> Modeling of Turbulence Effects within an Evaporating Droplet in Atomizing Sprays</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Balasubramanyam, M. S.; Chen, C. P.; Trinh, H. P.</p> <p>2006-01-01</p> <p>A new approach to account for finite thermal conductivity and turbulence effects within atomizing liquid sprays is presented in this paper. The model is an extension of the T-blob and T-TAB atomization/spray model of Trinh and Chen (2005). This finite conductivity model is based on the two-temperature film theory, where the turbulence characteristics of the droplet are used to estimate the effective thermal diffhsivity within the droplet phase. Both one-way and two-way coupled calculations were performed to investigate the performance of this model. The current evaporation model is incorporated into the T-blob atomization model of Trinh and Chen (2005) and implemented in an existing CFD Eulerian-<span class="hlt">Lagrangian</span> two-way coupling <span class="hlt">numerical</span> <span class="hlt">scheme</span>. Validation studies were carried out by comparing with available evaporating atomization spray experimental data in terms of jet penetration, temperature field, and droplet SMD distribution within the spray. Validation results indicate the superiority of the finite-conductivity model in low speed parallel flow evaporating spray.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/4131841','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/4131841"><span>Transient three-dimensional thermal-hydraulic analysis of nuclear reactor fuel rod arrays: general equations and <span class="hlt">numerical</span> <span class="hlt">scheme</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>Wnek, W.J.; Ramshaw, J.D.; Trapp, J.A.</p> <p>1975-11-01</p> <p>A mathematical model and a <span class="hlt">numerical</span> solution <span class="hlt">scheme</span> for thermal- hydraulic analysis of fuel rod arrays are given. The model alleviates the two major deficiencies associated with existing rod array analysis models, that of a correct transverse momentum equation and the capability of handling reversing and circulatory flows. Possible applications of the model include steady state and transient subchannel calculations as well as analysis of flows in heat exchangers, other engineering equipment, and porous media. (auth)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AIPC.1561...68K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AIPC.1561...68K"><span>Four-level conservative finite-difference <span class="hlt">schemes</span> for Boussinesq paradigm equation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kolkovska, N.</p> <p>2013-10-01</p> <p>In this paper a two-parametric family of four level conservative finite difference <span class="hlt">schemes</span> is constructed for the multidimensional Boussinesq paradigm equation. The <span class="hlt">schemes</span> are explicit in the sense that no inner iterations are needed for evaluation of the <span class="hlt">numerical</span> solution. The preservation of the discrete energy with this method is proved. The <span class="hlt">schemes</span> have been <span class="hlt">numerically</span> tested on one soliton propagation model and two solitons interaction model. The <span class="hlt">numerical</span> experiments demonstrate that the proposed family of <span class="hlt">schemes</span> has second order of convergence in space and time steps in the discrete maximal norm.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19147874','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19147874"><span>Handwritten <span class="hlt">numeral</span> databases of Indian scripts and multistage recognition of mixed <span class="hlt">numerals</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Bhattacharya, Ujjwal; Chaudhuri, B B</p> <p>2009-03-01</p> <p>This article primarily concerns the problem of isolated handwritten <span class="hlt">numeral</span> recognition of major Indian scripts. The principal contributions presented here are (a) pioneering development of two databases for handwritten <span class="hlt">numerals</span> of two most popular Indian scripts, (b) a multistage cascaded recognition <span class="hlt">scheme</span> using wavelet based multiresolution representations and multilayer perceptron classifiers and (c) application of (b) for the recognition of mixed handwritten <span class="hlt">numerals</span> of three Indian scripts Devanagari, Bangla and English. The present databases include respectively 22,556 and 23,392 handwritten isolated <span class="hlt">numeral</span> samples of Devanagari and Bangla collected from real-life situations and these can be made available free of cost to researchers of other academic Institutions. In the proposed <span class="hlt">scheme</span>, a <span class="hlt">numeral</span> is subjected to three multilayer perceptron classifiers corresponding to three coarse-to-fine resolution levels in a cascaded manner. If rejection occurred even at the highest resolution, another multilayer perceptron is used as the final attempt to recognize the input <span class="hlt">numeral</span> by combining the outputs of three classifiers of the previous stages. This <span class="hlt">scheme</span> has been extended to the situation when the script of a document is not known a priori or the <span class="hlt">numerals</span> written on a document belong to different scripts. Handwritten <span class="hlt">numerals</span> in mixed scripts are frequently found in Indian postal mails and table-form documents.</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/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('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> Eulerian 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> Eulerian (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> Eulerian 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> Eulerian (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('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 Eulerian 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> codes 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 <span class="hlt">numerically</span> 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('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 Eulerian grid-box based models, like no <span class="hlt">numerical</span> diffusion, no limitation of the time step of the model by the CFL criterion, conservation of mixing ratios by design and easy parallelization of code. The transport module is based on a trajectory code 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/2005PhDT.......189B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005PhDT.......189B"><span><span class="hlt">Lagrangian</span> averaging, nonlinear waves, and shock regularization</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bhat, Harish S.</p> <p></p> <p>In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the <span class="hlt">Lagrangian</span> averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given <span class="hlt">Lagrangian</span> flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out <span class="hlt">numerical</span> experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940032139','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940032139"><span>A flux splitting <span class="hlt">scheme</span> with high-resolution and robustness for discontinuities</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wada, Yasuhiro; Liou, Meng-Sing</p> <p>1994-01-01</p> <p>A flux splitting <span class="hlt">scheme</span> is proposed for the general nonequilibrium flow equations with an aim at removing <span class="hlt">numerical</span> dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The <span class="hlt">scheme</span> obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight <span class="hlt">numerical</span> overshoot immediately behind the shock is eliminated. The proposed <span class="hlt">scheme</span> has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; <span class="hlt">numerical</span> efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this <span class="hlt">scheme</span> gives the <span class="hlt">numerical</span> flux of the exact solution of the Riemann problem. Various <span class="hlt">numerical</span> experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the <span class="hlt">scheme</span> for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20050175858','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20050175858"><span>Explicit Von Neumann Stability Conditions for the c-tau <span class="hlt">Scheme</span>: A Basic <span class="hlt">Scheme</span> in the Development of the CE-SE Courant Number Insensitive <span class="hlt">Schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chang, Sin-Chung</p> <p>2005-01-01</p> <p>As part of the continuous development of the space-time conservation element and solution element (CE-SE) method, recently a set of so call ed "Courant number insensitive <span class="hlt">schemes</span>" has been proposed. The key advantage of these new <span class="hlt">schemes</span> is that the <span class="hlt">numerical</span> dissipation associa ted with them generally does not increase as the Courant number decre ases. As such, they can be applied to problems with large Courant number disparities (such as what commonly occurs in Navier-Stokes problem s) without incurring excessive <span class="hlt">numerical</span> dissipation.</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 Eulerian residual circulation and the Stokes' drift. Unfortunately, this definition of the <span class="hlt">Lagrangian</span> residual circulation is conceptually incorrect because both the Eulerian residual circulation and the Stokes' drift are Eulerian 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 Eulerian 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 Eulerian 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 Eulerian 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/2014JGRC..119.2827L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JGRC..119.2827L"><span>Evaluation of altimetry-derived surface current products using <span class="hlt">Lagrangian</span> drifter trajectories in the eastern Gulf of Mexico</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Yonggang; Weisberg, Robert H.; Vignudelli, Stefano; Mitchum, Gary T.</p> <p>2014-05-01</p> <p><span class="hlt">Lagrangian</span> particle trajectory models based on several altimetry-derived surface current products are used to hindcast the drifter trajectories observed in the eastern Gulf of Mexico during May to August 2010 (the Deepwater Horizon oil spill incident). The performances of the trajectory models are gauged in terms of <span class="hlt">Lagrangian</span> separation distances (d) and a nondimensional skill score (s), respectively. A series of <span class="hlt">numerical</span> experiments show that these altimetry-based trajectory models have about the same performance, with a certain improvement by adding surface wind Ekman components, especially over the shelf region. However, their hindcast skills are slightly better than those of the data assimilative <span class="hlt">numerical</span> model output. After 3 days' simulation the altimetry-based trajectory models have mean d values of 75-83 and 34-42 km (s values of 0.49-0.51 and 0.35-0.43) in the Gulf of Mexico deep water area and on the West Florida Continental Shelf, respectively. These satellite altimetry data products are useful for providing essential information on ocean surface currents of use in water property transports, offshore oil and gas operations, hazardous spill mitigation, search and rescue, etc.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DFDKP1135D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DFDKP1135D"><span><span class="hlt">Numerical</span> investigation of complex flooding <span class="hlt">schemes</span> for surfactant polymer based enhanced oil recovery</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dutta, Sourav; Daripa, Prabir</p> <p>2015-11-01</p> <p>Surfactant-polymer flooding is a widely used method of chemical enhanced oil recovery (EOR) in which an array of complex fluids containing suitable and varying amounts of surfactant or polymer or both mixed with water is injected into the reservoir. This is an example of multiphase, multicomponent and multiphysics porous media flow which is characterized by the spontaneous formation of complex viscous fingering patterns and is modeled by a system of strongly coupled nonlinear partial differential equations with appropriate initial and boundary conditions. Here we propose and discuss a modern, hybrid method based on a combination of a discontinuous, multiscale finite element formulation and the method of characteristics to accurately solve the system. Several types of flooding <span class="hlt">schemes</span> and rheological properties of the injected fluids are used to <span class="hlt">numerically</span> study the effectiveness of various injection policies in minimizing the viscous fingering and maximizing oil recovery. <span class="hlt">Numerical</span> simulations are also performed to investigate the effect of various other physical and model parameters such as heterogeneity, relative permeability and residual saturation on the quantities of interest like cumulative oil recovery, sweep efficiency, fingering intensity to name a few. Supported by the grant NPRP 08-777-1-141 from the Qatar National Research Fund (a member of The Qatar Foundation).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26520072','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26520072"><span>Direct experimental visualization of the global Hamiltonian progression of two-dimensional <span class="hlt">Lagrangian</span> flow topologies from integrable to chaotic state.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Baskan, O; Speetjens, M F M; Metcalfe, G; Clercx, H J H</p> <p>2015-10-01</p> <p>Countless theoretical/<span class="hlt">numerical</span> studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the <span class="hlt">Lagrangian</span> dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the <span class="hlt">Lagrangian</span> flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing <span class="hlt">Lagrangian</span> dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUOSPO41B..05A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUOSPO41B..05A"><span><span class="hlt">Lagrangian</span> clustering detection of internal wave boluses</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Allshouse, M.; Salvador Vieira, G.; Swinney, H. L.</p> <p>2016-02-01</p> <p>The shoaling of internal waves on a continental slope or shelf produces boluses that travel up the slope with the wave. The boluses are regions of trapped fluid that are transported along with the wave, unlike fluid in the bulk that is temporarily pertubed by a passing wave. Boluses have been observed to transport oxygen-depleted water and induce rapid changes in temperature (Walter et al, JGR, 2012), both of which have potential ramifications for marine biology. Several previous studies have investigated boluses in systems with two layers of different density (e.g., Helfrich, JFM, 1992, and Sutherland et al., JGR, 2013). We conduct laboratory and computational studies of bolus generation and material transport in continuously stratified fluids with a pycnocline, as in the oceans. Our laboratory experiments in a 4 m long tank are complemented by 2-dimensional direct <span class="hlt">numerical</span> simulations of the Navier-Stokes equations. Efforts have been made to identify boluses with Eularian measures in the past, but a <span class="hlt">Lagrangian</span> perspective is necessary to objectively identify the bolus over its lifespan. Here we use a <span class="hlt">Lagrangian</span> based coherent structure method relying on trajectory clustering using the fuzzy c-means approach (Froyland and Padberg-Gehle, Chaos, 2015). The objective detection of a bolus enables examination of the volume, distance traveled, and increased available potential energy of a bolus, as a function of the stratification, wave properties, and the angle of the sloping topography. The decay of a bolus through turbulent mixing is investigated by locating where the Richardson number drops below ¼, where velocity shear overcomes the tendency of a stratified fluid to remain stratified. (supported by ONR MURI grant N000141110701)</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://hdl.handle.net/2060/20110008058','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20110008058"><span>Aerosol Observability and Predictability: From Research to Operations for Chemical Weather Forecasting. <span class="hlt">Lagrangian</span> Displacement Ensembles for Aerosol Data Assimilation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>da Silva, Arlindo</p> <p>2010-01-01</p> <p>A challenge common to many constituent data assimilation applications is the fact that one observes a much smaller fraction of the phase space that one wishes to estimate. For example, remotely sensed estimates of the column average concentrations are available, while one is faced with the problem of estimating 3D concentrations for initializing a prognostic model. This problem is exacerbated in the case of aerosols because the observable Aerosol Optical Depth (AOD) is not only a column integrated quantity, but it also sums over a large number of species (dust, sea-salt, carbonaceous and sulfate aerosols. An aerosol transport model when driven by high-resolution, state-of-the-art analysis of meteorological fields and realistic emissions can produce skillful forecasts even when no aerosol data is assimilated. The main task of aerosol data assimilation is to address the bias arising from inaccurate emissions, and <span class="hlt">Lagrangian</span> misplacement of plumes induced by errors in the driving meteorological fields. As long as one decouples the meteorological and aerosol assimilation as we do here, the classic baroclinic growth of error is no longer the main order of business. We will describe an aerosol data assimilation <span class="hlt">scheme</span> in which the analysis update step is conducted in observation space, using an adaptive maximum-likelihood <span class="hlt">scheme</span> for estimating background errors in AOD space. This <span class="hlt">scheme</span> includes e explicit sequential bias estimation as in Dee and da Silva. Unlikely existing aerosol data assimilation <span class="hlt">schemes</span> we do not obtain analysis increments of the 3D concentrations by scaling the background profiles. Instead we explore the <span class="hlt">Lagrangian</span> characteristics of the problem for generating local displacement ensembles. These high-resolution state-dependent ensembles are then used to parameterize the background errors and generate 3D aerosol increments. The algorithm has computational complexity running at a resolution of 1/4 degree, globally. We will present the result of</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940019081','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940019081"><span>An implicit <span class="hlt">numerical</span> <span class="hlt">scheme</span> for the simulation of internal viscous flows on unstructured grids</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jorgenson, Philip C. E.; Pletcher, Richard H.</p> <p>1994-01-01</p> <p>The Navier-Stokes equations are solved <span class="hlt">numerically</span> for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color <span class="hlt">scheme</span> is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. <span class="hlt">Numerical</span> results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhyD..346...59X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhyD..346...59X"><span>Assimilating Eulerian and <span class="hlt">Lagrangian</span> data in traffic-flow models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Xia, Chao; Cochrane, Courtney; DeGuire, Joseph; Fan, Gaoyang; Holmes, Emma; McGuirl, Melissa; Murphy, Patrick; Palmer, Jenna; Carter, Paul; Slivinski, Laura; Sandstede, Björn</p> <p>2017-05-01</p> <p>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 <span class="hlt">Lagrangian</span> data collected from individual cars relied on specific properties of the underlying computational model or its reformulation in <span class="hlt">Lagrangian</span> coordinates. These approaches make it hard to assimilate both Eulerian density and <span class="hlt">Lagrangian</span> positional data simultaneously. In this paper, we propose an alternative approach that allows us to assimilate both Eulerian and <span class="hlt">Lagrangian</span> 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.</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('https://ntrs.nasa.gov/search.jsp?R=20030013624&hterms=blending+traditional&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dblending%2Btraditional','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20030013624&hterms=blending+traditional&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dblending%2Btraditional"><span>Efficient Low Dissipative High Order <span class="hlt">Schemes</span> for Multiscale MHD Flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Sjoegreen, Bjoern; Yee, Helen C.; Mansour, Nagi (Technical Monitor)</p> <p>2002-01-01</p> <p>Accurate <span class="hlt">numerical</span> simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order <span class="hlt">schemes</span> with adaptive <span class="hlt">numerical</span> dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of <span class="hlt">numerical</span> dissipation in high order <span class="hlt">schemes</span> for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These <span class="hlt">schemes</span> are suitable for the problems in question. Basically, the <span class="hlt">scheme</span> consists of sixth-order or higher non-dissipative spatial difference operators as the base <span class="hlt">scheme</span>. To control the amount of <span class="hlt">numerical</span> dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of <span class="hlt">numerical</span> dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing <span class="hlt">schemes</span> for the MHD in the literature, these <span class="hlt">schemes</span> are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution <span class="hlt">schemes</span> to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate <span class="hlt">numerical</span> <span class="hlt">schemes</span> for multiscale MHD equations pose a great</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://ntrs.nasa.gov/search.jsp?R=19850066050&hterms=mathematics&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dmathematics','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19850066050&hterms=mathematics&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dmathematics"><span>Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Engquist, B. E. (Editor); Osher, S. (Editor); Somerville, R. C. J. (Editor)</p> <p>1985-01-01</p> <p>Papers are presented on such topics as the use of semi-<span class="hlt">Lagrangian</span> advective <span class="hlt">schemes</span> in meteorological modeling; computation with high-resolution upwind <span class="hlt">schemes</span> for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing <span class="hlt">scheme</span> using flux-limited dissipation. Consideration is also given to the use of spectral techniques in <span class="hlt">numerical</span> weather prediction; <span class="hlt">numerical</span> methods for the incorporation of mountains in atmospheric models; techniques for the <span class="hlt">numerical</span> simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD <span class="hlt">schemes</span> using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.</p> </li> <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('https://www.osti.gov/biblio/22521515-numerical-scheme-special-relativistic-radiation-magnetohydrodynamics-based-solving-time-dependent-radiative-transfer-equation','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22521515-numerical-scheme-special-relativistic-radiation-magnetohydrodynamics-based-solving-time-dependent-radiative-transfer-equation"><span>A <span class="hlt">NUMERICAL</span> <span class="hlt">SCHEME</span> FOR SPECIAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS BASED ON SOLVING THE TIME-DEPENDENT RADIATIVE TRANSFER 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>Ohsuga, Ken; Takahashi, Hiroyuki R.</p> <p>2016-02-20</p> <p>We develop a <span class="hlt">numerical</span> <span class="hlt">scheme</span> for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The <span class="hlt">numerical</span> method of MHDs is the same as that of our previous work. The advection terms are explicitlymore » solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some <span class="hlt">numerical</span> tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.« less</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://www.ncbi.nlm.nih.gov/pubmed/22168678','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22168678"><span>Geometric integration in 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>Odell, Anders; Delin, Anna; Johansson, Börje; Cawkwell, Marc J; Niklasson, Anders M N</p> <p>2011-12-14</p> <p>Geometric integration <span class="hlt">schemes</span> for extended <span class="hlt">Lagrangian</span> self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove <span class="hlt">numerical</span> noise, are developed and analyzed. The extended <span class="hlt">Lagrangian</span> framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration <span class="hlt">schemes</span>: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of <span class="hlt">numerical</span> noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. © 2011 American Institute of Physics</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/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/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('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('http://adsabs.harvard.edu/abs/2016APS..DFDR34003B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDR34003B"><span><span class="hlt">Lagrangian</span> statistics of turbulent dispersion from 81923 direct <span class="hlt">numerical</span> simulation of isotropic turbulence</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Buaria, Dhawal; Yeung, P. K.; Sawford, B. L.</p> <p>2016-11-01</p> <p>An efficient massively parallel algorithm has allowed us to obtain the trajectories of 300 million fluid particles in an 81923 simulation of isotropic turbulence at Taylor-scale Reynolds number 1300. Conditional single-particle statistics are used to investigate the effect of extreme events in dissipation and enstrophy on turbulent dispersion. The statistics of pairs and tetrads, both forward and backward in time, are obtained via post-processing of single-particle trajectories. For tetrads, since memory of shape is known to be short, we focus, for convenience, on samples which are initially regular, with all sides of comparable length. The statistics of tetrad size show similar behavior as the two-particle relative dispersion, i.e., stronger backward dispersion at intermediate times with larger backward Richardson constant. In contrast, the statistics of tetrad shape show more robust inertial range scaling, in both forward and backward frames. However, the distortion of shape is stronger for backward dispersion. Our results suggest that the Reynolds number reached in this work is sufficient to settle some long-standing questions concerning <span class="hlt">Lagrangian</span> scale similarity. Supported by NSF Grants CBET-1235906 and ACI-1036170.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29104452','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29104452"><span><span class="hlt">Numerical</span> Hydrodynamics in General Relativity.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Font, José A</p> <p>2003-01-01</p> <p>The current status of <span class="hlt">numerical</span> solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on <span class="hlt">numerical</span> <span class="hlt">schemes</span>, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced <span class="hlt">numerical</span> methods. A large sample of available <span class="hlt">numerical</span> <span class="hlt">schemes</span> is discussed, paying particular attention to solution procedures based on <span class="hlt">schemes</span> exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the <span class="hlt">numerical</span> challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the <span class="hlt">numerical</span> methodology designed to solve them. Supplementary material is available for this article at 10.12942/lrr-2003-4.</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> </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://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 <span class="hlt">numerical</span> 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 Eulerian 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 <span class="hlt">scheme</span>, 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 Eulerian mesh.</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> <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/2017JCoPh.330..401C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.330..401C"><span>A positive and entropy-satisfying finite volume <span class="hlt">scheme</span> for the Baer-Nunziato model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled</p> <p>2017-02-01</p> <p>We present a relaxation <span class="hlt">scheme</span> for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation <span class="hlt">scheme</span> is straightforwardly obtained as an extension of the relaxation <span class="hlt">scheme</span> designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing <span class="hlt">scheme</span> for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the <span class="hlt">numerical</span> <span class="hlt">scheme</span>. It is also the only <span class="hlt">scheme</span> for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the <span class="hlt">numerical</span> method, is satisfied for any admissible equation of state. We provide a <span class="hlt">numerical</span> study for the convergence of the approximate solutions towards some exact Riemann solutions. The <span class="hlt">numerical</span> simulations show that the relaxation <span class="hlt">scheme</span> compares well with two of the most popular existing <span class="hlt">schemes</span> available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type <span class="hlt">scheme</span> [39] and Tokareva-Toro's HLLC <span class="hlt">scheme</span> [44]. The relaxation <span class="hlt">scheme</span> also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard <span class="hlt">numerical</span> <span class="hlt">scheme</span> used in the nuclear industry, namely Rusanov's <span class="hlt">scheme</span>. Finally, we assess the good behavior of the <span class="hlt">scheme</span> when approximating vanishing phase solutions.</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/2017JCoPh.340..575N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.340..575N"><span>Overcoming <span class="hlt">numerical</span> shockwave anomalies using energy balanced <span class="hlt">numerical</span> <span class="hlt">schemes</span>. Application to the Shallow Water Equations with discontinuous topography</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Navas-Montilla, A.; Murillo, J.</p> <p>2017-07-01</p> <p>When designing a <span class="hlt">numerical</span> <span class="hlt">scheme</span> for the resolution of conservation laws, the selection of a particular source term discretization (STD) may seem irrelevant whenever it ensures convergence with mesh refinement, but it has a decisive impact on the solution. In the framework of the Shallow Water Equations (SWE), well-balanced STD based on quiescent equilibrium are unable to converge to physically based solutions, which can be constructed considering energy arguments. Energy based discretizations can be designed assuming dissipation or conservation, but in any case, the STD procedure required should not be merely based on ad hoc approximations. The STD proposed in this work is derived from the Generalized Hugoniot Locus obtained from the Generalized Rankine Hugoniot conditions and the Integral Curve across the contact wave associated to the bed step. In any case, the STD must allow energy-dissipative solutions: steady and unsteady hydraulic jumps, for which some <span class="hlt">numerical</span> anomalies have been documented in the literature. These anomalies are the incorrect positioning of steady jumps and the presence of a spurious spike of discharge inside the cell containing the jump. The former issue can be addressed by proposing a modification of the energy-conservative STD that ensures a correct dissipation rate across the hydraulic jump, whereas the latter is of greater complexity and cannot be fixed by simply choosing a suitable STD, as there are more variables involved. The problem concerning the spike of discharge is a well-known problem in the scientific community, also known as slowly-moving shock anomaly, it is produced by a nonlinearity of the Hugoniot locus connecting the states at both sides of the jump. However, it seems that this issue is more a feature than a problem when considering steady solutions of the SWE containing hydraulic jumps. The presence of the spurious spike in the discharge has been taken for granted and has become a feature of the solution. Even though</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20070034888','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20070034888"><span>New, Improved Bulk-microphysical <span class="hlt">Schemes</span> for Studying Precipitation Processes in WRF. Part 1; Comparisons with Other <span class="hlt">Schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Tao, W.-K.; Shi, J.; Chen, S. S> <author type="secondary"/>; Lang, S.; Hong, S.-Y.; Thompson, G.; Peters-Lidard, C.; Hou, A.; Braun, S.; <a style="text-decoration: none; " href="javascript:void(0); " onClick="displayelement('author_20070034888'); toggleEditAbsImage('author_20070034888_show'); toggleEditAbsImage('author_20070034888_hide'); "> <img style="display:inline; width:12px; height:12px; " src="images/arrow-up.gif" width="12" height="12" border="0" alt="hide" id="author_20070034888_show"> <img style="width:12px; height:12px; display:none; " src="images/arrow-down.gif" width="12" height="12" border="0" alt="hide" id="author_20070034888_hide"></p> <p>2007-01-01</p> <p>Advances in computing power allow atmospheric prediction models to be mn at progressively finer scales of resolution, using increasingly more sophisticated physical parameterizations and <span class="hlt">numerical</span> methods. The representation of cloud microphysical processes is a key component of these models, over the past decade both research and operational <span class="hlt">numerical</span> weather prediction models have started using more complex microphysical <span class="hlt">schemes</span> that were originally developed for high-resolution cloud-resolving models (CRMs). A recent report to the United States Weather Research Program (USWRP) Science Steering Committee specifically calls for the replacement of implicit cumulus parameterization <span class="hlt">schemes</span> with explicit bulk <span class="hlt">schemes</span> in <span class="hlt">numerical</span> weather prediction (NWP) as part of a community effort to improve quantitative precipitation forecasts (QPF). An improved Goddard bulk microphysical parameterization is implemented into a state-of the-art of next generation of Weather Research and Forecasting (WRF) model. High-resolution model simulations are conducted to examine the impact of microphysical <span class="hlt">schemes</span> on two different weather events (a midlatitude linear convective system and an Atllan"ic hurricane). The results suggest that microphysics has a major impact on the organization and precipitation processes associated with a summer midlatitude convective line system. The 31CE <span class="hlt">scheme</span> with a cloud ice-snow-hail configuration led to a better agreement with observation in terms of simulated narrow convective line and rainfall intensity. This is because the 3ICE-hail <span class="hlt">scheme</span> includes dense ice precipitating (hail) particle with very fast fall speed (over 10 m/s). For an Atlantic hurricane case, varying the microphysical <span class="hlt">schemes</span> had no significant impact on the track forecast but did affect the intensity (important for air-sea interaction)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22482283-direct-experimental-visualization-global-hamiltonian-progression-two-dimensional-lagrangian-flow-topologies-from-integrable-chaotic-state','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22482283-direct-experimental-visualization-global-hamiltonian-progression-two-dimensional-lagrangian-flow-topologies-from-integrable-chaotic-state"><span>Direct experimental visualization of the global Hamiltonian progression of two-dimensional <span class="hlt">Lagrangian</span> flow topologies from integrable to chaotic state</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>Baskan, O.; Clercx, H. J. H; Speetjens, M. F. M.</p> <p></p> <p>Countless theoretical/<span class="hlt">numerical</span> studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the <span class="hlt">Lagrangian</span> dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the <span class="hlt">Lagrangian</span> flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progressionmore » by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing <span class="hlt">Lagrangian</span> dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1414290','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1414290"><span>An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains</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, Saumil S.; Fischer, Paul F.; Min, Misun</p> <p></p> <p>In this paper, we present a characteristic-based <span class="hlt">numerical</span> procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable <span class="hlt">numerical</span> <span class="hlt">scheme</span>. Using the spectral element method and an arbitrary <span class="hlt">Lagrangian</span>-Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the <span class="hlt">scheme</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940019637','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940019637"><span>On the dynamics of some grid adaption <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Sweby, Peter K.; Yee, Helen C.</p> <p>1994-01-01</p> <p>The dynamics of a one-parameter family of mesh equidistribution <span class="hlt">schemes</span> coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied <span class="hlt">numerically</span>. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall <span class="hlt">scheme</span>, but can also introduce spurious dynamics to the <span class="hlt">numerical</span> solution procedure.</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('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 <span class="hlt">numerical</span> 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 Eulerian 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/2016APS..DFDM34003W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDM34003W"><span>Characteristics of the mixing volume model with the interactions among spatially distributed particles for <span class="hlt">Lagrangian</span> simulations of turbulent mixing</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Watanabe, Tomoaki; Nagata, Koji</p> <p>2016-11-01</p> <p>The mixing volume model (MVM), which is a mixing model for molecular diffusion in <span class="hlt">Lagrangian</span> simulations of turbulent mixing problems, is proposed based on the interactions among spatially distributed particles in a finite volume. The mixing timescale in the MVM is derived by comparison between the model and the subgrid scale scalar variance equation. A-priori test of the MVM is conducted based on the direct <span class="hlt">numerical</span> simulations of planar jets. The MVM is shown to predict well the mean effects of the molecular diffusion under various conditions. However, a predicted value of the molecular diffusion term is positively correlated to the exact value in the DNS only when the number of the mixing particles is larger than two. Furthermore, the MVM is tested in the hybrid implicit large-eddy-simulation/<span class="hlt">Lagrangian</span>-particle-simulation (ILES/LPS). The ILES/LPS with the present mixing model predicts well the decay of the scalar variance in planar jets. This work was supported by JSPS KAKENHI Nos. 25289030 and 16K18013. The <span class="hlt">numerical</span> simulations presented in this manuscript were carried out on the high performance computing system (NEC SX-ACE) in the Japan Agency for Marine-Earth Science and Technology.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29104401','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29104401"><span>An accelerated proximal augmented <span class="hlt">Lagrangian</span> method and its application in compressive sensing.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Sun, Min; Liu, Jing</p> <p>2017-01-01</p> <p>As a first-order method, the augmented <span class="hlt">Lagrangian</span> method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable's subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear constraints, which generalizes the proximal terms from semi-definite to indefinite. Under mild assumptions, we establish the worst-case [Formula: see text] convergence rate of PALM-IPR in a non-ergodic sense. Finally, <span class="hlt">numerical</span> results show that our new method is feasible and efficient for solving compressive sensing.</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 Eulerian 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 <span class="hlt">numerical</span> 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 <span class="hlt">numerical</span> optimisation methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920016570&hterms=levels+law&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3DA%2Blevels%2Blaw','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920016570&hterms=levels+law&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3DA%2Blevels%2Blaw"><span><span class="hlt">Numerical</span> simulation of conservation laws</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chang, Sin-Chung; To, Wai-Ming</p> <p>1992-01-01</p> <p>A new <span class="hlt">numerical</span> framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current <span class="hlt">scheme</span> include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current <span class="hlt">scheme</span>, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel <span class="hlt">scheme</span>. As a result, the current <span class="hlt">scheme</span> has no <span class="hlt">numerical</span> diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and <span class="hlt">numerically</span> that, by using an easily determined optimal time step, the accuracy of the current <span class="hlt">scheme</span> may reach a level which is several orders of magnitude higher than that of the MacCormack <span class="hlt">scheme</span>, with virtually identical operation count.</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><span class="hlt">Numerical</span> 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> Eulerian (ALE) code 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 <span class="hlt">numerical</span> 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('http://adsabs.harvard.edu/abs/2017CG.....99...28L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CG.....99...28L"><span>A modified symplectic PRK <span class="hlt">scheme</span> for seismic wave modeling</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Shaolin; Yang, Dinghui; Ma, Jian</p> <p>2017-02-01</p> <p>A new <span class="hlt">scheme</span> for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) <span class="hlt">scheme</span> is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK <span class="hlt">scheme</span> to create a modified symplectic PRK <span class="hlt">scheme</span>. The symplectic coefficients of the new <span class="hlt">scheme</span> are determined via Taylor series expansion. The positive coefficients of the <span class="hlt">scheme</span> indicate that its long-term computational capability is more powerful than that of conventional symplectic <span class="hlt">schemes</span>. An exhaustive theoretical analysis reveals that the new <span class="hlt">scheme</span> is highly stable and has low <span class="hlt">numerical</span> dispersion. The results of three <span class="hlt">numerical</span> experiments demonstrate the high efficiency of this method for seismic wave modeling.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22622247-positive-entropy-satisfying-finite-volume-scheme-baernunziato-model','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22622247-positive-entropy-satisfying-finite-volume-scheme-baernunziato-model"><span>A positive and entropy-satisfying finite volume <span class="hlt">scheme</span> for the Baer–Nunziato 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>Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr; Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr; Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr</p> <p></p> <p>We present a relaxation <span class="hlt">scheme</span> for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation <span class="hlt">scheme</span> is straightforwardly obtained as an extension of the relaxation <span class="hlt">scheme</span> designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing <span class="hlt">scheme</span> for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound aremore » also proven to be maintained by the <span class="hlt">numerical</span> <span class="hlt">scheme</span>. It is also the only <span class="hlt">scheme</span> for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the <span class="hlt">numerical</span> method, is satisfied for any admissible equation of state. We provide a <span class="hlt">numerical</span> study for the convergence of the approximate solutions towards some exact Riemann solutions. The <span class="hlt">numerical</span> simulations show that the relaxation <span class="hlt">scheme</span> compares well with two of the most popular existing <span class="hlt">schemes</span> available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type <span class="hlt">scheme</span> and Tokareva–Toro's HLLC <span class="hlt">scheme</span> . The relaxation <span class="hlt">scheme</span> also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard <span class="hlt">numerical</span> <span class="hlt">scheme</span> used in the nuclear industry, namely Rusanov's <span class="hlt">scheme</span>. Finally, we assess the good behavior of the <span class="hlt">scheme</span> when approximating vanishing phase solutions.« 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_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('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('http://adsabs.harvard.edu/abs/2017GMD....10.1961T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017GMD....10.1961T"><span>Vorticity-divergence semi-<span class="hlt">Lagrangian</span> global atmospheric model SL-AV20: dynamical core</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tolstykh, Mikhail; Shashkin, Vladimir; Fadeev, Rostislav; Goyman, Gordey</p> <p>2017-05-01</p> <p>SL-AV (semi-<span class="hlt">Lagrangian</span>, based on the absolute vorticity equation) is a global hydrostatic atmospheric model. Its latest version, SL-AV20, provides global operational medium-range weather forecast with 20 km resolution over Russia. The lower-resolution configurations of SL-AV20 are being tested for seasonal prediction and climate modeling. The article presents the model dynamical core. Its main features are a vorticity-divergence formulation at the unstaggered grid, high-order finite-difference approximations, semi-<span class="hlt">Lagrangian</span> semi-implicit discretization and the reduced latitude-longitude grid with variable resolution in latitude. The accuracy of SL-AV20 <span class="hlt">numerical</span> solutions using a reduced lat-lon grid and the variable resolution in latitude is tested with two idealized test cases. Accuracy and stability of SL-AV20 in the presence of the orography forcing are tested using the mountain-induced Rossby wave test case. The results of all three tests are in good agreement with other published model solutions. It is shown that the use of the reduced grid does not significantly affect the accuracy up to the 25 % reduction in the number of grid points with respect to the regular grid. Variable resolution in latitude allows us to improve the accuracy of a solution in the region of interest.</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://hdl.handle.net/2060/20060022551','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20060022551"><span>Convergence Acceleration for Multistage Time-Stepping <span class="hlt">Schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Swanson, R. C.; Turkel, Eli L.; Rossow, C-C; Vasta, V. N.</p> <p>2006-01-01</p> <p>The convergence of a Runge-Kutta (RK) <span class="hlt">scheme</span> with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta <span class="hlt">scheme</span>, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. <span class="hlt">Numerical</span> dissipation operators (based on the Roe <span class="hlt">scheme</span>, a matrix formulation, and the CUSP <span class="hlt">scheme</span>) as well as the number of RK stages are considered in evaluating the RK/implicit <span class="hlt">scheme</span>. Both the <span class="hlt">numerical</span> and computational efficiency of the <span class="hlt">scheme</span> with the different dissipation operators are discussed. The RK/implicit <span class="hlt">scheme</span> is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK <span class="hlt">scheme</span> is reduced at least a factor of four.</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/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 <span class="hlt">numerical</span> 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 Eulerian 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://hdl.handle.net/2060/19890001486','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890001486"><span><span class="hlt">Numerical</span> investigation of a jet in ground effect using the fortified Navier-Stokes <span class="hlt">scheme</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Vandalsem, William R.; Steger, Joseph L.</p> <p>1988-01-01</p> <p>One of the flows inherent in VSTOL operations, the jet in ground effect with a crossflow, is studied using the Fortified Navier-Stokes (FNS) <span class="hlt">scheme</span>. Through comparison of the simulation results and the experimental data, and through the variation of the flow parameters (in the simulation) a number of interesting characteristics of the flow have been observed. For example, it appears that the forward penetration of the ground vortex is a strong inverse function of the level of mixing in the ground vortex. Also, an effort has been made to isolate issues which require additional work in order to improve the <span class="hlt">numerical</span> simulation of the jet in ground effect flow. The FNS approach simplifies the simulation of a single jet in ground effect, but it will be even more effective in applications to more complex topologies.</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/2016AGUOSEC14C1023C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUOSEC14C1023C"><span>On modeling heterogeneous coastal sediment transport - A <span class="hlt">numerical</span> study using multiphase Eulerian 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 Eulerian 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('http://hdl.handle.net/2060/19930006613','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930006613"><span>Runge-Kutta methods combined with compact difference <span class="hlt">schemes</span> for the unsteady Euler equations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Yu, Sheng-Tao</p> <p>1992-01-01</p> <p>Recent development using compact difference <span class="hlt">schemes</span> to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the <span class="hlt">numerical</span> characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference <span class="hlt">schemes</span> to calculate the unsteady Euler equations. The accuracy of finite difference <span class="hlt">schemes</span> is assessed based on the evaluations of dissipative error. The objectives are reducing the <span class="hlt">numerical</span> damping and, at the same time, preserving <span class="hlt">numerical</span> stability. While this approach has tremendous success solving steady flows, <span class="hlt">numerical</span> characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the <span class="hlt">numerical</span> results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive <span class="hlt">numerical</span> medium. Consequently, the dispersion characteristics of the <span class="hlt">numerical</span> <span class="hlt">schemes</span> which relate the phase velocity and wave number may greatly impact the <span class="hlt">numerical</span> accuracy. The aim is to assess the <span class="hlt">numerical</span> accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various <span class="hlt">numerical</span> <span class="hlt">schemes</span>. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step <span class="hlt">schemes</span> and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference <span class="hlt">schemes</span> are presented. The <span class="hlt">schemes</span> are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the <span class="hlt">numerical</span> methods is shown by <span class="hlt">numerical</span> examples. These examples</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26328579','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26328579"><span>Identifying finite-time coherent sets from limited quantities of <span class="hlt">Lagrangian</span> data.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Williams, Matthew O; Rypina, Irina I; Rowley, Clarence W</p> <p>2015-08-01</p> <p>A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of <span class="hlt">Lagrangian</span> data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that "leak" from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, "data rich" test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or "mesh-free" methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of <span class="hlt">Lagrangian</span> data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from <span class="hlt">numerically</span> simulated drifters in the Sulu Sea.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22482317-identifying-finite-time-coherent-sets-from-limited-quantities-lagrangian-data','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22482317-identifying-finite-time-coherent-sets-from-limited-quantities-lagrangian-data"><span>Identifying finite-time coherent sets from limited quantities of <span class="hlt">Lagrangian</span> data</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>Williams, Matthew O.; Rypina, Irina I.; Rowley, Clarence W.</p> <p></p> <p>A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of <span class="hlt">Lagrangian</span> data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods basedmore » on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of <span class="hlt">Lagrangian</span> data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from <span class="hlt">numerically</span> simulated drifters in the Sulu Sea.« less</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> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1919540P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1919540P"><span>The <span class="hlt">Lagrangian</span> particle dispersion model FLEXPART version 10</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; Sollum, Espen; Grythe, Henrik; Kristiansen, Nina; Cassiani, Massimo; Eckhardt, Sabine; Thompson, Rona; Groot Zwaaftnik, Christine; Evangeliou, Nikolaos; Hamburger, Thomas; Sodemann, Harald; Haimberger, Leopold; Henne, Stephan; Brunner, Dominik; Burkhart, John; Fouilloux, Anne; Fang, Xuekun; Phillip, Anne; Seibert, Petra; Stohl, Andreas</p> <p>2017-04-01</p> <p>The <span class="hlt">Lagrangian</span> particle dispersion model FLEXPART was in its first original release in 1998 designed for calculating the long-range and mesoscale dispersion of air pollutants from point sources, such as after an accident in a nuclear power plant. The model has now evolved into a comprehensive tool for atmospheric transport modelling and analysis. Its application fields are extended to a range of atmospheric transport processes for both atmospheric gases and aerosols, e.g. greenhouse gases, short-lived climate forces like black carbon, volcanic ash and gases as well as studies of the water cycle. We present the newest release, FLEXPART version 10. Since the last publication fully describing FLEXPART (version 6.2), the model code has been parallelised in order to allow for the possibility to speed up computation. A new, more detailed gravitational settling parametrisation for aerosols was implemented, and the wet deposition <span class="hlt">scheme</span> for aerosols has been heavily modified and updated to provide a more accurate representation of this physical process. In addition, an optional new turbulence <span class="hlt">scheme</span> for the convective boundary layer is available, that considers the skewness in the vertical velocity distribution. Also, temporal variation and temperature dependence of the OH-reaction are included. Finally, user input files are updated to a more convenient and user-friendly namelist format, and the option to produce the output-files in netCDF-format instead of binary format is implemented. We present these new developments and show recent model applications. Moreover, we also introduce some tools for the preparation of the meteorological input data, as well as for the processing of FLEXPART output data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19990027615','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19990027615"><span>Gas Evolution Dynamics in Godunov-Type <span class="hlt">Schemes</span> and Analysis of <span class="hlt">Numerical</span> Shock Instability</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Xu, Kun</p> <p>1999-01-01</p> <p>In this paper we are going to study the gas evolution dynamics of the exact and approximate Riemann solvers, e.g., the Flux Vector Splitting (FVS) and the Flux Difference Splitting (FDS) <span class="hlt">schemes</span>. Since the FVS <span class="hlt">scheme</span> and the Kinetic Flux Vector Splitting (KFVS) <span class="hlt">scheme</span> have the same physical mechanism and similar flux function, based on the analysis of the discretized KFVS <span class="hlt">scheme</span> the weakness and advantage of the FVS <span class="hlt">scheme</span> are closely observed. The subtle dissipative mechanism of the Godunov method in the 2D case is also analyzed, and the physical reason for shock instability, i.e., carbuncle phenomena and odd-even decoupling, is presented.</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 Code 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 Eulerian 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/2018PhRvF...3f4303L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhRvF...3f4303L"><span><span class="hlt">Numerical</span> investigation of homogeneous cavitation nucleation in a microchannel</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lyu, Xiuxiu; Pan, Shucheng; Hu, Xiangyu; Adams, Nikolaus A.</p> <p>2018-06-01</p> <p>The physics of nucleation in water is an important issue for many areas, ranging from biomedical to engineering applications. Within the present study, we investigate <span class="hlt">numerically</span> homogeneous nucleation in a microchannel induced by shock reflection to gain a better understanding of the mechanism of homogeneous nucleation. The liquid expands due to the reflected shock and homogeneous cavitation nuclei are generated. An Eulerian-<span class="hlt">Lagrangian</span> approach is employed for modeling this process in a microchanel. Two-dimensional axisymmetric Euler equations are solved for obtaining the time evolution of shock, gas bubble, and the ambient fluid. The dynamics of dispersed vapor bubbles is coupled with the surrounding fluid in a <span class="hlt">Lagrangian</span> framework, describing bubble location and bubble size variation. Our results reproduce nuclei distributions at different stages of homogeneous nucleation and are in good agreement with experimental results. We obtain <span class="hlt">numerical</span> data for the negative pressure that water can sustain under the process of homogeneous nucleation. An energy transformation description for the homogeneous nucleation inside a microchannel flow is derived and analyzed in detail.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900007085','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900007085"><span>Triangle based TVD <span class="hlt">schemes</span> for hyperbolic conservation laws</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Durlofsky, Louis J.; Osher, Stanley; Engquist, Bjorn</p> <p>1990-01-01</p> <p>A triangle based total variation diminishing (TVD) <span class="hlt">scheme</span> for the <span class="hlt">numerical</span> approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the <span class="hlt">scheme</span> lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this <span class="hlt">scheme</span>, approximate the flux up to second order accuracy. <span class="hlt">Numerical</span> results for linear advection and Burgers' equation are presented.</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('http://adsabs.harvard.edu/abs/2013EGUGA..1510218B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..1510218B"><span>Assimilation of drifters' trajectories in velocity fields from coastal radar and model via the <span class="hlt">Lagrangian</span> assimilation algorithm LAVA.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Berta, Maristella; Bellomo, Lucio; Griffa, Annalisa; Gatimu Magaldi, Marcello; Marmain, Julien; Molcard, Anne; Taillandier, Vincent</p> <p>2013-04-01</p> <p>The <span class="hlt">Lagrangian</span> assimilation algorithm LAVA (<span class="hlt">LAgrangian</span> Variational Analysis) is customized for coastal areas in the framework of the TOSCA (Tracking Oil Spills & Coastal Awareness network) Project, to improve the response to maritime accidents in the Mediterranean Sea. LAVA assimilates drifters' trajectories in the velocity fields which may come from either coastal radars or <span class="hlt">numerical</span> models. In the present study, LAVA is applied to the coastal area in front of Toulon (France). Surface currents are available from a WERA radar network (2km spatial resolution, every 20 minutes) and from the GLAZUR model (1/64° spatial resolution, every hour). The cluster of drifters considered is constituted by 7 buoys, transmitting every 15 minutes for a period of 5 days. Three assimilation cases are considered: i) correction of the radar velocity field, ii) correction of the model velocity field and iii) reconstruction of the velocity field from drifters only. It is found that drifters' trajectories compare well with the ones obtained by the radar and the correction to radar velocity field is therefore minimal. Contrarily, observed and <span class="hlt">numerical</span> trajectories separate rapidly and the correction to the model velocity field is substantial. For the reconstruction from drifters only, the velocity fields obtained are similar to the radar ones, but limited to the neighbor of the drifter paths.</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('http://hdl.handle.net/2060/19900017279','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900017279"><span>On central-difference and upwind <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Swanson, R. C.; Turkel, Eli</p> <p>1990-01-01</p> <p>A class of <span class="hlt">numerical</span> dissipation models for central-difference <span class="hlt">schemes</span> constructed with second- and fourth-difference terms is considered. The notion of matrix dissipation associated with upwind <span class="hlt">schemes</span> is used to establish improved shock capturing capability for these models. In addition, conditions are given that guarantee that such dissipation models produce a Total Variation Diminishing (TVD) <span class="hlt">scheme</span>. Appropriate switches for this type of model to ensure satisfaction of the TVD property are presented. Significant improvements in the accuracy of a central-difference <span class="hlt">scheme</span> are demonstrated by computing both inviscid and viscous transonic airfoil flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDM30006C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDM30006C"><span><span class="hlt">Numerical</span> Simulations of Reacting Flows Using Asynchrony-Tolerant <span class="hlt">Schemes</span> for Exascale Computing</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cleary, Emmet; Konduri, Aditya; Chen, Jacqueline</p> <p>2017-11-01</p> <p>Communication and data synchronization between processing elements (PEs) are likely to pose a major challenge in scalability of solvers at the exascale. Recently developed asynchrony-tolerant (AT) finite difference <span class="hlt">schemes</span> address this issue by relaxing communication and synchronization between PEs at a mathematical level while preserving accuracy, resulting in improved scalability. The performance of these <span class="hlt">schemes</span> has been validated for simple linear and nonlinear homogeneous PDEs. However, many problems of practical interest are governed by highly nonlinear PDEs with source terms, whose solution may be sensitive to perturbations caused by communication asynchrony. The current work applies the AT <span class="hlt">schemes</span> to combustion problems with chemical source terms, yielding a stiff system of PDEs with nonlinear source terms highly sensitive to temperature. Examples shown will use single-step and multi-step CH4 mechanisms for 1D premixed and nonpremixed flames. Error analysis will be discussed both in physical and spectral space. Results show that additional errors introduced by the AT <span class="hlt">schemes</span> are negligible and the <span class="hlt">schemes</span> preserve their accuracy. We acknowledge funding from the DOE Computational Science Graduate Fellowship administered by the Krell Institute.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1013773','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1013773"><span>ESPC Coupled Global Prediction System</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><span class="hlt">numerical</span> transport algorithms. Adapted from WRF , a Semi-<span class="hlt">Lagrangian</span> advection <span class="hlt">scheme</span> is being implemented in the vertical in NAVGEM to process the...used in the sedimentation of cloud species, especially in the WRF research-community model for all cloud microphysics modules. We have started to</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012MNRAS.426.3112H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012MNRAS.426.3112H"><span>Gas stripping and mixing in galaxy clusters: a <span class="hlt">numerical</span> comparison study</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Heß, Steffen; Springel, Volker</p> <p>2012-11-01</p> <p>The ambient hot intrahalo gas in clusters of galaxies is constantly fed and stirred by infalling galaxies, a process that can be studied in detail with cosmological hydrodynamical simulations. However, different <span class="hlt">numerical</span> methods yield discrepant predictions for crucial hydrodynamical processes, leading for example to different entropy profiles in clusters of galaxies. In particular, the widely used <span class="hlt">Lagrangian</span> smoothed particle hydrodynamics (SPH) <span class="hlt">scheme</span> is suspected to strongly damp fluid instabilities and turbulence, which are both crucial to establish the thermodynamic structure of clusters. In this study, we test to which extent our recently developed Voronoi particle hydrodynamics (VPH) <span class="hlt">scheme</span> yields different results for the stripping of gas out of infalling galaxies and for the bulk gas properties of cluster. We consider both the evolution of isolated galaxy models that are exposed to a stream of intracluster medium or are dropped into cluster models, as well as non-radiative cosmological simulations of cluster formation. We also compare our particle-based method with results obtained with a fundamentally different discretization approach as implemented in the moving-mesh code AREPO. We find that VPH leads to noticeably faster stripping of gas out of galaxies than SPH, in better agreement with the mesh-code than with SPH. We show that despite the fact that VPH in its present form is not as accurate as the moving mesh code in our investigated cases, its improved accuracy of gradient estimates makes VPH an attractive alternative to SPH.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JTST...25..451J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JTST...25..451J"><span><span class="hlt">Numerical</span> Modeling of Suspension HVOF Spray</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jadidi, M.; Moghtadernejad, S.; Dolatabadi, A.</p> <p>2016-02-01</p> <p>A three-dimensional two-way coupled Eulerian-<span class="hlt">Lagrangian</span> <span class="hlt">scheme</span> is used to simulate suspension high-velocity oxy-fuel spraying process. The mass, momentum, energy, and species equations are solved together with the realizable k-ɛ turbulence model to simulate the gas phase. Suspension is assumed to be a mixture of solid particles [mullite powder (3Al2O3·2SiO2)], ethanol, and ethylene glycol. The process involves premixed combustion of oxygen-propylene, and non-premixed combustion of oxygen-ethanol and oxygen-ethylene glycol. One-step global reaction is used for each mentioned reaction together with eddy dissipation model to compute the reaction rate. To simulate the droplet breakup, Taylor Analogy Breakup model is applied. After the completion of droplet breakup, and solvent evaporation/combustion, the solid suspended particles are tracked through the domain to determine the characteristics of the coating particles. <span class="hlt">Numerical</span> simulations are validated against the experimental results in the literature for the same operating conditions. Seven or possibly eight shock diamonds are captured outside the nozzle. In addition, a good agreement between the predicted particle temperature, velocity, and diameter, and the experiment is obtained. It is shown that as the standoff distance increases, the particle temperature and velocity reduce. Furthermore, a correlation is proposed to determine the spray cross-sectional diameter and estimate the particle trajectories as a function of standoff distance.</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('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4454442','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4454442"><span>Central Upwind <span class="hlt">Scheme</span> for a Compressible Two-Phase Flow Model</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Ahmed, Munshoor; Saleem, M. Rehan; Zia, Saqib; Qamar, Shamsul</p> <p>2015-01-01</p> <p>In this article, a compressible two-phase reduced five-equation flow model is <span class="hlt">numerically</span> investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the <span class="hlt">numerical</span> approximation of the model a high resolution central upwind <span class="hlt">scheme</span> is implemented. This is a non-oscillatory upwind biased finite volume <span class="hlt">scheme</span> which does not require a Riemann solver at each time step. Few <span class="hlt">numerical</span> case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central <span class="hlt">schemes</span>. It was found that central upwind <span class="hlt">scheme</span> produces comparable results to the KFVS <span class="hlt">scheme</span>. PMID:26039242</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26039242','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26039242"><span>Central upwind <span class="hlt">scheme</span> for a compressible two-phase flow model.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul</p> <p>2015-01-01</p> <p>In this article, a compressible two-phase reduced five-equation flow model is <span class="hlt">numerically</span> investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the <span class="hlt">numerical</span> approximation of the model a high resolution central upwind <span class="hlt">scheme</span> is implemented. This is a non-oscillatory upwind biased finite volume <span class="hlt">scheme</span> which does not require a Riemann solver at each time step. Few <span class="hlt">numerical</span> case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central <span class="hlt">schemes</span>. It was found that central upwind <span class="hlt">scheme</span> produces comparable results to the KFVS <span class="hlt">scheme</span>.</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://adsabs.harvard.edu/abs/2018JCoPh.352..637K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.352..637K"><span>Corrigendum to ;<span class="hlt">Numerical</span> dissipation control in high order shock-capturing <span class="hlt">schemes</span> for LES of low speed flows; [J. Comput. Phys. 307 (2016) 189-202</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kotov, D. V.; Yee, H. C.; Wray, A. A.; Sjögreen, Björn; Kritsuk, A. G.</p> <p>2018-01-01</p> <p>The authors regret for the typographic errors that were made in equation (4) and missing phrase after equation (4) in the article "<span class="hlt">Numerical</span> dissipation control in high order shock-capturing <span class="hlt">schemes</span> for LES of low speed flows" [J. Comput. Phys. 307 (2016) 189-202].</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.350..550A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.350..550A"><span>High-order asynchrony-tolerant finite difference <span class="hlt">schemes</span> for partial differential equations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Aditya, Konduri; Donzis, Diego A.</p> <p>2017-12-01</p> <p>Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference <span class="hlt">schemes</span> to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard <span class="hlt">schemes</span> can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference <span class="hlt">schemes</span> of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these <span class="hlt">schemes</span> and discuss their effect on <span class="hlt">numerical</span> and computational performance. We provide a simple classification of <span class="hlt">schemes</span> based on the stencil and derive <span class="hlt">schemes</span> that are representative of different classes. Their <span class="hlt">numerical</span> error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from <span class="hlt">numerical</span> experiments are used to validate the performance of the <span class="hlt">schemes</span>.</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('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://hdl.handle.net/2060/19880018124','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19880018124"><span><span class="hlt">Numerical</span> methods for incompressible viscous flows with engineering applications</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Rose, M. E.; Ash, R. L.</p> <p>1988-01-01</p> <p>A <span class="hlt">numerical</span> <span class="hlt">scheme</span> has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the <span class="hlt">numerical</span> approximation <span class="hlt">schemes</span> for the divergence and curl of the velocity vector fields and the development of compact <span class="hlt">schemes</span> for handling boundary and initial boundary value problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19830014814','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19830014814"><span>Implicit Total Variation Diminishing (TVD) <span class="hlt">schemes</span> for steady-state calculations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Yee, H. C.; Warming, R. F.; Harten, A.</p> <p>1983-01-01</p> <p>The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) <span class="hlt">scheme</span> to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate <span class="hlt">schemes</span> developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This <span class="hlt">scheme</span> is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. <span class="hlt">Numerical</span> experiments show that this <span class="hlt">scheme</span> not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit <span class="hlt">scheme</span> for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some <span class="hlt">numerical</span> computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new <span class="hlt">scheme</span>.</p> </li> <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> </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('http://adsabs.harvard.edu/abs/2009AIPC.1159..276K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009AIPC.1159..276K"><span>A New <span class="hlt">Lagrangian</span> Relaxation Method Considering Previous Hour Scheduling for Unit Commitment Problem</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Khorasani, H.; Rashidinejad, M.; Purakbari-Kasmaie, M.; Abdollahi, A.</p> <p>2009-08-01</p> <p>Generation scheduling is a crucial challenge in power systems especially under new environment of liberalization of electricity industry. A new <span class="hlt">Lagrangian</span> relaxation method for unit commitment (UC) has been presented for solving generation scheduling problem. This paper focuses on the economical aspect of UC problem, while the previous hour scheduling as a very important issue is studied. In this paper generation scheduling of present hour has been conducted by considering the previous hour scheduling. The impacts of hot/cold start-up cost have been taken in to account in this paper. Case studies and <span class="hlt">numerical</span> analysis presents significant outcomes while it demonstrates the effectiveness of the proposed method.</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/2012PhDT........54M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012PhDT........54M"><span>Estimation of liquefaction-induced lateral spread from <span class="hlt">numerical</span> modeling and its application</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Meng, Xianhong</p> <p></p> <p>A noncoupled <span class="hlt">numerical</span> procedure was developed using a <span class="hlt">scheme</span> of pore water generation that causes shear modulus degradation and shear strength degradation resulting from earthquake cyclic motion. The designed Fast <span class="hlt">Lagrangian</span> Analysis of Continua (FLAC) model procedure was tested using the liquefaction-induced lateral spread and ground response for Wildlife and Kobe sites. Sixteen well-documented case histories of lateral spread were reviewed and modeled using the modeling procedure. The dynamic residual strength ratios were back-calculated by matching the predicted displacement with the measured lateral spread, or with the displacement predicted by the Yound et al. model. Statistical analysis on the modeling results and soil properties show that most significant parameters governing the residual strength of the liquefied soil are the SPT blow count, fine content and soil particle size of the lateral spread layer. A regression equation was developed to express the residual strength values with these soil properties. Overall, this research demonstrated that a calibrated <span class="hlt">numerical</span> model can predict the first order effectiveness of liquefaction-induced lateral spread using relatively simple parameters obtained from routine geotechnical investigation. In addition, the model can be used to plan a soil improvement program for cases where liquefaction remediation is needed. This allows the model to be used for design purposes at bridge approaches structured on liquefiable materials.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GMD.....9..749B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GMD.....9..749B"><span>Adjoint of the global Eulerian-<span class="hlt">Lagrangian</span> coupled atmospheric transport model (A-GELCA v1.0): development and validation</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 A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander</p> <p>2016-02-01</p> <p>We present the development of the Adjoint of the Global Eulerian-<span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">Lagrangian</span> 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 <span class="hlt">numerical</span> 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 <span class="hlt">Lagrangian</span> backward trajectory formulation. A-GELCA will be incorporated</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</span>-Eulerian 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</span>-Eulerian 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 <span class="hlt">numerical</span> 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</span>-Eulerian 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://hdl.handle.net/2060/20020045218','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20020045218"><span>Improved Boundary Conditions for Cell-centered Difference <span class="hlt">Schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>VanderWijngaart, Rob F.; Klopfer, Goetz H.; Chancellor, Marisa K. (Technical Monitor)</p> <p>1997-01-01</p> <p>Cell-centered finite-volume (CCFV) <span class="hlt">schemes</span> have certain attractive properties for the solution of the equations governing compressible fluid flow. Among others, they provide a natural vehicle for specifying flux conditions at the boundaries of the physical domain. Unfortunately, they lead to slow convergence for <span class="hlt">numerical</span> programs utilizing them. In this report a method for investigating and improving the convergence of CCFV <span class="hlt">schemes</span> is presented, which focuses on the effect of the <span class="hlt">numerical</span> boundary conditions. The key to the method is the computation of the spectral radius of the iteration matrix of the entire demoralized system of equations, not just of the interior point <span class="hlt">scheme</span> or the boundary conditions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870014712','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870014712"><span>Upwind and symmetric shock-capturing <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Yee, H. C.</p> <p>1987-01-01</p> <p>The development of <span class="hlt">numerical</span> methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis is on the construction of the basic nonlinear scalar second-order <span class="hlt">schemes</span> and the methods of extending these nonlinear scalar <span class="hlt">schemes</span> to nonlinear systems via the extact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows is discussed. The performance of some of these <span class="hlt">schemes</span> is illustrated by <span class="hlt">numerical</span> examples for one-, two- and three-dimensional gas dynamics problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/5594222-some-results-numerical-methods-hyperbolic-conservation-laws','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/5594222-some-results-numerical-methods-hyperbolic-conservation-laws"><span>Some results on <span class="hlt">numerical</span> methods for hyperbolic conservation laws</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>Yang Huanan.</p> <p>1989-01-01</p> <p>This dissertation contains some results on the <span class="hlt">numerical</span> solutions of hyperbolic conservation laws. (1) The author introduced an artificial compression method as a correction to the basic ENO <span class="hlt">schemes</span>. The method successfully prevents contact discontinuities from being smeared. This is achieved by increasing the slopes of the ENO reconstructions in such a way that the essentially non-oscillatory property of the <span class="hlt">schemes</span> is kept. He analyzes the non-oscillatory property of the new artificial compression method by applying it to the UNO <span class="hlt">scheme</span> which is a second order accurate ENO <span class="hlt">scheme</span>, and proves that the resulting <span class="hlt">scheme</span> is indeed non-oscillatory. Extensive 1-Dmore » <span class="hlt">numerical</span> results and some preliminary 2-D ones are provided to show the strong performance of the method. (2) He combines the ENO <span class="hlt">schemes</span> and the centered difference <span class="hlt">schemes</span> into self-adjusting hybrid <span class="hlt">schemes</span> which will be called the localized ENO <span class="hlt">schemes</span>. At or near the jumps, he uses the ENO <span class="hlt">schemes</span> with the field by field decompositions, otherwise he simply uses the centered difference <span class="hlt">schemes</span> without the field by field decompositions. The method involves a new interpolation analysis. In the <span class="hlt">numerical</span> experiments on several standard test problems, the quality of the <span class="hlt">numerical</span> results of this method is close to that of the pure ENO results. The localized ENO <span class="hlt">schemes</span> can be equipped with the above artificial compression method. In this way, he dramatically improves the resolutions of the contact discontinuities at very little additional costs. (3) He introduces a space-time mesh refinement method for time dependent problems.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22608262-crank-nicholson-difference-scheme-stochastic-parabolic-equation-dependent-operator-coefficient','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22608262-crank-nicholson-difference-scheme-stochastic-parabolic-equation-dependent-operator-coefficient"><span>Crank-Nicholson difference <span class="hlt">scheme</span> for a stochastic parabolic equation with a dependent operator coefficient</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>Ashyralyev, Allaberen; Okur, Ulker</p> <p></p> <p>In the present paper, the Crank-Nicolson difference <span class="hlt">scheme</span> for the <span class="hlt">numerical</span> solution of the stochastic parabolic equation with the dependent operator coefficient is considered. Theorem on convergence estimates for the solution of this difference <span class="hlt">scheme</span> is established. In applications, convergence estimates for the solution of difference <span class="hlt">schemes</span> for the <span class="hlt">numerical</span> solution of three mixed problems for parabolic equations are obtained. The <span class="hlt">numerical</span> results are given.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018BoLMe.tmp...12W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018BoLMe.tmp...12W"><span>A Backward-<span class="hlt">Lagrangian</span>-Stochastic Footprint Model for the Urban Environment</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wang, Chenghao; Wang, Zhi-Hua; Yang, Jiachuan; Li, Qi</p> <p>2018-02-01</p> <p>Built terrains, with their complexity in morphology, high heterogeneity, and anthropogenic impact, impose substantial challenges in Earth-system modelling. In particular, estimation of the source areas and footprints of atmospheric measurements in cities requires realistic representation of the landscape characteristics and flow physics in urban areas, but has hitherto been heavily reliant on large-eddy simulations. In this study, we developed physical parametrization <span class="hlt">schemes</span> for estimating urban footprints based on the backward-<span class="hlt">Lagrangian</span>-stochastic algorithm, with the built environment represented by street canyons. The vertical profile of mean streamwise velocity is parametrized for the urban canopy and boundary layer. Flux footprints estimated by the proposed model show reasonable agreement with analytical predictions over flat surfaces without roughness elements, and with experimental observations over sparse plant canopies. Furthermore, comparisons of canyon flow and turbulence profiles and the subsequent footprints were made between the proposed model and large-eddy simulation data. The results suggest that the parametrized canyon wind and turbulence statistics, based on the simple similarity theory used, need to be further improved to yield more realistic urban footprint modelling.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22667253-second-order-divergence-constrained-multidimensional-numerical-scheme-relativistic-two-fluid-electrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22667253-second-order-divergence-constrained-multidimensional-numerical-scheme-relativistic-two-fluid-electrodynamics"><span>A SECOND-ORDER DIVERGENCE-CONSTRAINED MULTIDIMENSIONAL <span class="hlt">NUMERICAL</span> <span class="hlt">SCHEME</span> FOR RELATIVISTIC TWO-FLUID ELECTRODYNAMICS</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>Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp</p> <p></p> <p>A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell’s equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron–positron or an electron–proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A <span class="hlt">numerical</span> <span class="hlt">scheme</span> based on HLL (Harten–Lax–Van Leer) Riemann solver is proposed that exactlymore » preserves the two divergence constraints for Maxwell’s equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small scales. This shows that the RTFED model is a promising tool for high energy astrophysics application.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014EGUGA..16..915S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..16..915S"><span><span class="hlt">Numerical</span> simulation of the debris flow dynamics with an upwind <span class="hlt">scheme</span> and specific friction treatment</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sánchez Burillo, Guillermo; Beguería, Santiago; Latorre, Borja; Burguete, Javier</p> <p>2014-05-01</p> <p>Debris flows, snow and rock avalanches, mud and earth flows are often modeled by means of a particular realization of the so called shallow water equations (SWE). Indeed, a number of simulation models have been already developed [1], [2], [3], [4], [5], [6], [7]. Debris flow equations differ from shallow water equations in two main aspects. These are (a) strong bed gradient and (b) rheology friction terms that differ from the traditional SWE. A systematic analysis of the <span class="hlt">numerical</span> solution of the hyperbolic system of equations rising from the shallow water equations with different rheological laws has not been done. Despite great efforts have been done to deal with friction expressions common in hydraulics (such as Manning friction), landslide rheologies are characterized by more complicated expressions that may deal to unphysical solutions if not treated carefully. In this work, a software that solves the time evolution of sliding masses over complex bed configurations is presented. The set of non- linear equations is treated by means of a first order upwind explicit <span class="hlt">scheme</span>, and the friction contribution to the dynamics is treated with a suited <span class="hlt">numerical</span> <span class="hlt">scheme</span> [8]. In addition, the software incorporates various rheological models to accommodate for different flow types, such as the Voellmy frictional model [9] for rock and debris avalanches, or the Herschley-Bulkley model for debris and mud flows. The aim of this contribution is to release this code as a free, open source tool for the simulation of mass movements, and to encourage the scientific community to make use of it. The code uses as input data the friction coefficients and two input files: the topography of the bed and the initial (pre-failure) position of the sliding mass. In addition, another file with the final (post-event) position of the sliding mass, if desired, can be introduced to be compared with the simulation obtained result. If the deposited mass is given, an error estimation is computed by</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19890054432&hterms=1956&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3D%253F%253F%253F%253F%253F%253F%253F%253F%253F%253F%2B%253F.%2B%253F.%2B%253F%253F%253F%253F%253F%253F%253F%253F%2B%253F%253F%253F%253F%253F%253F%253F%253F%253F%253F.%2B%253F.%2B1956','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19890054432&hterms=1956&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3D%253F%253F%253F%253F%253F%253F%253F%253F%253F%253F%2B%253F.%2B%253F.%2B%253F%253F%253F%253F%253F%253F%253F%253F%2B%253F%253F%253F%253F%253F%253F%253F%253F%253F%253F.%2B%253F.%2B1956"><span>Assessment of <span class="hlt">numerical</span> techniques for unsteady flow calculations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hsieh, Kwang-Chung</p> <p>1989-01-01</p> <p>The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, <span class="hlt">numerical</span> approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several <span class="hlt">numerical</span> <span class="hlt">schemes</span> for unsteady flow calculations. In the present study, Fourier error analysis is performed for various <span class="hlt">numerical</span> <span class="hlt">schemes</span> based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between <span class="hlt">numerical</span> and exact solutions, although second-order upwind <span class="hlt">scheme</span> captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference <span class="hlt">scheme</span>. Among various <span class="hlt">numerical</span> approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JHyDy..30...49K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JHyDy..30...49K"><span>Towards development of enhanced fully-<span class="hlt">Lagrangian</span> mesh-free computational methods for fluid-structure interaction</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Khayyer, Abbas; Gotoh, Hitoshi; Falahaty, Hosein; Shimizu, Yuma</p> <p>2018-02-01</p> <p>Simulation of incompressible fluid flow-elastic structure interactions is targeted by using fully-<span class="hlt">Lagrangian</span> mesh-free computational methods. A projection-based fluid model (moving particle semi-implicit (MPS)) is coupled with either a Newtonian or a Hamiltonian <span class="hlt">Lagrangian</span> structure model (MPS or HMPS) in a mathematically-physically consistent manner. The fluid model is founded on the solution of Navier-Stokes and continuity equations. The structure models are configured either in the framework of Newtonian mechanics on the basis of conservation of linear and angular momenta, or Hamiltonian mechanics on the basis of variational principle for incompressible elastodynamics. A set of enhanced <span class="hlt">schemes</span> are incorporated for projection-based fluid model (Enhanced MPS), thus, the developed coupled solvers for fluid structure interaction (FSI) are referred to as Enhanced MPS-MPS and Enhanced MPS-HMPS. Besides, two smoothed particle hydrodynamics (SPH)-based FSI solvers, being developed by the authors, are considered and their potential applicability and comparable performance are briefly discussed in comparison with MPS-based FSI solvers. The SPH-based FSI solvers are established through coupling of projection-based incompressible SPH (ISPH) fluid model and SPH-based Newtonian/Hamiltonian structure models, leading to Enhanced ISPH-SPH and Enhanced ISPH-HSPH. A comparative study is carried out on the performances of the FSI solvers through a set of benchmark tests, including hydrostatic water column on an elastic plate, high speed impact of an elastic aluminum beam, hydroelastic slamming of a marine panel and dam break with elastic gate.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930013937','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930013937"><span>Time-stable boundary conditions for finite-difference <span class="hlt">schemes</span> solving hyperbolic systems: Methodology and application to high-order compact <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul</p> <p>1993-01-01</p> <p>We present a systematic method for constructing boundary conditions (<span class="hlt">numerical</span> and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference <span class="hlt">schemes</span> for hyperbolic systems. First, a roper summation-by-parts formula is found for the approximate derivative. A 'simultaneous approximation term' (SAT) is then introduced to treat the boundary conditions. This procedure leads to time-stable <span class="hlt">schemes</span> even in the system case. An explicit construction of the fourth-order compact case is given. <span class="hlt">Numerical</span> studies are presented to verify the efficacy of the approach.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1434487-augmented-lagrangian-filter-method-real-time-embedded-optimization','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1434487-augmented-lagrangian-filter-method-real-time-embedded-optimization"><span>An Augmented <span class="hlt">Lagrangian</span> Filter Method for Real-Time Embedded Optimization</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Chiang, Nai -Yuan; Huang, Rui; Zavala, Victor M.</p> <p>2017-04-17</p> <p>We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented <span class="hlt">Lagrangian</span> function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal–dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and airmore » conditioning system. Our <span class="hlt">numerical</span> tests are performed on a standard processor and on an embedded platform. Lastly, we demonstrate that the approach reduces solution times by a factor of over 1000.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1434487','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1434487"><span>An Augmented <span class="hlt">Lagrangian</span> Filter Method for Real-Time Embedded Optimization</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>Chiang, Nai -Yuan; Huang, Rui; Zavala, Victor M.</p> <p></p> <p>We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented <span class="hlt">Lagrangian</span> function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal–dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and airmore » conditioning system. Our <span class="hlt">numerical</span> tests are performed on a standard processor and on an embedded platform. Lastly, we demonstrate that the approach reduces solution times by a factor of over 1000.« less</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('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/2016MNRAS.460.4382F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MNRAS.460.4382F"><span>Testing hydrodynamics <span class="hlt">schemes</span> in galaxy disc simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Few, C. G.; Dobbs, C.; Pettitt, A.; Konstandin, L.</p> <p>2016-08-01</p> <p>We examine how three fundamentally different <span class="hlt">numerical</span> hydrodynamics codes follow the evolution of an isothermal galactic disc with an external spiral potential. We compare an adaptive mesh refinement code (RAMSES), a smoothed particle hydrodynamics code (SPHNG), and a volume-discretized mesh-less code (GIZMO). Using standard refinement criteria, we find that RAMSES produces a disc that is less vertically concentrated and does not reach such high densities as the SPHNG or GIZMO runs. The gas surface density in the spiral arms increases at a lower rate for the RAMSES simulations compared to the other codes. There is also a greater degree of substructure in the SPHNG and GIZMO runs and secondary spiral arms are more pronounced. By resolving the Jeans length with a greater number of grid cells, we achieve more similar results to the <span class="hlt">Lagrangian</span> codes used in this study. Other alterations to the refinement <span class="hlt">scheme</span> (adding extra levels of refinement and refining based on local density gradients) are less successful in reducing the disparity between RAMSES and SPHNG/GIZMO. Although more similar, SPHNG displays different density distributions and vertical mass profiles to all modes of GIZMO (including the smoothed particle hydrodynamics version). This suggests differences also arise which are not intrinsic to the particular method but rather due to its implementation. The discrepancies between codes (in particular, the densities reached in the spiral arms) could potentially result in differences in the locations and time-scales for gravitational collapse, and therefore impact star formation activity in more complex galaxy disc simulations.</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/2017APS..DFDA32008C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDA32008C"><span><span class="hlt">Lagrangian</span> Particle Tracking in a Discontinuous Galerkin Method for Hypersonic Reentry Flows in Dusty Environments</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ching, Eric; Lv, Yu; Ihme, Matthias</p> <p>2017-11-01</p> <p>Recent interest in human-scale missions to Mars has sparked active research into high-fidelity simulations of reentry flows. A key feature of the Mars atmosphere is the high levels of suspended dust particles, which can not only enhance erosion of thermal protection systems but also transfer energy and momentum to the shock layer, increasing surface heat fluxes. Second-order finite-volume <span class="hlt">schemes</span> are typically employed for hypersonic flow simulations, but such <span class="hlt">schemes</span> suffer from a number of limitations. An attractive alternative is discontinuous Galerkin methods, which benefit from arbitrarily high spatial order of accuracy, geometric flexibility, and other advantages. As such, a <span class="hlt">Lagrangian</span> particle method is developed in a discontinuous Galerkin framework to enable the computation of particle-laden hypersonic flows. Two-way coupling between the carrier and disperse phases is considered, and an efficient particle search algorithm compatible with unstructured curved meshes is proposed. In addition, variable thermodynamic properties are considered to accommodate high-temperature gases. The performance of the particle method is demonstrated in several test cases, with focus on the accurate prediction of particle trajectories and heating augmentation. Financial support from a Stanford Graduate Fellowship and the NASA Early Career Faculty program are gratefully acknowledged.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900009889','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900009889"><span><span class="hlt">Numerical</span> solution of 3D Navier-Stokes equations with upwind implicit <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Marx, Yves P.</p> <p>1990-01-01</p> <p>An upwind MUSCL type implicit <span class="hlt">scheme</span> for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions <span class="hlt">schemes</span> on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind <span class="hlt">schemes</span>. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28179854','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28179854"><span><span class="hlt">Numerical</span> Hydrodynamics in General Relativity.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Font, José A</p> <p>2000-01-01</p> <p>The current status of <span class="hlt">numerical</span> solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced <span class="hlt">numerical</span> methods. A representative sample of available <span class="hlt">numerical</span> <span class="hlt">schemes</span> is discussed and particular emphasis is paid to solution procedures based on <span class="hlt">schemes</span> exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented. Supplementary material is available for this article at 10.12942/lrr-2000-2.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19810058896&hterms=levels+law&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DA%2Blevels%2Blaw','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19810058896&hterms=levels+law&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3DA%2Blevels%2Blaw"><span>On a fourth order accurate implicit finite difference <span class="hlt">scheme</span> for hyperbolic conservation laws. II - Five-point <span class="hlt">schemes</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Harten, A.; Tal-Ezer, H.</p> <p>1981-01-01</p> <p>This paper presents a family of two-level five-point implicit <span class="hlt">schemes</span> for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson <span class="hlt">scheme</span> to fourth order accuracy (4-4) in both time and space. These 4-4 <span class="hlt">schemes</span> are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit <span class="hlt">schemes</span>. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit <span class="hlt">schemes</span> brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. <span class="hlt">Numerical</span> results are presented to illustrate some properties of the proposed <span class="hlt">scheme</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19870066401&hterms=1593&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3D%2526%25231593','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19870066401&hterms=1593&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3D%2526%25231593"><span>CONDIF - A modified central-difference <span class="hlt">scheme</span> for convective flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Runchal, Akshai K.</p> <p>1987-01-01</p> <p>The paper presents a method, called CONDIF, which modifies the CDS (central-difference <span class="hlt">scheme</span>) by introducing a controlled amount of <span class="hlt">numerical</span> diffusion based on the local gradients. The <span class="hlt">numerical</span> diffusion can be adjusted to be negligibly low for most problems. CONDIF results are significantly more accurate than those obtained from the hybrid <span class="hlt">scheme</span> when the Peclet number is very high and the flow is at large angles to the grid.</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–Eulerian (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 <span class="hlt">scheme</span>. 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–Eulerian (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 <span class="hlt">scheme</span>. 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/2012PhyA..391.1009L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012PhyA..391.1009L"><span>A practically unconditionally gradient stable <span class="hlt">scheme</span> for the N-component Cahn-Hilliard system</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lee, Hyun Geun; Choi, Jeong-Whan; Kim, Junseok</p> <p>2012-02-01</p> <p>We present a practically unconditionally gradient stable conservative nonlinear <span class="hlt">numerical</span> <span class="hlt">scheme</span> for the N-component Cahn-Hilliard system modeling the phase separation of an N-component mixture. The <span class="hlt">scheme</span> is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The <span class="hlt">scheme</span> allows us to convert the N-component Cahn-Hilliard system into a system of N-1 binary Cahn-Hilliard equations and significantly reduces the required computer memory and CPU time. We observe that our <span class="hlt">numerical</span> solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed <span class="hlt">scheme</span> with various <span class="hlt">numerical</span> experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AIPC.1910c0004F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AIPC.1910c0004F"><span>Fourth order <span class="hlt">scheme</span> for wavelet based solution of Black-Scholes equation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Finěk, Václav</p> <p>2017-12-01</p> <p>The present paper is devoted to the <span class="hlt">numerical</span> solution of the Black-Scholes equation for pricing European options. We apply the Crank-Nicolson <span class="hlt">scheme</span> with Richardson extrapolation for time discretization and Hermite cubic spline wavelets with four vanishing moments for space discretization. This <span class="hlt">scheme</span> is the fourth order accurate both in time and in space. Computational results indicate that the Crank-Nicolson <span class="hlt">scheme</span> with Richardson extrapolation significantly decreases the amount of computational work. We also <span class="hlt">numerically</span> show that optimal convergence rate for the used <span class="hlt">scheme</span> is obtained without using startup procedure despite the data irregularities in the model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhDT........44R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhDT........44R"><span><span class="hlt">Lagrangian</span> Visualization and Real-Time Identification of the Vortex Shedding Time in the Wake of a Circular Cylinder</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rockwood, Matthew P.</p> <p></p> <p> on a circular cylinder in crossflow. The acceleration of the <span class="hlt">Lagrangian</span> saddle occurs simultaneously with a maximum in lift in both <span class="hlt">numerical</span> cases, and with a minimum in the static pressure at a location slightly upstream of the mean separation location in the <span class="hlt">numerical</span> cases, as well as the experimental data at a Reynolds number of 19,000. This allows the von Karman vortex shedding time, determined objectively by the acceleration of the <span class="hlt">Lagrangian</span> saddle away from the circular cylinder, to be detected by a minimum in the static pressure at one location on the cylinder, a quantity that can be measured in real-time using available pressure sensors. These results can be used to place sensors in optimal locations on bluff bodies to inform closed-loop flow control algorithms of the timing of von Karman vortex shedding.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/956372','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/956372"><span>A pressure relaxation closure model for one-dimensional, two-material <span class="hlt">Lagrangian</span> hydrodynamics based on the Riemann problem</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>Kamm, James R; Shashkov, Mikhail J</p> <p>2009-01-01</p> <p>Despite decades of development, <span class="hlt">Lagrangian</span> hydrodynamics of strengthfree materials presents <span class="hlt">numerous</span> open issues, even in one dimension. We focus on the problem of closing a system of equations for a two-material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider the case in which the change in heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast asmore » four equations in four unknowns, comprised of the updated values of the specific internal energy and the specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which the updated values of the sub-cell, relaxing-toward-equilibrium constituent pressures are related to a local Riemann problem through an optimization principle. This approach couples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the framework of a standard predictor-corrector time integration <span class="hlt">scheme</span>. We evaluate our model using idealized, two material problems using either ideal-gas or stiffened-gas equations of state and compare these results to those computed with the method of Tipton and with corresponding pure-material calculations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27839859','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27839859"><span>Comprehensive computational model for combining fluid hydrodynamics, light transport and biomass growth in a Taylor vortex algal photobioreactor: <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>Gao, Xi; Kong, Bo; Vigil, R Dennis</p> <p>2017-01-01</p> <p>A comprehensive quantitative model incorporating the effects of fluid flow patterns, light distribution, and algal growth kinetics on biomass growth rate is developed in order to predict the performance of a Taylor vortex algal photobioreactor for culturing Chlorella vulgaris. A commonly used <span class="hlt">Lagrangian</span> strategy for coupling the various factors influencing algal growth was employed whereby results from computational fluid dynamics and radiation transport simulations were used to compute <span class="hlt">numerous</span> microorganism light exposure histories, and this information in turn was used to estimate the global biomass specific growth rate. The simulations provide good quantitative agreement with experimental data and correctly predict the trend in reactor performance as a key reactor operating parameter is varied (inner cylinder rotation speed). However, biomass growth curves are consistently over-predicted and potential causes for these over-predictions and drawbacks of the <span class="hlt">Lagrangian</span> approach are addressed. Copyright © 2016 Elsevier Ltd. All rights reserved.</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 codes. The Programmers Manual is intended for the model user who needs to modify code 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/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('http://adsabs.harvard.edu/abs/2017AGUFMDI43A0346H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFMDI43A0346H"><span>A new hybrid <span class="hlt">numerical</span> <span class="hlt">scheme</span> for simulating fault ruptures with near-fault bulk inhomogeneities</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hajarolasvadi, S.; Elbanna, A. E.</p> <p>2017-12-01</p> <p>The Finite Difference (FD) and Boundary Integral (BI) Method have been extensively used to model spontaneously propagating shear cracks, which can serve as a useful idealization of natural earthquakes. While FD suffers from artificial dispersion and <span class="hlt">numerical</span> dissipation and has a large computational cost as it requires the discretization of the whole volume of interest, it can be applied to a wider range of problems including ones with bulk nonlinearities and heterogeneities. On the other hand, in the BI method, the <span class="hlt">numerical</span> consideration is confined to the crack path only, with the elastodynamic response of the bulk expressed in terms of integral relations between displacement discontinuities and tractions along the crack. Therefore, this method - its spectral boundary integral (SBI) formulation in particular - is much faster and more computationally efficient than other bulk methods such as FD. However, its application is restricted to linear elastic bulk and planar faults. This work proposes a novel hybrid <span class="hlt">numerical</span> <span class="hlt">scheme</span> that combines FD and the SBI to enable treating fault zone nonlinearities and heterogeneities with unprecedented resolution and in a more computationally efficient way. The main idea of the method is to enclose the inhomgeneities in a virtual strip that is introduced for computational purposes only. This strip is then discretized using a volume-based <span class="hlt">numerical</span> method, chosen here to be the finite difference method while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces needs to be carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We demonstrate the validity of the</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://hdl.handle.net/2060/20000121222','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000121222"><span>An Energy Decaying <span class="hlt">Scheme</span> for Nonlinear Dynamics of Shells</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)</p> <p>2000-01-01</p> <p>A novel integration <span class="hlt">scheme</span> for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the <span class="hlt">scheme</span> features tunable high frequency <span class="hlt">numerical</span> damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, <span class="hlt">scheme</span> is illustrated with the help of <span class="hlt">numerical</span> examples.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/21167766-spectral-lagrangian-methods-collisional-models-non-equilibrium-statistical-states','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/21167766-spectral-lagrangian-methods-collisional-models-non-equilibrium-statistical-states"><span>Spectral-<span class="hlt">Lagrangian</span> methods for collisional models of non-equilibrium statistical states</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>Gamba, Irene M.; Tharkabhushanam, Sri Harsha</p> <p></p> <p>We propose a new spectral <span class="hlt">Lagrangian</span> based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d-dimensions for variable hard sphere (VHS) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computation is reduced to a separate integral over the unit sphere S{sup d-1}. The conservation of moments is enforced by <span class="hlt">Lagrangian</span> constraints. The resulting <span class="hlt">scheme</span>, implemented in free space, is very versatile and adjusts in a very simple manner to several cases that involve energy dissipation due to local micro-reversibilitymore » (inelastic interactions) or elastic models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the <span class="hlt">numerical</span> distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403-417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL: (<http://arxiv.org/abs/math-ph/0608035>)]. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods [T.V. Noije, M</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://adsabs.harvard.edu/abs/2015AGUFM.H21A1348C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFM.H21A1348C"><span>A new approach to enforce element-wise mass/species balance using the augmented <span class="hlt">Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chang, J.; Nakshatrala, K.</p> <p>2015-12-01</p> <p>The least-squares finite element method (LSFEM) is one of many ways in which one can discretize and express a set of first ordered partial differential equations as a mixed formulation. However, the standard LSFEM is not locally conservative by design. The absence of this physical property can have serious implications in the <span class="hlt">numerical</span> simulation of subsurface flow and transport. Two commonly employed ways to circumvent this issue is through the Lagrange multiplier method, which explicitly satisfies the element-wise divergence by introducing new unknowns, or through appending a penalty factor to the continuity constraint, which reduces the violation in the mass balance. However, these methodologies have some well-known drawbacks. Herein, we propose a new approach to improve the local balance of species/mass balance. The approach augments constraints to a least-square function by a novel mathematical construction of the local species/mass balance, which is different from the conventional ways. The resulting constrained optimization problem is solved using the augmented <span class="hlt">Lagrangian</span>, which corrects the balance errors in an iterative fashion. The advantages of this methodology are that the problem size is not increased (thus preserving the symmetry and positive definite-ness) and that one need not provide an accurate guess for the initial penalty to reach a prescribed mass balance tolerance. We derive the least-squares weighting needed to ensure accurate solutions. We also demonstrate the robustness of the weighted LSFEM coupled with the augmented <span class="hlt">Lagrangian</span> by solving large-scale heterogenous and variably saturated flow through porous media problems. The performance of the iterative solvers with respect to various user-defined augmented <span class="hlt">Lagrangian</span> parameters will be documented.</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. Their policies may differ from this site.</div> </div><!-- container --> <footer><a id="backToTop" href="#top"> </a><nav><a id="backToTop" href="#top"> </a><ul class="links"><a id="backToTop" href="#top"> </a><li><a id="backToTop" href="#top"></a><a href="/sitemap.html">Site Map</a></li> <li><a href="/members/index.html">Members Only</a></li> <li><a href="/website-policies.html">Website Policies</a></li> <li><a href="https://doe.responsibledisclosure.com/hc/en-us" target="_blank">Vulnerability Disclosure Program</a></li> <li><a href="/contact.html">Contact Us</a></li> </ul> <div class="small">Science.gov is maintained by the U.S. Department of Energy's <a href="https://www.osti.gov/" target="_blank">Office of Scientific and Technical Information</a>, in partnership with <a href="https://www.cendi.gov/" target="_blank">CENDI</a>.</div> </nav> </footer> <script type="text/javascript"><!-- // var lastDiv = ""; function showDiv(divName) { // hide last div if (lastDiv) { document.getElementById(lastDiv).className = "hiddenDiv"; } //if value of the box is not nothing and an object with that name exists, then change the class if (divName && document.getElementById(divName)) { document.getElementById(divName).className = "visibleDiv"; lastDiv = divName; } } //--> </script> <script> /** * Function that tracks a click on an outbound link in Google Analytics. * This function takes a valid URL string as an argument, and uses that URL string * as the event label. */ var trackOutboundLink = function(url,collectionCode) { try { h = window.open(url); setTimeout(function() { ga('send', 'event', 'topic-page-click-through', collectionCode, url); }, 1000); } catch(err){} }; </script> <!-- Google Analytics --> <script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-1122789-34', 'auto'); ga('send', 'pageview'); </script> <!-- End Google Analytics --> <script> showDiv('page_1') </script> </body> </html>