PHURBAS: AN ADAPTIVE, LAGRANGIAN, MESHLESS, MAGNETOHYDRODYNAMICS CODE. I. ALGORITHM
Maron, Jason L.; McNally, Colin P.; Mac Low, Mordecai-Mark E-mail: cmcnally@amnh.org
2012-05-01
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares interpolations) are calculated from the field values of neighboring particles to obtain field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second-order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is implemented to ensure the particles fill the computational volume, which gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. Particle addition and deletion is based on a local void and clump detection algorithm. Dynamic artificial viscosity fields provide stability to the integration. The resulting algorithm provides a robust solution for modeling flows that require Lagrangian or adaptive discretizations to resolve. This paper derives and documents the Phurbas algorithm as implemented in Phurbas version 1.1. A following paper presents the implementation and test problem results.
Modeling pollutant transport using a meshless-lagrangian particle model
Carrington, D. B.; Pepper, D. W.
2002-01-01
A combined meshless-Lagrangian particle transport model is used to predict pollutant transport over irregular terrain. The numerical model for initializing the velocity field is based on a meshless approach utilizing multiquadrics established by Kansa. The Lagrangian particle transport technique uses a random walk procedure to depict the advection and dispersion of pollutants over any type of surface, including street and city canyons
PHURBAS: AN ADAPTIVE, LAGRANGIAN, MESHLESS, MAGNETOHYDRODYNAMICS CODE. II. IMPLEMENTATION AND TESTS
McNally, Colin P.; Mac Low, Mordecai-Mark; Maron, Jason L. E-mail: jmaron@amnh.org
2012-05-01
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is required to ensure the particles fill the computational volume and gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. We have parallelized the code by adapting the framework provided by GADGET-2. A set of standard test problems, including 10{sup -6} amplitude linear magnetohydrodynamics waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities is presented. Finally, we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. This paper documents the Phurbas algorithm as implemented in Phurbas version 1.1.
Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement
Koniges, A.; Eder, D.; Masters, N.; Fisher, A.; Anderson, R.; Gunney, B.; Wang, P.; Benson, D.; Dixit, P.
2009-09-29
This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being applied to slurry flow (landslides).
Accurate, meshless methods for magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Hopkins, Philip F.; Raives, Matthias J.
2016-01-01
Recently, we explored new meshless finite-volume Lagrangian methods for hydrodynamics: the `meshless finite mass' (MFM) and `meshless finite volume' (MFV) methods; these capture advantages of both smoothed particle hydrodynamics (SPH) and adaptive mesh refinement (AMR) schemes. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains nabla \\cdot B≈ 0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure nabla \\cdot B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, `modern' SPH can handle most test problems, at the cost of larger kernels and `by hand' adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced `grid noise' but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1995-01-01
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 scheme 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 Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.
Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement
Energy Science and Technology Software Center (ESTSC)
2009-09-29
This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being appliedmore » to slurry flow (landslides).« less
Adaptive meshless local maximum-entropy finite element method for convection-diffusion problems
NASA Astrophysics Data System (ADS)
Wu, C. T.; Young, D. L.; Hong, H. K.
2014-01-01
In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection-diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1994-01-01
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 scheme 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 Lagrangian 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.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2004-01-28
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2002-10-19
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian 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 Lagrangian 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 Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALE 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.
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian 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 Lagrangian 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 Lagrangian 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
Adaptive rezoner in a two-dimensional Lagrangian hydrodynamic code
Pyun, J.J.; Saltzman, J.S.; Scannapieco, A.J.; Carroll, D.
1985-01-01
In an effort to increase spatial resolution without adding additional meshes, an adaptive mesh was incorporated into a two-dimensional Lagrangian hydrodynamics code along with two-dimensional flux corrected (FCT) remapper. The adaptive mesh automatically generates a mesh based on smoothness and orthogonality, and at the same time also tracks physical conditions of interest by focusing mesh points in regions that exhibit those conditions; this is done by defining a weighting function associated with the physical conditions to be tracked. The FCT remapper calculates the net transportive fluxes based on a weighted average of two fluxes computed by a low-order scheme and a high-order scheme. This averaging procedure produces solutions which are conservative and nondiffusive, and maintains positivity. 10 refs., 12 figs.
NASA Astrophysics Data System (ADS)
Domingues, Margarete O.; Gomes, Anna Karina F.; Mendes, Odim; Schneider, Kai
2013-10-01
We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via multiresolution analysis, which allows the reliable introduction of a locally refined mesh while controlling the error. The explicit time discretization uses a compact Runge-Kutta method for local time stepping and an embedded Runge-Kutta scheme for automatic time step control. An extended generalized Lagrangian multiplier approach with the mixed hyperbolic-parabolic correction type is used to control the incompressibility of the magnetic field. Applications to a two-dimensional problem illustrate the properties of the method. Memory savings and numerical divergences of the magnetic field are reported and the accuracy of the adaptive computations is assessed by comparing with the available exact solution. This work was supported by the contract SiCoMHD (ANR-Blanc 2011-045).
Meshless Simulation of Friction Stir Welding
NASA Astrophysics Data System (ADS)
Alfaro, I.; Fratini, L.; Cueto, E.; Chinesta, F.; Micari, F.
2007-05-01
This paper encompasses our first efforts towards the numerical simulation of friction stir welding by employing a Lagrangian approach. To this end, we have employed a meshless method, namely the Natural Element Method (NEM). Friction Stir welding is a welding process where the union between the work pieces is achieved through the extremely high deformation imposed by a rotating pin, which moves between the two pieces. This extremely high strain is the main responsible of the difficulties associated with the numerical simulation of this forming process. Eulerian and Arbitrary Lagrangian-Eulerian (ALE) frameworks encounter difficulties in some aspects of the simulation. For instance, these approaches need additional techniques for the description of the boundary between materials, such as level sets, boundary markers or similar. In this paper we address the issue of employing a Lagrangian framework, which adequately describes the evolution in time of the interphase. The meshless character of the technique also ensures that no degeneracy on the accuracy is obtained due to mesh distortion. Some examples are presented that show the potential of the technique in simulating such a process.
Anderson, R W; Pember, R B; Elliott, N S
2001-10-22
A new method that combines staggered grid Arbitrary Lagrangian-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 Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditional AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.
A Quasi-Conservative Adaptive Semi-Lagrangian Advection-Diffusion Scheme
NASA Astrophysics Data System (ADS)
Behrens, Joern
2014-05-01
Many processes in atmospheric or oceanic tracer transport are conveniently represented by advection-diffusion type equations. Depending on the magnitudes of both components, the mathematical representation and consequently the discretization is a non-trivial problem. We will focus on advection-dominated situations and will introduce a semi-Lagrangian scheme with adaptive mesh refinement for high local resolution. This scheme is well suited for pollutant transport from point sources, or transport processes featuring fine filamentation with corresponding local concentration maxima. In order to achieve stability, accuracy and conservation, we combine an adaptive mesh refinement quasi-conservative semi-Lagrangian scheme, based on an integral formulation of the underlying advective conservation law (Behrens, 2006), with an advection diffusion scheme as described by Spiegelman and Katz (2006). The resulting scheme proves to be conservative and stable, while maintaining high computational efficiency and accuracy.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Solution of the Euler Equations
Anderson, R W; Elliott, N S; Pember, R B
2003-02-14
A new method that combines staggered grid arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. The novel components of the methods are driven by the need to reconcile traditional AMR techniques with the staggered variables and moving, deforming meshes associated with Lagrange based ALE schemes. We develop interlevel solution transfer operators and interlevel boundary conditions first in the case of purely Lagrangian hydrodynamics, and then extend these ideas into an ALE method by developing adaptive extensions of elliptic mesh relaxation techniques. Conservation properties of the method are analyzed, and a series of test problem calculations are presented which demonstrate the utility and efficiency of the method.
A Lagrangian-Eulerian finite element method with adaptive gridding for advection-dispersion problems
Ijiri, Y.; Karasaki, K.
1994-02-01
In the present paper, a Lagrangian-Eulerian finite element method with adaptive gridding for solving advection-dispersion equations is described. The code creates new grid points in the vicinity of sharp fronts at every time step in order to reduce numerical dispersion. The code yields quite accurate solutions for a wide range of mesh Peclet numbers and for mesh Courant numbers well in excess of 1.
NOTE: Solving the ECG forward problem by means of a meshless finite element method
NASA Astrophysics Data System (ADS)
Li, Z. S.; Zhu, S. A.; He, Bin
2007-07-01
The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions.
NASA Astrophysics Data System (ADS)
Gotovac, Hrvoje; Srzic, Veljko
2014-05-01
Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large
Adaptive gridding strategies for Free-Lagrangian calculations of low speed flows
NASA Astrophysics Data System (ADS)
Fritts, Martin J.
1988-01-01
Free-Lagrangian methods have been employed in two-dimensional simulations of the long-term evolution of fluid instabilities for low speed flows. For example, calculations of the Rayleigh-Taylor instability have proceeded through the inversion and mixing of two fluid layers and simulations of droplet deformations have continued well beyond droplet shattering. The freedom to choose grid connections permits several important benefits for these calculations. 1. Mass conservation is enforced for all individual fluid elements. 2. Vertex movement is always Lagrangian. 3. Grid adjustments can be made automatically, with no user intervention. 4. Grid connections may be selected to ensure accuracy in the difference equations. 5. Adaptive gridding schemes are local, adding and deleting vertices as dictated by local accuracy estimators. 6. Any geometric configuration may be easily gridded, for any vertex distribution on the boundaries or in the interior of the fluids. This paper will review some two-dimensional results, with the emphasis on the adaptive gridding algorithms and the accuracy of the resultant difference templates for the mathematical operators. The relation of the triangular mesh to the Voronoi mesh will be explored, particularly for the case when they are dual meshes. Three-dimensional algorithms for adaptive gridding will be presented which are exact analogues to the two-dimensional case. Gridding efficiencies will be discussed for several schemes.
New techniques for meshless flow simulation generalizing moving least squares
NASA Astrophysics Data System (ADS)
Trask, Nathaniel; Maxey, Martin
2015-11-01
While the Lagrangian nature of SPH offers unique flexibility in application problems, practitioners are forced to choose between compatibility in div/grad operators or low accuracy limiting the scope of the method. In this work, two new discretization frameworks are introduced that extend concepts from finite difference methods to a meshless context: one generalizing the high-order convergence of compact finite differences and another generalizing the enhanced stability of staggered marker-and-cell schemes. The discretizations are based on a novel polynomial reconstruction process that allows arbitrary order polynomial accuracy for both the differential operators and general boundary conditions while maintaining stability and computational efficiency. We demonstrate how the method fits neatly into the ISPH framework and offers a new degree of fidelity and accuracy in Lagrangian particle methods. Supported by the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4), DOE Award DE-SC0009247.
NASA Astrophysics Data System (ADS)
Nejadmalayeri, Alireza
The current work develops a wavelet-based adaptive variable fidelity approach that integrates Wavelet-based Direct Numerical Simulation (WDNS), Coherent Vortex Simulations (CVS), and Stochastic Coherent Adaptive Large Eddy Simulations (SCALES). The proposed methodology employs the notion of spatially and temporarily varying wavelet thresholding combined with hierarchical wavelet-based turbulence modeling. The transition between WDNS, CVS, and SCALES regimes is achieved through two-way physics-based feedback between the modeled SGS dissipation (or other dynamically important physical quantity) and the spatial resolution. The feedback is based on spatio-temporal variation of the wavelet threshold, where the thresholding level is adjusted on the fly depending on the deviation of local significant SGS dissipation from the user prescribed level. This strategy overcomes a major limitation for all previously existing wavelet-based multi-resolution schemes: the global thresholding criterion, which does not fully utilize the spatial/temporal intermittency of the turbulent flow. Hence, the aforementioned concept of physics-based spatially variable thresholding in the context of wavelet-based numerical techniques for solving PDEs is established. The procedure consists of tracking the wavelet thresholding-factor within a Lagrangian frame by exploiting a Lagrangian Path-Line Diffusive Averaging approach based on either linear averaging along characteristics or direct solution of the evolution equation. This innovative technique represents a framework of continuously variable fidelity wavelet-based space/time/model-form adaptive multiscale methodology. This methodology has been tested and has provided very promising results on a benchmark with time-varying user prescribed level of SGS dissipation. In addition, a longtime effort to develop a novel parallel adaptive wavelet collocation method for numerical solution of PDEs has been completed during the course of the current work
NASA Astrophysics Data System (ADS)
Souto, M. J.; Souto, J. A.; Pérez-Muñuzuri, V.; Casares, J. J.; Bermúdez, J. L.
Transport and dispersion of pollutants in the lower atmosphere are predicted by using both a Lagrangian particle model (LPM) and an adaptive puff model (APM2) coupled to the same mesoscale meteorological prediction model PMETEO. LPM and APM2 apply the same numerical solutions for plume rise; but, for advection and plume growth, LPM uses a stochastic surrogate to the pollutant conservation equation, and APM2 applies interpolated winds and standard deviations from the meteorological model, using a step-wise Gaussian approach. The results of both models in forecasting the SO 2 ground level concentration (glc) around the 1400 MWe coal-fired As Pontes Power Plant are compared under unstable conditions. In addition, meteorological and SO 2 glc numerical results are compared to field measurements provided by 17 fully automated SO 2 glc remote stations, nine meteorological towers and one Remtech PA-3 SODAR, from a meteorological and air quality monitoring network located 30 km around the power plant.
Adaptive time stepping algorithm for Lagrangian transport models: Theory and idealised test cases
NASA Astrophysics Data System (ADS)
Shah, Syed Hyder Ali Muttaqi; Heemink, Arnold Willem; Gräwe, Ulf; Deleersnijder, Eric
2013-08-01
Random walk simulations have an excellent potential in marine and oceanic modelling. This is essentially due to their relative simplicity and their ability to represent advective transport without being plagued by the deficiencies of the Eulerian methods. The physical and mathematical foundations of random walk modelling of turbulent diffusion have become solid over the years. Random walk models rest on the theory of stochastic differential equations. Unfortunately, the latter and the related numerical aspects have not attracted much attention in the oceanic modelling community. The main goal of this paper is to help bridge the gap by developing an efficient adaptive time stepping algorithm for random walk models. Its performance is examined on two idealised test cases of turbulent dispersion; (i) pycnocline crossing and (ii) non-flat isopycnal diffusion, which are inspired by shallow-sea dynamics and large-scale ocean transport processes, respectively. The numerical results of the adaptive time stepping algorithm are compared with the fixed-time increment Milstein scheme, showing that the adaptive time stepping algorithm for Lagrangian random walk models is more efficient than its fixed step-size counterpart without any loss in accuracy.
Carson, James P.; Kuprat, Andrew P.; Jiao, Xiangmin; Dyedov, Volodymyr; del Pin, Facundo; Guccione, Julius M.; Ratcliffe, Mark B.; Einstein, Daniel R.
2010-04-01
Spatial discretization of complex imaging-derived fluid-solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where, the fluid and solid phases must match geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to share the same surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid-solid mesh of the mouse heart. An MRI perfusion-fixed dataset of a mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue and background. Subsequently, a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid-structure interaction computations will tend to have relative error equilibrated over the whole mesh.
Meshless analysis of shear deformable shells: boundary and interface constraints
NASA Astrophysics Data System (ADS)
Costa, Jorge C.; Pimenta, Paulo M.; Wriggers, Peter
2016-04-01
Meshless methods provide a highly continuous approximation field, convenient for thin structures like shells. Nevertheless, the lack of Kronecker Delta property makes the formulation of essential boundary conditions not straightforward, as the trial and test fields cannot be tailored to boundary values. Similar problem arise when different approximation regions must be joined, in a multi-region problem, such as kinks, folds or joints. This work presents three approaches to impose both kinematic conditions: the well-known Lagrange multiplier method, used since the beginning of the element free Galerkin method; a pure penalty approach; and the recently rediscovered alternative of Nitsche's method. We use the discretization technique for thick Reissner-Mindlin shells and adapt the weak form as to separate displacement and rotational degrees of freedom and obtain suitable and separate stabilization parameters. This approach enables the modeling of discontinuous shells and local refinement on multi-region problems.
Multicloud: Multigrid convergence with a meshless operator
Katz, Aaron Jameson, Antony
2009-08-01
The primary objective of this work is to develop and test a new convergence acceleration technique we call multicloud. Multicloud is well-founded in the mathematical basis of multigrid, but relies on a meshless operator on coarse levels. The meshless operator enables extremely simple and automatic coarsening procedures for arbitrary meshes using arbitrary fine level discretization schemes. The performance of multicloud is compared with established multigrid techniques for structured and unstructured meshes for the Euler equations on two-dimensional test cases. Results indicate comparable convergence rates per unit work for multicloud and multigrid. However, because of its mesh and scheme transparency, multicloud may be applied to a wide array of problems with no modification of fine level schemes as is often required with agglomeration techniques. The implication is that multicloud can be implemented in a completely modular fashion, allowing researchers to develop fine level algorithms independent of the convergence accelerator for complex three-dimensional problems.
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system
Besse, Nicolas Latu, Guillaume Ghizzo, Alain Sonnendruecker, Eric Bertrand, Pierre
2008-08-10
In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to
NASA Astrophysics Data System (ADS)
Bourantas, Georgios; Lavier, Luc; Claus, Susanne; Van Dam, Tonie; Bordas, Stephane
2015-04-01
Geodynamic modeling is an important branch of Earth Sciences. Direct observation of geodynamic processes is limited in both time and space, while on the other hand numerical methods are capable of simulating millions of years in a matter of days on a desktop computer. The model equations can be reduced to a set of Partial Differential Equations with possibly discontinuous coefficients, governing mass, momentum and heat transfer over the domain. Some of the major challenges associated with such simulations are (1) geological time scales, which require long (in physical time) simulations using small time steps; (2) the presence of localization zones over which large gradients are present and which are much smaller than the overall physical dimensions of the computational domain and require much more refined discretization than for the rest of the domain, much like in fracture or shear band mechanics. An added difficulty is that such structures in the solution may appear after long periods of stagnant behaviour; (3) the definition of boundary conditions, material parameters and that of a suitable computational domain in terms of size; (4) a posteriori error estimation, sensitivity analysis and discretization adaptivity for the resulting coupled problem, including error propagation between different unknown fields. Consequently, it is arguable that any suitable numerical methods aimed at the solution of such problems on a large scale must be able to (i) provide ease of discretization refinement, including possible partition of unity enrichment; (ii) offer a large stability domain, so that "large" time steps can be chosen; (iii) ease of parallelization and good scalability. Our approach is to rely on "meshless" methods based on a point collocation strategy for the discretization of the set of PDEs. The method is hybrid Eulerian/Lagrangian, which enables to switch easily between stagnant periods and periods of localization. Mass and momentum equations are solved using a
Meshless method for solving fixed boundary problem of plasma equilibrium
NASA Astrophysics Data System (ADS)
Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi
2015-07-01
This study solves the Grad-Shafranov equation with a fixed plasma boundary by utilizing a meshless method for the first time. Previous studies have utilized a finite element method (FEM) to solve an equilibrium inside the fixed separatrix. In order to avoid difficulties of FEM (such as mesh problem, difficulty of coding, expensive calculation cost), this study focuses on the meshless methods, especially RBF-MFS and KANSA's method to solve the fixed boundary problem. The results showed that CPU time of the meshless methods was ten to one hundred times shorter than that of FEM to obtain the same accuracy.
Laser ray tracing in a parallel arbitrary Lagrangian-Eulerian adaptive mesh refinement hydrocode
NASA Astrophysics Data System (ADS)
Masters, N. D.; Kaiser, T. B.; Anderson, R. W.; Eder, D. C.; Fisher, A. C.; Koniges, A. E.
2010-08-01
ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray tracing in ALE-AMR. We present the basic concepts of laser ray tracing and our approach to efficiently traverse the adaptive mesh hierarchy.
Laser Ray Tracing in a Parallel Arbitrary Lagrangian-Eulerian Adaptive Mesh Refinement Hydrocode
Masters, N D; Kaiser, T B; Anderson, R W; Eder, D C; Fisher, A C; Koniges, A E
2009-09-28
ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray-tracing in ALE-AMR. We present the equations of laser ray tracing, our approach to efficient traversal of the adaptive mesh hierarchy in which we propagate computational rays through a virtual composite mesh consisting of the finest resolution representation of the modeled space, and anticipate simulations that will be compared to experiments for code validation.
A meshless method for unbounded acoustic problems.
Shojaei, Arman; Boroomand, Bijan; Soleimanifar, Ehsan
2016-05-01
In this paper an effective meshless method is proposed to solve time-harmonic acoustic problems defined on unbounded domains. To this end, the near field is discretized by a set of nodes and the far field effect is taken into account by considering radiative boundary conditions. The approximation within the near field is performed using a set of local residual-free basis functions defined on a series of finite clouds. For considering the far field effect, a series of infinite clouds are defined on which another set of residual-free bases, satisfying the radiation conditions, are considered for the approximation. Validation of the results is performed through solving some acoustic problems. PMID:27250155
Meshless Local Petrov-Galerkin Method for Bending Problems
NASA Technical Reports Server (NTRS)
Phillips, Dawn R.; Raju, Ivatury S.
2002-01-01
Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques.
An, Yu; Liu, Jie; Zhang, Guanglei; Ye, Jinzuo; Mao, Yamin; Jiang, Shixin; Shang, Wenting; Du, Yang; Chi, Chongwei; Tian, Jie
2015-10-01
Fluorescence molecular tomography (FMT) is a promising tool in the study of cancer, drug discovery, and disease diagnosis, enabling noninvasive and quantitative imaging of the biodistribution of fluorophores in deep tissues via image reconstruction techniques. Conventional reconstruction methods based on the finite-element method (FEM) have achieved acceptable stability and efficiency. However, some inherent shortcomings in FEM meshes, such as time consumption in mesh generation and a large discretization error, limit further biomedical application. In this paper, we propose a meshless method for reconstruction of FMT (MM-FMT) using compactly supported radial basis functions (CSRBFs). With CSRBFs, the image domain can be accurately expressed by continuous CSRBFs, avoiding the discretization error to a certain degree. After direct collocation with CSRBFs, the conventional optimization techniques, including Tikhonov, L1-norm iteration shrinkage (L1-IS), and sparsity adaptive matching pursuit, were adopted to solve the meshless reconstruction. To evaluate the performance of the proposed MM-FMT, we performed numerical heterogeneous mouse experiments and in vivo bead-implanted mouse experiments. The results suggest that the proposed MM-FMT method can reduce the position error of the reconstruction result to smaller than 0.4 mm for the double-source case, which is a significant improvement for FMT. PMID:26451513
NASA Astrophysics Data System (ADS)
An, Yu; Liu, Jie; Zhang, Guanglei; Ye, Jinzuo; Mao, Yamin; Jiang, Shixin; Shang, Wenting; Du, Yang; Chi, Chongwei; Tian, Jie
2015-10-01
Fluorescence molecular tomography (FMT) is a promising tool in the study of cancer, drug discovery, and disease diagnosis, enabling noninvasive and quantitative imaging of the biodistribution of fluorophores in deep tissues via image reconstruction techniques. Conventional reconstruction methods based on the finite-element method (FEM) have achieved acceptable stability and efficiency. However, some inherent shortcomings in FEM meshes, such as time consumption in mesh generation and a large discretization error, limit further biomedical application. In this paper, we propose a meshless method for reconstruction of FMT (MM-FMT) using compactly supported radial basis functions (CSRBFs). With CSRBFs, the image domain can be accurately expressed by continuous CSRBFs, avoiding the discretization error to a certain degree. After direct collocation with CSRBFs, the conventional optimization techniques, including Tikhonov, L1-norm iteration shrinkage (L1-IS), and sparsity adaptive matching pursuit, were adopted to solve the meshless reconstruction. To evaluate the performance of the proposed MM-FMT, we performed numerical heterogeneous mouse experiments and in vivo bead-implanted mouse experiments. The results suggest that the proposed MM-FMT method can reduce the position error of the reconstruction result to smaller than 0.4 mm for the double-source case, which is a significant improvement for FMT.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1992-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian methods. Unlike the Lagrangian 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.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1993-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous Lagrangian 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.
A meshless approach to thermomechanics of DC casting of aluminium billets
NASA Astrophysics Data System (ADS)
Mavrič, B.; Šarler, B.
2016-03-01
The ability to model thermomechanics in DC casting is important due to the technological challenges caused by physical phenomena such as different ingot distortions, cracking, hot tearing and residual stress. Many thermomechanical models already exist and usually take into account three contributions: elastic, thermal expansion, and viscoplastic to model the mushy zone. These models are, in a vast majority, solved by the finite element method. In the present work the elastic model that accounts for linear thermal expansion is considered. The method used for solving the model is of a novel meshless type and extends our previous meshless attempts in solving fluid mechanics problems. The solution to the problem is constructed using collocation on the overlapping subdomains, which are composed of computational nodes. Multiquadric radial basis functions, augmented by monomials, are used for the displacement interpolation. The interpolation is constructed in such a manner that it readily satisfies the boundary conditions. The discretization results in construction of a global square sparse matrix representing the system of linear equations for the displacement field. The developed method has many advantages. The system of equations can be easily constructed and efficiently solved. There is no need to perform expensive meshing of the domain and the formulation of the method is similar in two and three dimensions. Since no meshing is required, the nodes can easily be added or removed, which allows for efficient adaption of the node arrangement density. The order of convergence, estimated through an analytically solvable test, can be adjusted through the number of interpolation nodes in the subdomain, with 6 nodes being enough for the second order convergence. Simulations of axisymmetric mechanical problems, associated with low frequency electromagnetic DC casting are presented.
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing
1995-01-01
A unique formulation of describing fluid motion is presented. The method, referred to as 'extended Lagrangian method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the Lagrangian 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.
A localized meshless method for diffusion on folded surfaces
NASA Astrophysics Data System (ADS)
Cheung, Ka Chun; Ling, Leevan; Ruuth, Steven J.
2015-09-01
Partial differential equations (PDEs) on surfaces arise in a variety of application areas including biological systems, medical imaging, fluid dynamics, mathematical physics, image processing and computer graphics. In this paper, we propose a radial basis function (RBF) discretization of the closest point method. The corresponding localized meshless method may be used to approximate diffusion on smooth or folded surfaces. Our method has the benefit of having an a priori error bound in terms of percentage of the norm of the solution. A stable solver is used to avoid the ill-conditioning that arises when the radial basis functions (RBFs) become flat.
Boundary conditions in a meshless staggered particle code
Libersky, L.D.; Randles, P.W.
1998-07-01
A meshless method utilizing two sets of particles and generalized boundary conditions is introduced. Companion sets of particles, one carrying velocity and the other carrying stress, are employed to reduce the undesirable effects of colocation of all field variables and increase accuracy. Boundary conditions implemented within this staggered framework include contact, stress-free, stress, velocity, and symmetry constraints. Several test problems are used to evaluate the method. Of particular importance is the motion of stress particles relative to velocity particles in higher dimensions. Early results show promise, but difficulties remain that must be overcome if the staggered technique is to be successful.
A meshless method for modeling convective heat transfer
Carrington, David B
2010-01-01
A meshless method is used in a projection-based approach to solve the primitive equations for fluid flow with heat transfer. The method is easy to implement in a MATLAB format. Radial basis functions are used to solve two benchmark test cases: natural convection in a square enclosure and flow with forced convection over a backward facing step. The results are compared with two popular and widely used commercial codes: COMSOL, a finite element model, and FLUENT, a finite volume-based model.
Solution of Macrosegregation in Continuously Cast Billets by a Meshless Method
NASA Astrophysics Data System (ADS)
Vertnik, R.; Šarler, B.; Senčič, B.
2012-01-01
The main aim of this paper is to demonstrate the applicability and the advantages of a novel meshless method for simulation of macrosegregation in steel billets. The physical model is established on a set of macroscopic equations for mass, energy, momentum, species, turbulent kinetic energy, and dissipation rate in two dimensions. The mixture continuum model is used to treat the solidification system. The mushy zone is modelled as a Darcy porous media with Kozeny-Karman permeability relation, where the morphology of the porous media is modelled by a constant value. The incompressible turbulent flow of the molten steel is described by the Low-Reynolds-Number (LRN) k-epsilon turbulence model, closed by the Launder and Sharma closure coefficients and damping functions. The microsegregation equations rely on lever rule. The numerical method is established on explicit timestepping, and collocation with multiquadrics radial basis functions on non-uniform five-noded influence domains, and adaptive upwinding technique. The velocity-pressure coupling of the incompressible flow is resolved by the explicit Chorin's fractional step method, with the intermediate velocity field, calculated without the pressure term. A recently proposed standard continuous casting configuration with Fe-C system has been used for verification of the model. The advantages of the method are its simplicity and efficiency, since no polygonisation is involved, easy adaptation of the nodal points in areas with high gradients, almost the same formulation in two and three dimensions, high accuracy and low numerical diffusion.
Meshless Method for Solving Fixed Boundary Problem of Axisymmetric Plasma Equilibrium
NASA Astrophysics Data System (ADS)
Imazawa, Ryota; Kawano, Yasunori; Itami, Kiyoshi
2013-10-01
This study is to solve Grad-Shafranov (GS) equation with the fixed plasma boundary by utilizing the meshless method for the first time. The previous studies have utilized the finite element method (FEM) to solve the equilibrium inside the fixed separatrix. In order to avoid the difficulty of FEM (e.g. mesh problem, difficulty of coding, expensive calculation cost, etc.), this study proposes the new method to apply the meshless methods, especially RBF-MFS and Kansa's method to inhomogeneous and nonlinear partial differential equations (PDE). Although the RBF-MFS and Kansa's method are applicable to the inhomogeneous PDE, the application of these methods to the GS equation is not straight-forward. Since the current profile is usually parameterized by the normalized poloidal flux, the inhomogeneous term of the GS equation contains the normalized poloidal flux, not just a poloidal flux. This is the difficulty for solving the GS equation. Accuracy and calculation time of the meshless method and FEM are compared in the condition of the same total number of nodes. The results show that the error of magnetic field obtained by the meshless methods is one hundredth of that by FEM and that the calculation time of the meshless method is one tenth of that of FEM. Moreover, this study shows that the meshless methods can be easily accelerated by parallel computing.
Meshless Modeling of Deformable Shapes and their Motion
Adams, Bart; Ovsjanikov, Maks; Wand, Michael; Seidel, Hans-Peter; Guibas, Leonidas J.
2010-01-01
We present a new framework for interactive shape deformation modeling and key frame interpolation based on a meshless finite element formulation. Starting from a coarse nodal sampling of an object’s volume, we formulate rigidity and volume preservation constraints that are enforced to yield realistic shape deformations at interactive frame rates. Additionally, by specifying key frame poses of the deforming shape and optimizing the nodal displacements while targeting smooth interpolated motion, our algorithm extends to a motion planning framework for deformable objects. This allows reconstructing smooth and plausible deformable shape trajectories in the presence of possibly moving obstacles. The presented results illustrate that our framework can handle complex shapes at interactive rates and hence is a valuable tool for animators to realistically and efficiently model and interpolate deforming 3D shapes. PMID:24839614
An hourglass control algorithm for Lagrangian Smooth Particle Hydrodynamics
NASA Astrophysics Data System (ADS)
Ganzenmüller, Georg C.
2015-04-01
This paper presents a stabilization scheme which addresses the rank-deficiency problem in meshless collocation methods for solid mechanics. Specifically, Smooth-Particle Hydrodynamics (SPH) in the Total Lagrangian formalism is considered. This method is rank-deficient in the sense that the SPH approximation of the deformation gradient is not unique with respect to the positions of the integration points. The non-uniqueness can result in the formation of zero-energy modes. If undetected, these modes can grow and completely dominate the solution. Here, an algorithm is introduced, which effectively suppresses these modes in a fashion similar to hour-glass control mechanisms in Finite-Element methods. Simulations utilizing this control algorithm result exhibit much improved stability, accuracy, and error convergence properties. In contrast to an alternative method which eliminates zero-energy modes, namely the use of additional integration points, the here presented algorithm is easy to implement and computationally very efficient.
Predicting abrasive wear with coupled Lagrangian methods
NASA Astrophysics Data System (ADS)
Beck, Florian; Eberhard, Peter
2015-05-01
In this paper, a mesh-less approach for the simulation of a fluid with particle loading and the prediction of abrasive wear is presented. We are using the smoothed particle hydrodynamics (SPH) method for modeling the fluid and the discrete element method (DEM) for the solid particles, which represent the loading of the fluid. These Lagrangian methods are used to describe heavily sloshing fluids with their free surfaces as well as the interface between the fluid and the solid particles accurately. A Reynolds-averaged Navier-Stokes equations model is applied for handling turbulences. We are predicting abrasive wear on the boundary geometry with two different wear models taking cutting and deformation mechanisms into account. The boundary geometry is discretized with special DEM particles. In doing so, it is possible to use the same particle type for both the calculation of the boundary conditions for the SPH method as well as the DEM and for predicting the abrasive wear. After a brief introduction to the SPH method and the DEM, the handling of the boundary and the coupling of the fluid and the solid particles are discussed. Then, the applied wear models are presented and the simulation scenarios are described. The first numerical experiment is the simulation of a fluid with loading which is sloshing inside a tank. The second numerical experiment is the simulation of the impact of a free jet with loading to a simplified pelton bucket. We are especially investigating the wear patterns inside the tank and the bucket.
A Meshless Method for Magnetohydrodynamics and Applications to Protoplanetary Disks
NASA Astrophysics Data System (ADS)
McNally, Colin P.
2012-08-01
This thesis presents an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares interpolations) are calculated from the field values of neighboring particles to obtain field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is implemented to ensure the particles fill the computational volume, which gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. Particle addition and deletion is based on a local void and clump detection algorithm. Dynamic artificial viscosity fields provide stability to the integration. The resulting algorithm provides a robust solution for modeling flows that require Lagrangian or adaptive discretizations to resolve. The code has been parallelized by adapting the framework provided by Gadget-2. A set of standard test problems, including one part in a million amplitude linear MHD waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities are presented. Finally we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. We provide a rigorous methodology for verifying a numerical method on two dimensional Kelvin-Helmholtz instability. The test problem was run in the Pencil Code, Athena, Enzo, NDSPHMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, although this work provides the mathematical framewor! k needed for such a
Spatiotemporal groundwater level modeling using hybrid artificial intelligence-meshless method
NASA Astrophysics Data System (ADS)
Nourani, Vahid; Mousavi, Shahram
2016-05-01
Uncertainties of the field parameters, noise of the observed data and unknown boundary conditions are the main factors involved in the groundwater level (GL) time series which limit the modeling and simulation of GL. This paper presents a hybrid artificial intelligence-meshless model for spatiotemporal GL modeling. In this way firstly time series of GL observed in different piezometers were de-noised using threshold-based wavelet method and the impact of de-noised and noisy data was compared in temporal GL modeling by artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS). In the second step, both ANN and ANFIS models were calibrated and verified using GL data of each piezometer, rainfall and runoff considering various input scenarios to predict the GL at one month ahead. In the final step, the simulated GLs in the second step of modeling were considered as interior conditions for the multiquadric radial basis function (RBF) based solve of governing partial differential equation of groundwater flow to estimate GL at any desired point within the plain where there is not any observation. In order to evaluate and compare the GL pattern at different time scales, the cross-wavelet coherence was also applied to GL time series of piezometers. The results showed that the threshold-based wavelet de-noising approach can enhance the performance of the modeling up to 13.4%. Also it was found that the accuracy of ANFIS-RBF model is more reliable than ANN-RBF model in both calibration and validation steps.
Strain field measurements around notches using SIFT features and meshless methods.
Gonzáles, Giancarlo; Meggiolaro, Marco
2015-05-10
This work proposes a hybrid experimental-numerical technique with the aim to improve strain measurements at stress concentration regions. The novel technique is performed employing the computer vision scale invariant feature transform (SIFT) algorithm and meshless methods, here termed SIFT-meshless. The SIFT is applied to perform feature points matching in two images of the specimen surface at different stages of mechanical deformation. The output data are provided as a set of displacement measurements by tracking matched feature points. This information is then used to model displacement and strain field on the surface by means of a meshless formulation based on the moving least squares approximation. By applying the proposed SIFT-meshless method, the strain distribution around a semicircular notch in a plate under bending load was investigated. The experimental results were compared with those obtained by a digital image correlation technique based on a subset approach and to simulations from finite element analysis software. The experimental results demonstrated that the present method is capable of performing reliable strain measurements at distances close to the notch where the peak strain value is expected, even in the presence of high strain gradients. PMID:25967511
Lagrangian Simulation of Combustion
Ahmed F. Ghoniem
2008-05-01
A Lagrangian approach for the simulation of reactive flows has been developed during the course of this project, and has been applied to a number of significant and challenging problems including the transverse jet simulations. An efficient strategy for parallel domain decomposition has also been developed to enable the implementation of the approach on massively parallel architecture. Since 2005, we focused our efforts on the development of a semi-Lagrangian treatment of diffusion, and fast and accurate Lagrangian simulation tools for multiphysics problems including combustion.
NASA Astrophysics Data System (ADS)
Sladek, J.; Sladek, V.; Zhang, Ch.
2008-02-01
A meshless local Petrov-Galerkin (MLPG) formulation is presented for analysis of shear deformable shallow shells with orthotropic material properties and continuously varying material properties through the shell thickness. Shear deformation of shells described by the Reissner theory is considered. Analyses of shells under static and dynamic loads are given here. For transient elastodynamic case the Laplace-transform is used to eliminate the time dependence of the field variables. A weak formulation with a unit test function transforms the set of the governing equations into local integral equations on local subdomains in the plane domain of the shell. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation.
Young, D L; Chen, K H; Liu, T Y; Wu, C S
2016-01-01
Three-dimensional exterior acoustic problems with irregular domains are solved using a hypersingular meshless method. In particular, the method of fundamental solutions (MFS) is used to formulate and analyze such acoustic problems. It is well known that source points for MFS cannot be located on the real boundary due to the singularity of the kernel functions. Thus, the diagonal terms of the influence matrices are unobtainable when source points are located on the boundary. An efficient approach is proposed to overcome such difficulties, when the MFS is used for three-dimensional exterior acoustic problems. This work is an extension of previous research on two-dimensional problems. The solution of the problem is expressed in terms of a double-layer potential representation on the physical boundary. Three examples are presented in which the proposed method is compared to the MFS and boundary element method. Good numerical performance is demonstrated by the proposed hypersingular meshless method. PMID:26827046
A novel numerical meshless approach for electric potential estimation in transcranial stimulation
NASA Astrophysics Data System (ADS)
Ala, Guido; Fasshauer, Gregory E.; Francomano, Elisa; Ganci, Salvatore; McCourt, Michael J.; Vitabile, Salvatore
2015-12-01
In this paper, a first application of the method of fundamental solutions in estimating the electric potential and the spatial current density distribution in the brain due to transcranial stimulation, is presented. The coupled boundary value p roblems for the electric potential are solved in a meshless way, so avoiding the use of grid based numerical methods. A multi-spherical geometry is considered and numerical results are discussed.
A Localized Meshless Approach for Modeling Spatial-temporal Calcium Dynamics in Ventricular Myocytes
Yao, Guangming; Yu, Zeyun
2011-01-01
SUMMARY Spatial-temporal calcium dynamics due to calcium release, buffering and re-uptaking plays a central role in studying excitation-contraction (E-C) coupling in both normal and diseased cardiac myocytes. In this paper, we employ a meshless method, namely, the local radial basis function collocation method (LRBFCM) to model such calcium behaviors by solving a nonlinear system of reaction-diffusion partial differential equations. In particular, a simplified structural unit containing a single transverse-tubule (or t-tubule) and its surrounding half sarcomeres is investigated using the meshless method. Numerical results are compared to those generated by finite element methods, showing the capability and efficiency of the LRBFCM in modeling calcium dynamics in ventricular myocytes. The single t-tubule model is also extended to the whole-cell scale with t-tubules excluded to demonstrate the scalability of the proposed meshless method in handling very large domains. The experiments have shown that the LRBFCM is suitable to multi-scale modeling of calcium dynamics in ventricular myocytes with high accuracy and efficiency. PMID:22408720
Lagrangian description of warm plasmas
NASA Technical Reports Server (NTRS)
Kim, H.
1970-01-01
Efforts are described to extend the averaged Lagrangian 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 Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, 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.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian 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…
Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash
NASA Technical Reports Server (NTRS)
Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.
2012-01-01
In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.
NASA Astrophysics Data System (ADS)
Blakely, Christopher D.
This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models. We provide numerical verification and validation of the meshless collocation scheme applied to the rotational shallow-water equations on the sphere and demonstrate computationally that the proposed model can compete with existing high performance methods for approximating the shallow-water equations such as the SEAM (spectral-element atmospheric model) developed at NCAR. A detailed analysis of the parallel implementation of the model, along with the introduction of parallel algorithmic routines for the high-performance simulation of the model will be given. We analyze the programming and computational aspects of the model using Fortran 90 and the message passing interface (mpi) library along with software and hardware specifications and performance tests. Details from many aspects of the implementation in regards to performance, optimization, and stabilization will be given. In order to verify the mathematical correctness of the algorithms presented and to validate the performance of the meshless collocation shallow-water model, we conclude the thesis with numerical experiments on some standardized test cases for the shallow-water equations on the sphere using the proposed method.
Yang, Chun; Tang, Dalin; Atluri, Satya
2011-01-01
Previously, we introduced a computational procedure based on three-dimensional meshless generalized finite difference (MGFD) method and serial magnetic resonance imaging (MRI) data to quantify patient-specific carotid atherosclerotic plaque growth functions and simulate plaque progression. Structure-only models were used in our previous report. In this paper, fluid-stricture interaction (FSI) was added to improve on prediction accuracy. One participating patient was scanned three times (T1, T2, and T3, at intervals of about 18 months) to obtain plaque progression data. Blood flow was assumed to laminar, Newtonian, viscous and incompressible. The Navier-Stokes equations with arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations. Plaque material was assumed to be uniform, homogeneous, isotropic, linear, and nearly incompressible. The linear elastic model was used. The 3D FSI plaque model was discretized and solved using a meshless generalized finite difference (GFD) method. Growth functions with a) morphology alone; b) morphology and plaque wall stress (PWS); morphology and flow shear stress (FSS), and d) morphology, PWS and FSS were introduced to predict future plaque growth based on previous time point data. Starting from the T2 plaque geometry, plaque progression was simulated by solving the FSI model and adjusting plaque geometry using plaque growth functions iteratively until T3 is reached. Numerically simulated plaque progression agreed very well with the target T3 plaque geometry with errors ranging from 8.62%, 7.22%, 5.77% and 4.39%, with the growth function including morphology, plaque wall stress and flow shear stress terms giving the best predictions. Adding flow shear stress term to the growth function improved the prediction error from 7.22% to 4.39%, a 40% improvement. We believe this is the first time 3D plaque progression FSI simulation based on multi-year patient-tracking data was reported. Serial MRI-based progression
An IPOT meshless method using DC PSE approximation for fluid flow equations in 2D and 3D geometries
NASA Astrophysics Data System (ADS)
Bourantas, G. C.; Loukopoulos, V. C.; Skouras, E. D.; Burganos, V. N.; Nikiforidis, G. C.
2016-06-01
Navier-Stokes (N-S) equations, in their primitive variable (u-v-p) formulation, are numerically solved using the Implicit Potential (IPOT) numerical scheme in the context of strong form Meshless Point Collocation (MPC) method. The unknown field functions are computed using the Discretization Correction Particle Strength Exchange (DC PSE) approximation method. The latter makes use of discrete moment conditions to derive the operator kernels, which leads to low condition number for the moment matrix compared to other meshless interpolation methods and increased stability for the numerical solution. The proposed meshless scheme is applied on 2D and 3D spatial domains, using uniform or irregular set of nodes to represent the domain. The numerical results obtained are compared against those obtained using well-established methods.
Gravity, Time, and Lagrangians
ERIC Educational Resources Information Center
Huggins, Elisha
2010-01-01
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 Lagrangian. (Why would one…
Compressible Lagrangian hydrodynamics without Lagrangian cells
NASA Astrophysics Data System (ADS)
Clark, Robert A.
The partial differential Eqs [2.1, 2.2, and 2.3], along with the equation of state 2.4, which describe the time evolution of compressible fluid flow can be solved without the use of a Lagrangian mesh. The method follows embedded fluid points and uses finite difference approximations to ěc nablaP and ěc nabla · ěc u to update p, ěc u and e. We have demonstrated that the method can accurately calculate highly distorted flows without difficulty. The finite difference approximations are not unique, improvements may be found in the near future. The neighbor selection is not unique, but the one being used at present appears to do an excellent job. The method could be directly extended to three dimensions. One drawback to the method is the failure toexplicitly conserve mass, momentum and energy. In fact, at any given time, the mass is not defined. We must perform an auxiliary calculation by integrating the density field over space to obtain mass, energy and momentum. However, in all cases where we have done this, we have found the drift in these quantities to be no more than a few percent.
A Meshless Local Petrov-Galerkin Method for Euler-Bernoulli Beam Problems
NASA Technical Reports Server (NTRS)
Raju, I. S.; Phillips, D. R.
2002-01-01
An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions. The use of these functions shows that the weak form can be integrated with conventional Gaussian integration. The MLPG method was evaluated by applying the formulation to a variety of patch test and thin beam problems. The formulation successfully reproduced exact solutions to machine accuracy when test functions with C2 continuity and an appropriate order of basis functions are used.
Three dimensional simulation of macrosegregation in steel billets by a meshless method
NASA Astrophysics Data System (ADS)
Vertnik, R.; Šarler, B.
2016-03-01
There is a continuously developing need for benchmarking of solidification simulations - from the theoretical as well as from the applied points of view. The history of related benchmarking shows differences of the results between different numerical methods, and differences in comparison with the experiments when solving even quite simple solidification situations. The present benchmark test proposes a three dimensional version of the recently developed two dimensional solidification benchmark of the continuous casting with turbulent fluid flow and solidification with macrosegregation. The macroscopic transport equations for mass, momentum, energy, species, turbulent kinetic energy and dissipation rate are considered. Turbulent effects are incorporated through the solution of a low-Re turbulence model. The solidification system is treated by the mixture-continuum model, where the mushy zone is modeled as a Darcy porous media with Kozeny-Karman permeability relation and columnar solid phase moving with the casting velocity. The Fe-C binary phase diagram and the lever rule microsegregation model are used to obtain the carbon segregation in the billet. The transport equations are solved by our newly developed and efficient meshless numerical technique, based on local collocation with radial basis functions and fractional step velocity- pressure coupling. The presented results represent first simulations of a three-dimensional solidification problem by a meshless method.
NASA Technical Reports Server (NTRS)
Chen, T.; Raju, I. S.
2002-01-01
A coupled finite element (FE) method and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. The analysis domain is subdivided into two regions, a finite element (FE) region and a meshless (MM) region. A single weighted residual form is written for the entire domain. Independent trial and test functions are assumed in the FE and MM regions. A transition region is created between the two regions. The transition region blends the trial and test functions of the FE and MM regions. The trial function blending is achieved using a technique similar to the 'Coons patch' method that is widely used in computer-aided geometric design. The test function blending is achieved by using either FE or MM test functions on the nodes in the transition element. The technique was evaluated by applying the coupled method to two potential problems governed by the Poisson equation. The coupled method passed all the patch test problems and gave accurate solutions for the problems studied.
Lagrangian methods of cosmic web classification
NASA Astrophysics Data System (ADS)
Fisher, J. D.; Faltenbacher, A.; Johnson, M. S. T.
2016-05-01
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 Lagrangian approach where the V-web algorithm proposed by Hoffman et al. is implemented with techniques borrowed from smoothed particle hydrodynamics. The Lagrangian approach allows one to classify individual objects (e.g. particles or haloes) based on properties of their nearest neighbours in an adaptive manner. It can be applied directly to a halo sample which dramatically reduces computational cost and potentially allows an application of this classification scheme to observed galaxy samples. Finally, the Lagrangian 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.
NASA Astrophysics Data System (ADS)
Labibzadeh, Mojtaba
2016-01-01
A new technique is used in Discrete Least Square Meshfree(DLSM) method to remove the common existing deficiencies of meshfree methods in handling of the problems containing cracks or concave boundaries. An enhanced Discrete Least Squares Meshless method named as VDLSM(Voronoi based Discrete Least Squares Meshless) is developed in order to solve the steady-state heat conduction problem in irregular solid domains including concave boundaries or cracks. Existing meshless methods cannot estimate precisely the required unknowns in the vicinity of the above mentioned boundaries. Conducted researches are limited to domains with regular convex boundaries. To this end, the advantages of the Voronoi tessellation algorithm are implemented. The support domains of the sampling points are determined using a Voronoi tessellation algorithm. For the weight functions, a cubic spline polynomial is used based on a normalized distance variable which can provide a high degree of smoothness near those mentioned above discontinuities. Finally, Moving Least Squares(MLS) shape functions are constructed using a varitional method. This straight-forward scheme can properly estimate the unknowns(in this particular study, the temperatures at the nodal points) near and on the crack faces, crack tip or concave boundaries without need to extra backward corrective procedures, i.e. the iterative calculations for modifying the shape functions of the nodes located near or on these types of the complex boundaries. The accuracy and efficiency of the presented method are investigated by analyzing four particular examples. Obtained results from VDLSM are compared with the available analytical results or with the results of the well-known Finite Elements Method(FEM) when an analytical solution is not available. By comparisons, it is revealed that the proposed technique gives high accuracy for the solution of the steady-state heat conduction problems within cracked domains or domains with concave boundaries
Stochastic modeling of Lagrangian accelerations
NASA Astrophysics Data System (ADS)
Reynolds, Andy
2002-11-01
It is shown how Sawford's second-order Lagrangian 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 Lagrangian stochastic model that is consistent with both the measured distribution of Lagrangian 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.
Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach
NASA Technical Reports Server (NTRS)
Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.
2003-01-01
A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.
A Meshless Method Using Radial Basis Functions for Beam Bending Problems
NASA Technical Reports Server (NTRS)
Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.
2004-01-01
A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions (RBFs) as trial functions in the study of Euler-Bernoulli beam problems is presented. RBFs, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as they are in the conventional MLPG method. Compactly and noncompactly supported RBFs are considered. Noncompactly supported cubic RBFs are found to be preferable. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. Results obtained from the radial basis MLPG method are either of comparable or better accuracy than those obtained when using the conventional MLPG method.
A New Hybrid Viscoelastic Soft Tissue Model based on Meshless Method for Haptic Surgical Simulation
Bao, Yidong; Wu, Dongmei; Yan, Zhiyuan; Du, Zhijiang
2013-01-01
This paper proposes a hybrid soft tissue model that consists of a multilayer structure and many spheres for surgical simulation system based on meshless. To improve accuracy of the model, tension is added to the three-parameter viscoelastic structure that connects the two spheres. By using haptic device, the three-parameter viscoelastic model (TPM) produces accurate deformationand also has better stress-strain, stress relaxation and creep properties. Stress relaxation and creep formulas have been obtained by mathematical formula derivation. Comparing with the experimental results of the real pig liver which were reported by Evren et al. and Amy et al., the curve lines of stress-strain, stress relaxation and creep of TPM are close to the experimental data of the real liver. Simulated results show that TPM has better real-time, stability and accuracy. PMID:24339837
Gu, Y. T.; Yarlagadda, Prasad K. D. V.
2010-05-21
This paper presents a multiscale study using the coupled Meshless technique/Molecular Dynamics (M{sup 2}) for exploring the deformation mechanism of mono-crystalline metal (focus on copper) under uniaxial tension. In M{sup 2}, an advanced transition algorithm using transition particles is employed to ensure the compatibility of both displacements and their gradients, and an effective local quasi-continuum approach is also applied to obtain the equivalent continuum strain energy density based on the atomistic potentials and Cauchy-Born rule. The key parameters used in M{sup 2} are firstly investigated using a benchmark problem. Then, M{sup 2} is applied to the multiscale simulation for a mono-crystalline copper bar. It has found that the mono-crystalline copper has very good elongation property, and the ultimate strength and Young's modulus are much higher than those obtained in macro-scale.
Meshless deformable models for 3D cardiac motion and strain analysis from tagged MRI.
Wang, Xiaoxu; Chen, Ting; Zhang, Shaoting; Schaerer, Joël; Qian, Zhen; Huh, Suejung; Metaxas, Dimitris; Axel, Leon
2015-01-01
Tagged magnetic resonance imaging (TMRI) provides a direct and noninvasive way to visualize the in-wall deformation of the myocardium. Due to the through-plane motion, the tracking of 3D trajectories of the material points and the computation of 3D strain field call for the necessity of building 3D cardiac deformable models. The intersections of three stacks of orthogonal tagging planes are material points in the myocardium. With these intersections as control points, 3D motion can be reconstructed with a novel meshless deformable model (MDM). Volumetric MDMs describe an object as point cloud inside the object boundary and the coordinate of each point can be written in parametric functions. A generic heart mesh is registered on the TMRI with polar decomposition. A 3D MDM is generated and deformed with MR image tagging lines. Volumetric MDMs are deformed by calculating the dynamics function and minimizing the local Laplacian coordinates. The similarity transformation of each point is computed by assuming its neighboring points are making the same transformation. The deformation is computed iteratively until the control points match the target positions in the consecutive image frame. The 3D strain field is computed from the 3D displacement field with moving least squares. We demonstrate that MDMs outperformed the finite element method and the spline method with a numerical phantom. Meshless deformable models can track the trajectory of any material point in the myocardium and compute the 3D strain field of any particular area. The experimental results on in vivo healthy and patient heart MRI show that the MDM can fully recover the myocardium motion in three dimensions. PMID:25157446
Meshless deformable models for 3D cardiac motion and strain analysis from tagged MRI
Wang, Xiaoxu; Chen, Ting; Zhang, Shaoting; Schaerer, Joël; Qian, Zhen; Huh, Suejung; Metaxas, Dimitris; Axel, Leon
2016-01-01
Tagged magnetic resonance imaging (TMRI) provides a direct and noninvasive way to visualize the in-wall deformation of the myocardium. Due to the through-plane motion, the tracking of 3D trajectories of the material points and the computation of 3D strain field call for the necessity of building 3D cardiac deformable models. The intersections of three stacks of orthogonal tagging planes are material points in the myocardium. With these intersections as control points, 3D motion can be reconstructed with a novel meshless deformable model (MDM). Volumetric MDMs describe an object as point cloud inside the object boundary and the coordinate of each point can be written in parametric functions. A generic heart mesh is registered on the TMRI with polar decomposition. A 3D MDM is generated and deformed with MR image tagging lines. Volumetric MDMs are deformed by calculating the dynamics function and minimizing the local Laplacian coordinates. The similarity transformation of each point is computed by assuming its neighboring points are making the same transformation. The deformation is computed iteratively until the control points match the target positions in the consecutive image frame. The 3D strain field is computed from the 3D displacement field with moving least squares. We demonstrate that MDMs outperformed the finite element method and the spline method with a numerical phantom. Meshless deformable models can track the trajectory of any material point in the myocardium and compute the 3D strain field of any particular area. The experimental results on in vivo healthy and patient heart MRI show that the MDM can fully recover the myocardium motion in three dimensions. PMID:25157446
NASA Astrophysics Data System (ADS)
Borsten, L.; Duff, M. J.; Ferrara, S.; Marrani, A.
2013-12-01
The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu-Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the world-sheet. An equivalent polynomial ‘Polyakov-type’ action is introduced using the so-called black hole potential. Such a construction allows for actions invariant under all groups of type E7, including E7 itself, although in this case the stringy interpretation is less clear.
Lagrangian Modeling of the Atmosphere
NASA Astrophysics Data System (ADS)
Schultz, Colin
2013-08-01
Like watching a balloon borne by the breeze, a Lagrangian model tracks a parcel of air as it flows through the atmosphere. Whether running forward or backward in time, Lagrangian models offer a powerful tool for tracking and understanding the fates, or origins, of atmospheric flows. In the AGU monograph Lagrangian Modeling of the Atmosphere, editors John Lin, Dominik Brunner, Christoph Gerbig, Andreas Stohl, Ashok Luhar, and Peter Webley explore the nuances of the modeling technique. In this interview Eos talks to Lin about the growing importance of Lagrangian modeling as the world settles on climate change mitigation strategies, the societal value of operational modeling, and how recent advances are making it possible to run these complex calculations at home.
Weyl's Lagrangian in teleparallel form
Burnett, James; Vassiliev, Dmitri
2009-10-15
The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable - the coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.
Lagrangian postprocessing of computational hemodynamics
Shadden, Shawn C.; Arzani, Amirhossein
2014-01-01
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 Lagrangian particle tracking, and other Lagrangian-based postprocessing. As described herein, Lagrangian 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 Lagrangian methods that have been used in post-processing velocity data of cardiovascular flows. PMID:25059889
Species doubling and effective Lagrangians
Creutz, M.; Tytgat, M.
1996-09-01
Coupling gauge fields to the chiral currents from an effective Lagrangian for pseudoscalar mesons naturally gives rise to a species doubling phenomenon similar to that seen with fermionic fields in lattice gauge theory. 17 refs.
Distributed Control by Lagrangian Steepest Descent
NASA Technical Reports Server (NTRS)
Wolpert, David H.; Bieniawski, Stefan
2004-01-01
Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information theory tells us that the most likely joint strategy of the players, given a value of the expectation of the overall control objective function, is the minimizer of a function o the joint strategy. So the goal of the system designer is to speed evolution of the joint strategy to that Lagrangian mhimbhgpoint,lowerthe expectated value of the control objective function, and repeat Here we elaborate the theory of algorithms that do this using local descent procedures, and that thereby achieve efficient, adaptive, distributed control.
Programmers manual for a one-dimensional Lagrangian transport model
Schoellhamer, D.H.; Jobson, H.E.
1986-01-01
A one-dimensional Lagrangian transport model for simulating water-quality constituents such as temperature, dissolved oxygen , and suspended sediment in rivers is presented in this Programmers Manual. Lagrangian 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)
Seakeeping with the semi-Lagrangian particle finite element method
NASA Astrophysics Data System (ADS)
Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio
2016-07-01
The application of the semi-Lagrangian 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 Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
NASA Astrophysics Data System (ADS)
Stevens, D.; Power, H.; Meng, C. Y.; Howard, D.; Cliffe, K. A.
2013-12-01
This work proposes an alternative decomposition for local scalable meshless RBF collocation. The proposed method operates on a dataset of scattered nodes that are placed within the solution domain and on the solution boundary, forming a small RBF collocation system around each internal node. Unlike other meshless local RBF formulations that are based on a generalised finite difference (RBF-FD) principle, in the proposed "finite collocation" method the solution of the PDE is driven entirely by collocation of PDE governing and boundary operators within the local systems. A sparse global collocation system is obtained not by enforcing the PDE governing operator, but by assembling the value of the field variable in terms of the field value at neighbouring nodes. In analogy to full-domain RBF collocation systems, communication between stencils occurs only over the stencil periphery, allowing the PDE governing operator to be collocated in an uninterrupted manner within the stencil interior. The local collocation of the PDE governing operator allows the method to operate on centred stencils in the presence of strong convective fields; the reconstruction weights assigned to nodes in the stencils being automatically adjusted to represent the flow of information as dictated by the problem physics. This "implicit upwinding" effect mitigates the need for ad-hoc upwinding stencils in convective dominant problems. Boundary conditions are also enforced within the local collocation systems, allowing arbitrary boundary operators to be imposed naturally within the solution construction. The performance of the method is assessed using a large number of numerical examples with two steady PDEs; the convection-diffusion equation, and the Lamé-Navier equations for linear elasticity. The method exhibits high-order convergence in each case tested (greater than sixth order), and the use of centred stencils is demonstrated for convective-dominant problems. In the case of linear elasticity
About non standard Lagrangians in cosmology
Dimitrijevic, Dragoljub D.; Milosevic, Milan
2012-08-17
A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.
Broom, Donald M
2006-01-01
The term adaptation is used in biology in three different ways. It may refer to changes which occur at the cell and organ level, or at the individual level, or at the level of gene action and evolutionary processes. Adaptation by cells, especially nerve cells helps in: communication within the body, the distinguishing of stimuli, the avoidance of overload and the conservation of energy. The time course and complexity of these mechanisms varies. Adaptive characters of organisms, including adaptive behaviours, increase fitness so this adaptation is evolutionary. The major part of this paper concerns adaptation by individuals and its relationships to welfare. In complex animals, feed forward control is widely used. Individuals predict problems and adapt by acting before the environmental effect is substantial. Much of adaptation involves brain control and animals have a set of needs, located in the brain and acting largely via motivational mechanisms, to regulate life. Needs may be for resources but are also for actions and stimuli which are part of the mechanism which has evolved to obtain the resources. Hence pigs do not just need food but need to be able to carry out actions like rooting in earth or manipulating materials which are part of foraging behaviour. The welfare of an individual is its state as regards its attempts to cope with its environment. This state includes various adaptive mechanisms including feelings and those which cope with disease. The part of welfare which is concerned with coping with pathology is health. Disease, which implies some significant effect of pathology, always results in poor welfare. Welfare varies over a range from very good, when adaptation is effective and there are feelings of pleasure or contentment, to very poor. A key point concerning the concept of individual adaptation in relation to welfare is that welfare may be good or poor while adaptation is occurring. Some adaptation is very easy and energetically cheap and
Lagrangian fronts in the ocean
NASA Astrophysics Data System (ADS)
Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.
2014-05-01
We introduce the concept of Lagrangian fronts (LFs) in the ocean and describe their importance for analyzing water mixing and transport and the specific features and differences from hydrological fronts. A method of calculating LFs in a given velocity field is proposed. Based on altimeter velocity fields from AVISO data in the northwestern Pacific, we calculate the Lagrangian synoptic maps and identify LFs of different spatial and temporal scales. Using statistical analysis of saury catches in different years according to the Goskomrybolovstvo (State Fisheries Committee of the Russian Federation), we show that LFs can serve as good indicators of places that are favorable for fishing.
COLAcode: COmoving Lagrangian Acceleration code
NASA Astrophysics Data System (ADS)
Tassev, Svetlin V.
2016-02-01
COLAcode is a serial particle mesh-based N-body code illustrating the COLA (COmoving Lagrangian Acceleration) method; it solves for Large Scale Structure (LSS) in a frame that is comoving with observers following trajectories calculated in Lagrangian 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.
Lagrangian continuum dynamics in ALEGRA.
Wong, Michael K. W.; Love, Edward
2007-12-01
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
A Student's Guide to Lagrangians and Hamiltonians
NASA Astrophysics Data System (ADS)
Hamill, Patrick
2013-11-01
Part I. Lagrangian Mechanics: 1. Fundamental concepts; 2. The calculus of variations; 3. Lagrangian dynamics; Part II. Hamiltonian Mechanics: 4. Hamilton's equations; 5. Canonical transformations: Poisson brackets; 6. Hamilton-Jacobi theory; 7. Continuous systems; Further reading; Index.
NASA Astrophysics Data System (ADS)
Bargatze, L. F.
2015-12-01
Active Data Archive Product Tracking (ADAPT) is a collection of software routines that permits one to generate XML metadata files to describe and register data products in support of the NASA Heliophysics Virtual Observatory VxO effort. ADAPT is also a philosophy. The ADAPT concept is to use any and all available metadata associated with scientific data to produce XML metadata descriptions in a consistent, uniform, and organized fashion to provide blanket access to the full complement of data stored on a targeted data server. In this poster, we present an application of ADAPT to describe all of the data products that are stored by using the Common Data File (CDF) format served out by the CDAWEB and SPDF data servers hosted at the NASA Goddard Space Flight Center. These data servers are the primary repositories for NASA Heliophysics data. For this purpose, the ADAPT routines have been used to generate data resource descriptions by using an XML schema named Space Physics Archive, Search, and Extract (SPASE). SPASE is the designated standard for documenting Heliophysics data products, as adopted by the Heliophysics Data and Model Consortium. The set of SPASE XML resource descriptions produced by ADAPT includes high-level descriptions of numerical data products, display data products, or catalogs and also includes low-level "Granule" descriptions. A SPASE Granule is effectively a universal access metadata resource; a Granule associates an individual data file (e.g. a CDF file) with a "parent" high-level data resource description, assigns a resource identifier to the file, and lists the corresponding assess URL(s). The CDAWEB and SPDF file systems were queried to provide the input required by the ADAPT software to create an initial set of SPASE metadata resource descriptions. Then, the CDAWEB and SPDF data repositories were queried subsequently on a nightly basis and the CDF file lists were checked for any changes such as the occurrence of new, modified, or deleted
A meshless EFG-based algorithm for 3D deformable modeling of soft tissue in real-time.
Abdi, Elahe; Farahmand, Farzam; Durali, Mohammad
2012-01-01
The meshless element-free Galerkin method was generalized and an algorithm was developed for 3D dynamic modeling of deformable bodies in real time. The efficacy of the algorithm was investigated in a 3D linear viscoelastic model of human spleen subjected to a time-varying compressive force exerted by a surgical grasper. The model remained stable in spite of the considerably large deformations occurred. There was a good agreement between the results and those of an equivalent finite element model. The computational cost, however, was much lower, enabling the proposed algorithm to be effectively used in real-time applications. PMID:22356947
Effective Lagrangian for Nonrelativistic Systems
NASA Astrophysics Data System (ADS)
Watanabe, Haruki; Murayama, Hitoshi
2014-07-01
The effective Lagrangian for Nambu-Goldstone bosons (NGBs) in systems without Lorentz invariance has a novel feature that some of the NGBs are canonically conjugate to each other, hence describing 1 dynamical degree of freedom by two NGB fields. We develop explicit forms of their effective Lagrangian up to the quadratic order in derivatives. We clarify the counting rules of NGB degrees of freedom and completely classify possibilities of such canonically conjugate pairs based on the topology of the coset spaces. Its consequence on the dispersion relations of the NGBs is clarified. We also present simple scaling arguments to see whether interactions among NGBs are marginal or irrelevant, which justifies a lore in the literature about the possibility of symmetry breaking in 1+1 dimensions.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of 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 Lagrangian 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, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian 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, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
Zhao, J.M.; Tan, J.Y.; Liu, L.H.
2013-01-01
A new second order form of radiative transfer equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order radiative transfer equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the radiative transfer equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order radiative transfer equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order radiative transfer equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form radiative transfer equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve radiative transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve radiative transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.
A practical Lagrangian transport model
Jobson, Harvey E.
1980-01-01
An unconditionally stable and practical transport model for use in upland streams and rivers has been developed and verified. Basing the model on the Lagrangian, rather than the Eulerian, reference frame greatly reduces the numerical problems associated with solving the advective terms of the convective-diffusion equation. The model contains almost no numerical dispersion, is conceptually simple, and is relatively easy to code. Model results closely simulated dye concentrations measured in the Chattahoochee River near Atlanta, Ga. under highly unsteady flow conditions. (USGS)
Lagrangian coherent structures in hurricanes
NASA Astrophysics Data System (ADS)
Lipinski, Doug; Mohseni, Kamran
2011-11-01
We present the results of a ``surface tracking'' algorithm for efficiently computing Lagrangian coherent structure (LCS) surfaces in three dimensions. The algorithm is applied to data from a Weather Research and Forecasting simulation of hurricane Rita. The highly complicated LCS surfaces reveal complex dynamics and transport in the hurricane, particularly in the lower atmosphere boundary layer and the upper level outflow. The lower level transport in the hurricane is of particular importance for accurate intensity prediction in hurricane forecasts due to the uncertainty in the ocean-atmosphere interaction. Understanding the lower level transport and mixing behavior in hurricanes could lead to significant advances in hurricane intensity prediction.
Isogeometric analysis of Lagrangian hydrodynamics
NASA Astrophysics Data System (ADS)
Bazilevs, Y.; Akkerman, I.; Benson, D. J.; Scovazzi, G.; Shashkov, M. J.
2013-06-01
Isogeometric analysis of Lagrangian shock hydrodynamics is proposed. The Euler equations of compressible hydrodynamics in the weak form are discretized using Non-Uniform Rational B-Splines (NURBS) in space. The discretization has all the advantages of a higher-order method, with the additional benefits of exact symmetry preservation and better per-degree-of-freedom accuracy. An explicit, second-order accurate time integration procedure, which conserves total energy, is developed and employed to advance the equations in time. The performance of the method is examined on a set of standard 2D and 3D benchmark examples, where good quality of the computational results is attained.
The Lagrangian structure of Calogero's goldfish model
NASA Astrophysics Data System (ADS)
Jairuk, U.; Yoo-Kong, S.; Tanasittikosol, M.
2015-05-01
From a Lax pair ansatz, we obtain the discrete-time rational Calogero goldfish system. The discrete-time Lagrangians of the system have a discrete-time 1- form structure similar to the Lagrangians in the discrete-time Calogero-Moser system and the discrete-time Ruijsenaars-Schneider system. We obtain the Lagrangian hierarchy for the system as a result of a two-step passage to the continuum limit. As expected, the continuous-time Lagrangian preserves the 1- form structure. We establish a connection with the Kadomtsev-Petviashvili lattice systems.
NASA Astrophysics Data System (ADS)
Sátor, Ladislav; Sládek, Vladimír; Sládek, Ján
2014-03-01
A numerical analysis based on the meshless local Petrov- Galerkin (MLPG) method is proposed for a functionally graded material FGM (FGMfunctionally graded material) beam. The planar bending of the beam is considered with a transversal gradation of Young's modulus and a variable depth of the beam. The collocation formulation is constructed from the equilibrium equations for the mechanical fields. Dirac's delta function is employed as a test function in the derivation of a strong formulation. The Moving Least Squares (MLS) approximation technique is applied for an approximation of the spatial variations of all the physical quantities. An investigation of the accuracy, the convergence of the accuracy, the computational efficiency and the effect of the level of the gradation of Young's modulus on the behaviour of coupled mechanical fields is presented in various boundary value problems for a rectangular beam with a functionally graded Young's modulus.
Lagrangian analysis. Modern tool of the dynamics of solids
NASA Astrophysics Data System (ADS)
Cagnoux, J.; Chartagnac, P.; Hereil, P.; Perez, M.; Seaman, L.
Lagrangian specificity of the required measurements is assured by the fact that a transducer enclosed within a solid material is necessarily linked in motion to the particles of the material which surround it. This Lagrangian instrumentation is described in the second chapter. The authors are concerned with the techniques considered today to be the most effective. These are, for stress : piezoresistive gauges (50 Ω and low impedance) and piezoelectric techniques (PVF2 gauges, quartz transducers) ; and for particle velocity : electromagnetic gauges, VISAR and IDL Doppler laser interferometers. In each case both the physical principles as well as techniques of use are set out in detail. For the most part, the authors use their own experience to describe the calibration of these instrumentation systems and to compare their characteristics : measurement range, response time, accuracy, useful recording time, detection area... These characteristics should be taken into account by the physicist when he has to choose the instrumentation systems best adapted to the Lagrangian analysis he intends to apply to any given material. The discussion at the end of chapter 2 should guide his choice both for plane and spherical one-dimensional motions. The third chapter examines to what extent the accuracy of Lagrangian analysis is affected by the accuracies of the numerical analysis methods and experimental techniques. By means of a discussion of different cases of analysis, the authors want to make the reader aware of the different kinds of sources of errors that may be encountered. This work brings up to date the state of studies on Lagrangian analysis methods based on a wide review of bibliographical sources together with the contribution made to research in this field by the four authors themselves in the course of the last ten years. Le formage des métaux par explosif, la consolidation dynamique des poudres, la balistique terminale, l'abattage des roches par explosif, sont autant d
Parallel computing using a Lagrangian formulation
NASA Technical Reports Server (NTRS)
Liou, May-Fun; Loh, Ching Yuen
1991-01-01
A new Lagrangian formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The Lagrangian 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 Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.
NASA Astrophysics Data System (ADS)
Owusu-Banson, Derek
In recent times, a variety of industries, applications and numerical methods including the meshless method have enjoyed a great deal of success by utilizing the graphical processing unit (GPU) as a parallel coprocessor. These benefits often include performance improvement over the previous implementations. Furthermore, applications running on graphics processors enjoy superior performance per dollar and performance per watt than implementations built exclusively on traditional central processing technologies. The GPU was originally designed for graphics acceleration but the modern GPU, known as the General Purpose Graphical Processing Unit (GPGPU) can be used for scientific and engineering calculations. The GPGPU consists of massively parallel array of integer and floating point processors. There are typically hundreds of processors per graphics card with dedicated high-speed memory. This work describes an application written by the author, titled GaussianRBF to show the implementation and results of a novel meshless method that in-cooperates the collocation of the Gaussian radial basis function by utilizing the GPU as a parallel co-processor. Key phases of the proposed meshless method have been executed on the GPU using the NVIDIA CUDA software development kit. Especially, the matrix fill and solution phases have been carried out on the GPU, along with some post processing. This approach resulted in a decreased processing time compared to similar algorithm implemented on the CPU while maintaining the same accuracy.
Alternative Expression for the Electromagnetic Lagrangian
NASA Astrophysics Data System (ADS)
Saldanha, Pablo L.
2016-06-01
We reintroduce an alternative expression for the Lagrangian density that governs the interaction of a charged particle with external electromagnetic fields, proposed by Livens about one century ago. This Lagrangian is written in terms of the local superposition of the particle fields with the applied electromagnetic fields, not in terms of the particle charge and of the electromagnetic potentials as is usual. Here, we show that the total Lagrangian for a set of charged particles assumes a simple elegant form with the alternative formulation, giving an aesthetic support for it. We also show that the alternative Lagrangian is equivalent to the traditional one in their domain of validity and that it provides an interesting description of the Aharonov-Bohm effect.
Option volatility and the acceleration Lagrangian
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.; Cao, Yang
2014-01-01
This paper develops a volatility formula for option on an asset from an acceleration Lagrangian model and the formula is calibrated with market data. The Black-Scholes model is a simpler case that has a velocity dependent Lagrangian. The acceleration Lagrangian 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 Lagrangian is fixed. The call option price is obtained using the conditional probability and the path integral method.
Relativistic Lagrangian displacement field and tensor perturbations
NASA Astrophysics Data System (ADS)
Rampf, Cornelius; Wiegand, Alexander
2014-12-01
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the Lagrangian frame. These techniques are (a) from defining a local set of Eulerian coordinates embedded into the Lagrangian frame; (b) from performing a specific gauge transformation; and (c) from a fully nonperturbative approach based on the Arnowitt-Deser-Misner (ADM) split. The latter approach shows that this decomposition is not tied to a specific perturbative formulation for the solution of the Einstein equations. Rather, it can be defined at the level of the nonperturbative coordinate change from the Lagrangian to the Eulerian description. Studying such different techniques is useful because it allows us to compare and develop further the various approximation techniques available in the Lagrangian formulation. We find that one has to solve the gravitational wave equation in the relativistic analysis, otherwise the corresponding Newtonian limit will necessarily contain spurious nonpropagating tensor artifacts at second order in the Eulerian frame. We also derive the magnetic part of the Weyl tensor in the Lagrangian frame, and find that it is not only excited by gravitational waves but also by tensor perturbations which are induced through the nonlinear frame dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a Λ CDM Universe in the presence of a local primordial non-Gaussian component. Finally, we also comment on recent claims about whether mass conservation in the Lagrangian frame is violated.
Lagrangian and arbitrary Lagrangian Eulerian simulations of complex roll-forming processes
NASA Astrophysics Data System (ADS)
Crutzen, Yanick; Boman, Romain; Papeleux, Luc; Ponthot, Jean-Philippe
2016-04-01
The Arbitrary Lagrangian Eulerian (ALE) formalism is a breakthrough technique in the numerical simulation of the continuous-type roll-forming process. In contrast to the classical Lagrangian approach, the ALE formalism can compute the hopefully stationary state for the entire mill length with definitely effortless set-up tasks thanks to a nearly-stationary mesh. In this paper, advantages of ALE and Lagrangian formalisms are extensively discussed for simulating such continuous-type processes. Through a highly complex industrial application, the ease of use of ALE modelling is illustrated with the in-house code METAFOR. ALE and Lagrangian results are in good agreement with each other.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding.
Krause, Katharina; Klopper, Wim
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian 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 Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian. PMID:26827193
An experimental Lagrangian study of inhomgeneous turbulence
NASA Astrophysics Data System (ADS)
Stelzenmuller, Nickolas; Mordant, Nicolas
2015-11-01
We investigate experimentally the Lagrangian properties of inhomogeneous turbulence in the general scope of dispersion studies in natural and industrial flows. Lagrangian studies of homogeneous turbulence are becoming common, but very little Lagrangian experimental data exists for inhomogeneous turbulence despite the vast range of applications. Particle tracking velocimetry using a very high speed camera in a fully developed turbulent channel flow in water is achieved at ReH = 33 , 000 . This technique provides Lagrangian velocity and acceleration statistics fully resolved at the smallest turbulent scales near the wall. These statistics, conditioned by the distance to the wall, allow the the investigation of the inhomogeneity of the statistical properties of this flow. Autocorrelations of velocity and acceleration show increasing Lagrangian turbulent scales as distance from the wall increases, as well as decreasing anisotropy. PDF's and moments of Lagrangian quantities are presented by showing the evolution of structure functions across the boundary layer. These results are compared to direct numerical simulation results from a similar flow, and their implications for stochastic models of inhomogeneous flows are discussed.
Multiphase Interface Tracking with Fast Semi-Lagrangian Contouring.
Li, Xiaosheng; He, Xiaowei; Liu, Xuehui; Zhang, Jian J; Liu, Baoquan; Wu, Enhua
2016-08-01
We propose a semi-Lagrangian method for multiphase interface tracking. In contrast to previous methods, our method maintains an explicit polygonal mesh, which is reconstructed from an unsigned distance function and an indicator function, to track the interface of arbitrary number of phases. The surface mesh is reconstructed at each step using an efficient multiphase polygonization procedure with precomputed stencils while the distance and indicator function are updated with an accurate semi-Lagrangian path tracing from the meshes of the last step. Furthermore, we provide an adaptive data structure, multiphase distance tree, to accelerate the updating of both the distance function and the indicator function. In addition, the adaptive structure also enables us to contour the distance tree accurately with simple bisection techniques. The major advantage of our method is that it can easily handle topological changes without ambiguities and preserve both the sharp features and the volume well. We will evaluate its efficiency, accuracy and robustness in the results part with several examples. PMID:26353373
Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum
NASA Astrophysics Data System (ADS)
Jang, Juhi; LeFloch, Philippe G.; Masmoudi, Nader
2016-03-01
We study the evolution of a compressible fluid surrounded by vacuum and introduce a new symmetrization in Lagrangian coordinates that allows us to encompass both relativistic and non-relativistic fluid flows. The problem under consideration is a free boundary problem of central interest in compressible fluid dynamics and, from the mathematical standpoint, the main challenge to be overcome lies in the loss of regularity in the fluid variables near the free boundary. Based on our Lagrangian formulation, we establish the necessary a priori estimates in weighted Sobolev spaces which are adapted to this loss of regularity.
Meshless Solution of the Vlasov Equation Using a Low Discrepancy Sequence
Warnock, R.L.; Ellison, J.A.; Heinemann, K.; Zhang, G.Q.; /New Mexico U.
2009-01-28
A good method for solving the nonlinear Vlasov equation is the semi-Lagrangian algorithm, in which the phase space density is represented by its values on a fixed Cartesian grid with interpolation to off-grid points. At each time step, orbits are followed backward from grid points. Since this method is expensive with phase space dimension D > 2, we seek a more efficient discretization of the density. Taking a cue from the theory of numerical quadrature in high dimensions, we explore the idea of replacing the grid by scattered data sites from a low-discrepancy (quasirandom) sequence. We hope to see a reduction in the required number of sites, especially for D > 2. In our first implementation we follow forward orbits rather than backward, and work only with D = 2. We are able to reduce the number of sites by a factor of 8, at least for a limited time of integration. A much bigger reduction is expected in higher dimensions.
Lagrangian floats as sea floor imaging platforms
NASA Astrophysics Data System (ADS)
Roman, Chris; Inglis, Gabrielle; McGilvray, Bryan
2011-10-01
There is a persistent need for high resolution photographic images of the sea floor and associated biota for marine habitat classification and fisheries stock assessment. This paper presents a novel low cost Lagrangian imaging platform that offers high quality images with reduced operational demands in comparison to existing methodologies such as diver surveys, drop cameras, ship towed systems and dedicated remote or autonomous underwater vehicles. The platform consists of a recently developed bottom following Lagrangian float fit with down looking stereo cameras and strobe lighting. The float can use active ballasting to perform constant altitude photographic drift surveys in coastal waters over varying bathymetry. Images from the float can be used to create large photomosaics, stereographic bathymetry estimates and image-derived current measurements. Test data are presented to demonstrate the operation of the Lagrangian float and summarize the data products.
Parallel computing using a Lagrangian formulation
NASA Technical Reports Server (NTRS)
Liou, May-Fun; Loh, Ching-Yuen
1992-01-01
This paper adopts a new Lagrangian formulation of the Euler equation for the calculation of two dimensional supersonic steady flow. The Lagrangian 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 Lagrangian formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a finite volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, we have achieved better than six times speed-up on a 8192-processor CM-2 over a single processor of a CRAY-2.
Lagrangian solution of supersonic real gas flows
Loh, Chingyuen; Liou, Mengsing )
1993-01-01
This paper details the procedure of the real gas Riemann solution in the Lagrangian approach originally proposed by Loh and Hui for perfect gases. The extension to real gases is nontrivial and requires substantial development of an exact real-gas Riemann solver for the Lagrangian form of conservation laws. The first-order Gudonov scheme is enhanced for accuracy by adding limited anti-diffusive terms according to Sweby. Extensive calculations were made to test the accuracy and robustness of the present real gas Lagrangian approach, including complex wave interactions of different types. The accuracy for capturing 2D oblique waves and slip line is clearly demonstrated. In addition, we also show the real gas effect in a generic engine nozzle.
Lagrangian solution of supersonic real gas flows
NASA Technical Reports Server (NTRS)
Loh, Ching-Yuen; Liou, Meng-Sing
1993-01-01
The present extention of a Lagrangian 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 Lagrangian 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.
Lagrangian analysis of a convective mixed layer
NASA Astrophysics Data System (ADS)
D'Asaro, Eric A.; Winters, Kraig B.; Lien, Ren-Chieh
2002-05-01
We characterize and quantify the transport of heat (Boussinesq density) in a highly idealized entraining convective mixed layer based on simulations of Lagrangian measurements in a two-dimensional model. The primary objectives are to assess and explore the merits and difficulties in estimating the heat budget from perfect and imperfect Lagrangian floats. A significant advantage of Lagrangian measurements is that the time derivative of temperature along these trajectories gives a direct measure of the diffusive heat flux. Using simulated perfect Lagrangian floats, estimates of the surface buoyancy flux, the depth of the mixed layer, vertical profiles of advective and diffusive heat flux, and the overall rate of cooling are shown to agree accurately with the known results extracted from the Eulerian simulations. The Lagrangian nature of the data is exploited to reveal the structure of the flow within the convective layer and to quantify the heat fluxes associated with the different types of eddies. Phase plots of Lagrangian trajectories in density-depth space reveal three distinct classes of motions: (1) plumes, which develop in the cold, heavy near-surface thermal boundary layer and plunge into the mixed layer interior carrying heavy water downward; (2) interior turbulence, comprising random motions between the base of the thermal boundary layer and the base of the surface mixed layer; and (3) entrainment of interior water into plumes below the thermal boundary layer, i.e., a transition from class 2 to class 1. Plumes dominate the heat transport. Simulations were also made using slightly buoyant floats; these are not perfectly Lagrangian. Buoyancy concentrates the floats near the surface resulting in an oversampling of the stronger plumes. Making the same heat budget calculations as with the perfect floats results in a nonzero estimated Lagrangian heating rate in the interior and a curved profile of vertical heat flux that is up to 3 times too large. The local time
EULER-LAGRANGIAN COMPUTATIONS IN ESTUARINE HYDRODYNAMICS.
Cheng, Ralph T.
1983-01-01
The transport of conservative and suspended matter in fluid flows is a phenomenon of Lagrangian nature because the process is usually convection dominant. Nearly all numerical 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 Lagrangian computational techniques.
On tide-induced lagrangian residual current and residual transport: 1. Lagrangian residual current
Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi
1986-01-01
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 Lagrangian 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 Lagrangian and Eulerian residual currents. When k is small, the first-order Lagrangian residual is shown to be the sum of the Eulerian residual current and the Stokes drift. The Lagrangian residual drift velocity or the second-order Lagrangian residual current has been shown to be dependent on the phase of tidal current. The Lagrangian 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 Lagrangian residual current.
On an order reduction theorem in the Lagrangian formalism
NASA Astrophysics Data System (ADS)
Grigore, D. R.
1996-11-01
We provide a new proof of a important theorem in the Lagrangian formalism about necessary and sufficient conditions for a second-order variational system of equations to follow from a first-order Lagrangian.
a Lagrangian Philosophy for Plume Modeling.
NASA Astrophysics Data System (ADS)
Frick, Walter Eugen
A Lagrangian plume model is described that has proven useful in water and air applications. It contrasts sharply with earlier Eulerian integral flux models even though they are shown to be equivalent. As an alternative and complementary approach, the Lagrangian formulation offers new insights into the problem. As a result, it furnished the first accurate statement of the Projected Area Entrainment (PAE) hypothesis that describes the assimilation of moving ambient fluid into the plume. The hypothesis allows--without tuning--average motion and dilution characteristics to be predicted for the first time. Further contemplation of the Lagrangian plume element resulted in the identification of the Negative Volume Anomaly (NVA). The NVA is an inconsistency in control volume conception resulting from the intersection of the cross-sections that bound it, causing the anomalous production of negative volume. Although the Lagrangian plume model, UM, has been adopted by the U.S. Environmental Protection Agency, is used in over a dozen foreign countries, and has been verified independently, a pervasive bias against the approach makes it difficult to publish findings in the peer reviewed literature. A case study describing the problem is presented. This analysis suggests that the phenomenon is not unique to plume modeling. The contributing causes are perpetuated by the closedness of the peer review system. Recommendations are given for improving peer review procedures to open the process to inspection. They include simple measures modifying anonymity and allowing authors to submit to multiple journals simultaneously.
Examination of Eulerian and Lagrangian Coordinate Systems.
ERIC Educational Resources Information Center
Remillard, Wilfred J.
1978-01-01
Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. Gives examples which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems. (Author/GA)
Three-dimensional free Lagrangian hydrodynamics
Trease, H.E.
1985-01-01
The purpose of the discussion is to describe the development of a 3-D free Lagrangian hyrodynamics algorithm. The 3-D algorithm is an outgrowth of an earlier 2-D free Lagrange model. Only the more pertinent issues of the free Lagrange algorithm are presented. A complete production code is being developed to support the free Lagrange algorithm described. 4 refs.
Chen Ting; Kim, Sung; Goyal, Sharad; Jabbour, Salma; Zhou Jinghao; Rajagopal, Gunaretnum; Haffty, Bruce; Yue Ning
2010-01-15
Purpose: High-speed nonrigid registration between the planning CT and the treatment CBCT data is critical for real time image guided radiotherapy (IGRT) to improve the dose distribution and to reduce the toxicity to adjacent organs. The authors propose a new fully automatic 3D registration framework that integrates object-based global and seed constraints with the grayscale-based ''demons'' algorithm. Methods: Clinical objects were segmented on the planning CT images and were utilized as meshless deformable models during the nonrigid registration process. The meshless models reinforced a global constraint in addition to the grayscale difference between CT and CBCT in order to maintain the shape and the volume of geometrically complex 3D objects during the registration. To expedite the registration process, the framework was stratified into hierarchies, and the authors used a frequency domain formulation to diffuse the displacement between the reference and the target in each hierarchy. Also during the registration of pelvis images, they replaced the air region inside the rectum with estimated pixel values from the surrounding rectal wall and introduced an additional seed constraint to robustly track and match the seeds implanted into the prostate. The proposed registration framework and algorithm were evaluated on 15 real prostate cancer patients. For each patient, prostate gland, seminal vesicle, bladder, and rectum were first segmented by a radiation oncologist on planning CT images for radiotherapy planning purpose. The same radiation oncologist also manually delineated the tumor volumes and critical anatomical structures in the corresponding CBCT images acquired at treatment. These delineated structures on the CBCT were only used as the ground truth for the quantitative validation, while structures on the planning CT were used both as the input to the registration method and the ground truth in validation. By registering the planning CT to the CBCT, a
Lagrangian statistics in laboratory 2D turbulence
NASA Astrophysics Data System (ADS)
Xia, Hua; Francois, Nicolas; Punzmann, Horst; Shats, Michael
2014-05-01
Turbulent mixing in liquids and gases is ubiquitous in nature and industrial flows. Understanding statistical properties of Lagrangian trajectories in turbulence is crucial for a range of problems such as spreading of plankton in the ocean, transport of pollutants, etc. Oceanic data on trajectories of the free-drifting instruments, indicate that the trajectory statistics can often be described by a Lagrangian integral scale. Turbulence however is a state of a flow dominated by a hierarchy of scales, and it is not clear which of these scales mostly affect particle dispersion. Moreover, coherent structures often coexist with turbulence in laboratory experiments [1]. The effect of coherent structures on particle dispersion in turbulent flows is not well understood. Recent progress in scientific imaging and computational power made it possible to tackle this problem experimentally. In this talk, we report the analysis of the higher order Lagrangian statistics in laboratory two-dimensional turbulence. Our results show that fluid particle dispersion is diffusive and it is determined by a single measurable Lagrangian scale related to the forcing scale [2]. Higher order moments of the particle dispersion show strong self-similarity in fully developed turbulence [3]. Here we introduce a new dispersion law that describes single particle dispersion during the turbulence development [4]. These results offer a new way of predicting dispersion in turbulent flows in which one of the low energy scales are persistent. It may help better understanding of drifter Lagrangian statistics in the regions of the ocean where small scale coherent eddies are present [5]. Reference: 1. H. Xia, H. Punzmann, G. Falkovich and M. Shats, Physical Review Letters, 101, 194504 (2008) 2. H. Xia, N. Francois, H. Punzmann, and M. Shats, Nature Communications, 4, 2013 (2013) 3. R. Ferrari, A.J. Manfroi , W.R. Young, Physica D 154 111 (2001) 4. H. Xia, N. Francois, H. Punzmann and M. Shats, submitted (2014
NASA Astrophysics Data System (ADS)
Diggs, Angela; Balachandar, S.
2016-05-01
The present work addresses numerical methods required to compute particle volume fraction or number density. Local volume fraction of the lth particle, αl, is the quantity of foremost importance in calculating the gas-mediated particle-particle interaction effect in multiphase flows. A general multiphase flow with a distribution of Lagrangian particles inside a fluid flow discretized on an Eulerian grid is considered. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the grid cell for Eulerian-Lagrangian simulations. In Grid-Based (GB) methods the particle volume fraction is first obtained within each grid cell as an Eulerian quantity and then the local particle volume fraction associated with any Lagrangian particle can be obtained from interpolation. The second class of methods presented are Particle-Based (PB) methods, where particle volume fraction will first be obtained at each particle as a Lagrangian quantity, which then can be projected onto the Eulerian grid. Traditionally, the GB methods are used in multiphase flow, but sub-grid resolution can be obtained through use of the PB methods. By evaluating the total error, and its discretization, bias and statistical error components, the performance of the different PB methods is compared against several common GB methods of calculating volume fraction. The standard von Neumann error analysis technique has been adapted for evaluation of rate of convergence of the different methods. The discussion and error analysis presented focus on the volume fraction calculation, but the methods can be extended to obtain field representations of other Lagrangian quantities, such as particle velocity and temperature.
NASA Technical Reports Server (NTRS)
Lewis, Robert Michael; Torczon, Virginia
1998-01-01
We give a pattern search adaptation of an augmented Lagrangian method due to Conn, Gould, and Toint. The algorithm proceeds by successive bound constrained minimization of an augmented Lagrangian. In the pattern search adaptation we solve this subproblem approximately using a bound constrained pattern search method. The stopping criterion proposed by Conn, Gould, and Toint for the solution of this subproblem requires explicit knowledge of derivatives. Such information is presumed absent in pattern search methods; however, we show how we can replace this with a stopping criterion based on the pattern size in a way that preserves the convergence properties of the original algorithm. In this way we proceed by successive, inexact, bound constrained minimization without knowing exactly how inexact the minimization is. So far as we know, this is the first provably convergent direct search method for general nonlinear programming.
NASA Astrophysics Data System (ADS)
Rad, Jamal Amani; Parand, Kourosh; Abbasbandy, Saeid
2015-05-01
For the first time in mathematical finance field, we propose the local weak form meshless methods for option pricing; especially in this paper we select and analysis two schemes of them named local boundary integral equation method (LBIE) based on moving least squares approximation (MLS) and local radial point interpolation (LRPI) based on Wu's compactly supported radial basis functions (WCS-RBFs). LBIE and LRPI schemes are the truly meshless methods, because, a traditional non-overlapping, continuous mesh is not required, either for the construction of the shape functions, or for the integration of the local sub-domains. In this work, the American option which is a free boundary problem, is reduced to a problem with fixed boundary using a Richardson extrapolation technique. Then the θ -weighted scheme is employed for the time derivative. Stability analysis of the methods is analyzed and performed by the matrix method. In fact, based on an analysis carried out in the present paper, the methods are unconditionally stable for implicit Euler (θ = 0) and Crank-Nicolson (θ = 0.5) schemes. It should be noted that LBIE and LRPI schemes lead to banded and sparse system matrices. Therefore, we use a powerful iterative algorithm named the Bi-conjugate gradient stabilized method (BCGSTAB) to get rid of this system. Numerical experiments are presented showing that the LBIE and LRPI approaches are extremely accurate and fast.
Alternative refined Gribov-Zwanziger Lagrangian
Gracey, J. A.
2010-10-15
We consider the implications of the condensation of a general local Becchi-Rouet-Stora-Tyutin invariant dimension two operator built out of the localizing ghost fields of the Gribov-Zwanziger Lagrangian which is a localized Lagrangian incorporating the Gribov problem in the Landau gauge. For different color tensor projections of the general operator, the properties of a frozen gluon propagator and unenhanced Faddeev-Popov ghost propagator, which are observed in lattice computations, can be reproduced. The alternative possibilities are distinguished by the infrared structure of the propagators of the spin-1 fields, other than those of the gluon and Faddeev-Popov ghost, for which there is no numerical simulation data to compare with yet.
Uses and abuses of effective Lagrangians
NASA Astrophysics Data System (ADS)
Burgess, C. P.; London, David
1993-11-01
Motivated by past and recent analyses we critically reexamine the use of effective Lagrangians in the literature to constrain new physics and to determine the ``physics reach'' of future experiments. We demonstrate that many calculations, such as those involving anomalous trilinear gauge-boson couplings, either considerably overestimate loop-induced effects or give ambiguous answers. The source of these problems is the use of cutoffs to evaluate the size of such operators in loop diagrams. In contrast with other critiques of these loop estimates, we prove that the inclusion of nonlinearly realized gauge invariance into the low-energy Lagrangian is irrelevant to this conclusion. We use an explicit example using known multi-Higgs-boson physics above the weak scale to underline these points. We show how to draw conclusions regarding the nature of the unknown high-energy physics without making reference to low-energy cutoffs.
Lagrangian computation of inviscid compressible flows
NASA Technical Reports Server (NTRS)
Klopfer, G. H.
1978-01-01
A Lagrangian method is developed to solve the Euler equations of gas dynamics. The solution of the equations is obtained by a numerical computation with the well-known Flux-Corrected-Transport (FCT) numerical method. This procedure is modified so that the boundary treatment is accurate and relatively simple. Shock waves and other flow discontinuities are captured monotonically without any type of fitting procedures. The Lagrangian method is employed so that the problem of mesh generation is completely avoided. The method is applicable to all Mach numbers except the low subsonic range where compressibility effects are small. The method is applied to a one-dimensional Riemann problem (shock tube) and to a two-dimensional supersonic channel flow with reflecting shock waves.
Measuring non-local Lagrangian peak bias
NASA Astrophysics Data System (ADS)
Biagetti, Matteo; Chan, Kwan Chuen; Desjacques, Vincent; Paranjape, Aseem
2014-06-01
We investigate non-local Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We begin by writing down a bias expansion which includes all the bias terms, including the non-local ones. Having checked that the model furnishes a reasonable fit to the halo mass function, we develop a one-point cross-correlation technique to measure bias factors associated with χ2-distributed quantities. We validate the method with numerical realizations of peaks of Gaussian random fields before we apply it to N-body simulations. We focus on the lowest (quadratic) order non-local contributions -2χ _{10}(k_1\\cdot k_2) and χ _{01}[3(k_1\\cdot k_2)^2-k_1^2 k_2^2], where k_1, k_2 are wave modes. We can reproduce our measurement of χ10 if we allow for an offset between the Lagrangian halo centre-of-mass and the peak position. The sign and magnitude of χ10 is consistent with Lagrangian haloes sitting near linear density maxima. The resulting contribution to the halo bias can safely be ignored for M = 1013 M⊙ h-1, but could become relevant at larger halo masses. For the second non-local bias χ01 however, we measure a much larger magnitude than predicted by our model. We speculate that some of this discrepancy might originate from non-local Lagrangian contributions induced by non-spherical collapse.
Lagrangian description of the radiation damping
NASA Astrophysics Data System (ADS)
Barone, P. M. V. B.; Mendes, A. C. R.
2007-05-01
We present a Lagrangian formalism to the dissipative system of a charge interacting with its own radiation field, which gives rise to the radiation damping [W. Heitler, The Quantum Theory of Radiation, third ed., Dover, New York, 1970; J.D. Jackson, Classical Electrodynamics, second ed., Wiley, New York, 1975 (Chapters 14, 17); G.N. Plass, Rev. Mod. Phys. 33 (1961) 37], by the indirect representation doubling the phase-space dimensions.
Perturbative Lagrangian approach to gravitational instability.
NASA Astrophysics Data System (ADS)
Bouchet, F. R.; Colombi, S.; Hivon, E.; Juszkiewicz, R.
1995-04-01
This paper deals with the time evolution in the matter era of perturbations in Friedman-Lemaitre models with arbitrary density parameter {OMEGA}, with either a zero cosmological constant, {LAMBDA}=0, or with a non-zero cosmological constant in a spatially flat Universe. Unlike the classical Eulerian approach where the density contrast is expanded in a perturbative series, this analysis relies instead on a perturbative expansion of particles trajectories in Lagrangian coordinates. This brings a number of advantages over the classical analysis. In particular, it enables the description of stronger density contrasts. Indeed the linear term in the Lagrangian perturbative series is the famous Zeldovich approximate solution (1970). The idea to consider the higher order terms was introduced by Moutarde et al. (1991), generalized by Bouchet et al. (1992), and further developed by many others. We present here a systematic and detailed account of this approach. We give analytical results (or fits to numerical results) up to the third order (which is necessary to compute, for instance, the four point spatial correlation function or the corrections to the linear evolution of the two-point correlation function, as well as the secondary temperature anisotropies of the Cosmic Microwave Background). We then proceed to explore the link between the Lagrangian description and statistical measures. We show in particular that Lagrangian perturbation theory provides a natural framework to compute the effect of redshift distortions, using the skewness of the density distribution function as an example. Finally, we show how well the second order theory does as compared to other approximations in the case of spherically symmetric perturbations. We also compare this second order approximation and Zeldovich solution to N-body simulations with scale-free (n=-2) Gaussian initial conditions. We find that second order theory is both simple and powerful.
Surface coastal circulation patterns by in-situ detection of Lagrangian coherent structures
NASA Astrophysics Data System (ADS)
Nencioli, F.; d'Ovidio, F.; Doglioli, A. M.; Petrenko, A. A.
2011-09-01
Coastal transport and cross-shelf exchanges are important factors in controlling the dispersal of human and river discharged pollutants, as well as the advection of nutrients and larvae. Altimetry-based Lagrangian techniques provide accurate information on horizontal transport in the open ocean but are unreliable close to the coast. In order to circumvent this problem, during the Lagrangian Transport Experiment 2010 campaign (Latex10, 1-24 September 2010) transport structures in the western Gulf of Lion were investigated with an adaptive sampling strategy, combining satellite data, ship-based ADCP measurements, and iterative Lagrangian drifter releases. The sampling strategy was able to identify errors in the surface transport patterns derived from altimetry, and to track with in-situ observations attractive and repelling Lagrangian coherent structures for a period of 12 days. The structures maintained a corridor ˜10 km-wide, roughly parallel to the coast, along which waters from the continental shelf leave the gulf. This is confirmed by high-resolution SST imagery. The use of this sampling strategy to explore surface transport structures may provide important information for the environmental management of coastal regions, and may serve for validating future coastal altimetric products.
Applications the Lagrangian description in aperiodic flows
NASA Astrophysics Data System (ADS)
Mendoza, Carolina; Mancho, Ana Maria
2012-11-01
We use several recently developed Lagrangian tools for describing transport in general aperiodic flows. In our approach the first step is based in a Lagrangian descriptor (the so called function M). It measures the length of particle trajectories on the ocean surface over a given interval of time. We describe its output over satellite altimetry data on the Kuroshio current. The technique is combined with the direct computation of manifolds of Distinguished Hyperbolic trajectories and a very detailed description of transport is achieved across an eddy and a jet on the Kuroshio current,. A second velocity data set is examined with the M function tool. These are obtained from the HYCOM project on the Gulf of Mexico during the time of the oil-spill. We have identified underlying Lagrangian structures and dynamics. We acknowledge to the hospitality of the university of Delaware and the assistance of Bruce Lipphardt and Helga Huntley in accessing the model data sets. We acknowledge to the grants: UPM-AL12-PAC-09, Becas de Movilidad de Caja Madrid 2011, MTM2011-26696 and ILINK-0145.
Lagrangian predictability characteristics of an Ocean Model
NASA Astrophysics Data System (ADS)
Lacorata, Guglielmo; Palatella, Luigi; Santoleri, Rosalia
2014-11-01
The Mediterranean Forecasting System (MFS) Ocean Model, provided by INGV, has been chosen as case study to analyze Lagrangian trajectory predictability by means of a dynamical systems approach. To this regard, numerical trajectories are tested against a large amount of Mediterranean drifter data, used as sample of the actual tracer dynamics across the sea. The separation rate of a trajectory pair is measured by computing the Finite-Scale Lyapunov Exponent (FSLE) of first and second kind. An additional kinematic Lagrangian model (KLM), suitably treated to avoid "sweeping"-related problems, has been nested into the MFS in order to recover, in a statistical sense, the velocity field contributions to pair particle dispersion, at mesoscale level, smoothed out by finite resolution effects. Some of the results emerging from this work are: (a) drifter pair dispersion displays Richardson's turbulent diffusion inside the [10-100] km range, while numerical simulations of MFS alone (i.e., without subgrid model) indicate exponential separation; (b) adding the subgrid model, model pair dispersion gets very close to observed data, indicating that KLM is effective in filling the energy "mesoscale gap" present in MFS velocity fields; (c) there exists a threshold size beyond which pair dispersion becomes weakly sensitive to the difference between model and "real" dynamics; (d) the whole methodology here presented can be used to quantify model errors and validate numerical current fields, as far as forecasts of Lagrangian dispersion are concerned.
Identifying Lagrangian fronts with favourable fishery conditions
NASA Astrophysics Data System (ADS)
Prants, S. V.; Budyansky, M. V.; Uleysky, M. Yu.
2014-08-01
Lagrangian fronts (LFs) in the ocean are defined as boundaries between surface waters with strongly different Lagrangian properties. They can be accurately detected in a given velocity field by computing synoptic maps for displacements of synthetic tracers and other Lagrangian 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.
Inverse Variational Problem for Nonstandard Lagrangians
NASA Astrophysics Data System (ADS)
Saha, A.; Talukdar, B.
2014-06-01
In the mathematical physics literature the nonstandard Lagrangians (NSLs) were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity, (iii) Lotka-Volterra model and (vi) a number of the generic equations for dissipative-like dynamical systems. Our method works for nonstandard Lagrangians corresponding to the usual action integral of mechanical systems but requires modification for those associated with the modified actions like S =∫abe L(x ,x˙ , t) dt and S =∫abL 1 - γ(x ,x˙ , t) dt because in the latter case one cannot construct expressions for the Jacobi integrals.
Dynamics of Multibody Systems Near Lagrangian Points
NASA Astrophysics Data System (ADS)
Wong, Brian
This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian 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 Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical 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 Lagrangian 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 Lagrangian 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. Numerical simulations are used to study the long term
Lagrangian bias in the local bias model
Frusciante, Noemi; Sheth, Ravi K. E-mail: sheth@ictp.it
2012-11-01
It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field. We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function. This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function. In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions. Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit. In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space. We discuss why things are more complicated in practice. We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not. We use the Lognormal model to illustrate many of our findings.
Lagrangian Coherent Structures in the Trieste Gulf
NASA Astrophysics Data System (ADS)
Besio, G.; Enrile, F.; Magaldi, M. G.; Mantovani, C.; Cosoli, S.; Gerin, R.; Poulain, P. M.
2013-12-01
One serious issue in Environmental Science and Engineering concerns the prediction of the fate of contaminants released in a water body. A possible way to tackle this problem consists in forecasting pollutant trajectories from velocity-field data sets obtained by measurements or numerical simulations. A shortcoming of such a traditional approach is the high sensitivity to initial conditions. Another way to understand transport in complex fluid flows comes from a new mathematical tool: Lagrangian Coherent Structures (LCS). The idea of using Lagrangian Structures rose as a meeting point between non-linear dynamics and fluid mechanics. It provides the means to identify material lines that shape trajectory patterns, dividing the flow field into regions with different dynamical behaviours. The objective of this study is the detection of Lagrangian Coherent Structures in the Gulf of Trieste. LCS are calculated from the 2D surface velocity field measured by the coastal radars of the TOSCA (Tracking Oil Spills & Coastal Awareness network) project. Blobs of simulated particles are subjected to chaotic stirring (transport and stretching) that is in agreement with the detected LCS. In the TOSCA project drifters were deployed, too. Therefore, a simple simulation of some of these drifters was carried out. The trajectory of the simulated drifters diverge from the real one: this result is due to the chaotic transport of passive tracers. However, the separation becomes more evident when velocity fields are less accurate because of lack of measurements, previously filled with nearest neighbourhood interpolation. In the light of such results, the use of LCS could be helpful in understanding the trajectory followed by drifters and passive tracers in general, because they can point out the directions along which transport is likely to develop.
Lagrangian transport properties of pulmonary interfacial flows
Smith, Bradford J.; Lukens, Sarah; Yamaguchi, Eiichiro; Gaver, Donald P.
2012-01-01
Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. Finite-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of Lagrangian coherent structures (LCSs) and their effects on transport. The Lagrangian perspective of these techniques reveals flow characteristics that are not readily apparent by observing Eulerian measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary element method, and measured experimentally with micro particle image velocimetry (μ-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air–liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The Lagrangian analysis is applied to velocity data measured with 0.01 mg ml−1 of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the Eulerian frame. PMID:23049141
Lagrangian aspects of the axisymmetric Euler equation
NASA Astrophysics Data System (ADS)
Preston, Stephen C.; Sarria, Alejandro
2016-03-01
In this paper we are interested in geometric aspects of blowup in the axisymmetric three-dimensional (3D) Euler equations with swirl on a cylinder. Writing the equations in Lagrangian form for the flow derivative along either the axis or the boundary and imposing oddness on the vertical component of the flow, we extend some blowup criteria due to Chae, Constantin and Wu related to assumptions on the sign of the pressure Hessian. In addition. we give a geometric interpretation of the results, both in terms of the local geometry along trajectories and in terms of the Riemannian geometry of the volume-preserving diffeomorphism group.
Stabilization by modification of the Lagrangian
NASA Technical Reports Server (NTRS)
Baumgarte, J. W.
1975-01-01
In order to reduce the error growth during a numerical integration, a method of stabilization of the differential equations of the Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as an independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Liapunov-stable set of differential equations. In contrast to other publications, here the equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.
Minimal Φ-LAGRANGIAN Surfaces in almost Hermitian Manifolds
NASA Astrophysics Data System (ADS)
Khong Van, Le
1990-02-01
A general method of calibrations is developed for the study of minimal Φ-Lagrangian surfaces in almost-Hermitian manifolds. A criterion for minimality of Φ-Lagrangian surfaces is given, along with a lower bound for the second variation of the volume functional on minimal Φ-Lagrangian surfaces in Hermitian manifolds. The generalized Maslov index of these surfaces is shown to be trivial. Bibliography: 11 titles.
NASA Astrophysics Data System (ADS)
Veiskarami, Mehdi; Bahar, Arash; Zandi Lak, Erfan
2015-12-01
Dynamic earth pressure induced by machine foundations on a neighboring retaining wall is analyzed with emphasis on factors which control the intensity and location of the design forces. The meshless local Petrov-Galerkin (MLPG) method is used to analyze the problem for a variety of retaining wall and machine foundation geometries. The soil medium is assumed to be homogeneous and visco-elastic. The machine foundation is idealized as a harmonic sinusoidal dynamic force often encountered in practice. A number of analyses have been made to reveal the effect of the loading frequency, the location and size of the foundation and the soil shear wave velocity on the distribution and magnitude of the dynamic earth pressure. Results indicate that there is a critical frequency and a critical location for which the passive pressure takes the maxima in the entire duration of the dynamic load.
Coupled Eulerian-Lagrangian transport of large debris by tsunamis
NASA Astrophysics Data System (ADS)
Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos
2016-04-01
Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-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 scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian 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-Lagrangian 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
Relativistic Lagrangians for the Lorentz–Dirac equation
Deguchi, Shinichi; Nakano, Kunihiko; Suzuki, Takafumi
2015-09-15
We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.
Variational contact symmetries of constrained Lagrangians
NASA Astrophysics Data System (ADS)
Terzis, Petros A.; Dimakis, N.; Christodoulakis, T.; Paliathanasis, Andronikos; Tsamparlis, Michael
2016-03-01
The investigation of contact symmetries of re-parametrization invariant Lagrangians of finite degrees of freedom and quadratic in the velocities is presented. The main concern of the paper is those symmetry generators which depend linearly in the velocities. A natural extension of the symmetry generator along the lapse function N(t) , with the appropriate extension of the dependence in N ˙ (t) of the gauge function, is assumed; this action yields new results. The central finding is that the integrals of motion are either linear or quadratic in velocities and are generated, respectively by the conformal Killing vector fields and the conformal Killing tensors of the configuration space metric deduced from the kinetic part of the Lagrangian (with appropriate conformal factors). The freedom of re-parametrization allows one to appropriately scale N(t) , so that the potential becomes constant; in this case the integrals of motion can be constructed from the Killing fields and Killing tensors of the scaled metric. A rather interesting result is the non-necessity of the gauge function in Noether's theorem due to the presence of the Hamiltonian constraint.
Generating functionals and Lagrangian partial differential equations
Vankerschaver, Joris; Liao, Cuicui; Leok, Melvin
2013-08-15
The main goal of this paper is to derive an alternative characterization of the multisymplectic form formula for classical field theories using the geometry of the space of boundary values. We review the concept of Type-I/II generating functionals defined on the space of boundary data of a Lagrangian field theory. On the Lagrangian side, we define an analogue of Jacobi's solution to the Hamilton–Jacobi equation for field theories, and we show that by taking variational derivatives of this functional, we obtain an isotropic submanifold of the space of Cauchy data, described by the so-called multisymplectic form formula. As an example of the latter, we show that Lorentz's reciprocity principle in electromagnetism is a particular instance of the multisymplectic form formula. We also define a Hamiltonian analogue of Jacobi's solution, and we show that this functional is a Type-II generating functional. We finish the paper by defining a similar framework of generating functions for discrete field theories, and we show that for the linear wave equation, we recover the multisymplectic conservation law of Bridges.
Sigma decomposition: the CP-odd Lagrangian
NASA Astrophysics Data System (ADS)
Hierro, I. M.; Merlo, L.; Rigolin, S.
2016-04-01
In Alonso et al., JHEP 12 (2014) 034, the CP-even sector of the effective chiral Lagrangian for a generic composite Higgs model with a symmetric coset has been constructed, up to four momenta. In this paper, the CP-odd couplings are studied within the same context. If only the Standard Model bosonic sources of custodial symmetry breaking are considered, then at most six independent operators form a basis. One of them is the weak- θ term linked to non-perturbative sources of CP violation, while the others describe CP-odd perturbative couplings between the Standard Model gauge bosons and an Higgs-like scalar belonging to the Goldstone boson sector. The procedure is then applied to three distinct exemplifying frameworks: the original SU(5)/SO(5) Georgi-Kaplan model, the minimal custodial-preserving SO(5)/SO(4) model and the minimal SU(3)/(SU(2) × U(1)) model, which intrinsically breaks custodial symmetry. Moreover, the projection of the high-energy electroweak effective theory to the low-energy chiral effective Lagrangian for a dynamical Higgs is performed, uncovering strong relations between the operator coefficients and pinpointing the differences with the elementary Higgs scenario.
Mars interplanetary trajectory design via Lagrangian points
NASA Astrophysics Data System (ADS)
Eapen, Roshan Thomas; Sharma, Ram Krishan
2014-09-01
With the increase in complexities of interplanetary missions, the main focus has shifted to reducing the total delta-V for the entire mission and hence increasing the payload capacity of the spacecraft. This paper develops a trajectory to Mars using the Lagrangian points of the Sun-Earth system and the Sun-Mars system. The whole trajectory can be broadly divided into three stages: (1) Trajectory from a near-Earth circular parking orbit to a halo orbit around Sun-Earth Lagrangian point L2. (2) Trajectory from Sun-Earth L2 halo orbit to Sun-Mars L1 halo orbit. (3) Sun-Mars L1 halo orbit to a circular orbit around Mars. The stable and unstable manifolds of the halo orbits are used for halo orbit insertion. The intermediate transfer arcs are designed using two-body Lambert's problem. The total delta-V for the whole trajectory is computed and found to be lesser than that for the conventional trajectories. For a 480 km Earth parking orbit, the total delta-V is found to be 4.6203 km/s. Another advantage in the present approach is that delta-V does not depend upon the synodic period of Earth with respect to Mars.
RELMAP: A REGIONAL LAGRANGIAN MODEL OF AIR POLLUTION - USER'S GUIDE
The regional Lagrangian Model of Air Pollution (RELMAP) is a mass conserving, Lagrangian model that simulates ambient concentrations and wet and dry depositions of SO2, SO4=, and fine and coarse particulate matter over the eastern United States and southeastern Canada (default do...
Attracting Lagrangian coherent structures on Riemannian manifolds.
Karrasch, Daniel
2015-08-01
It is a wide-spread convention to identify repelling Lagrangian Coherent Structures (LCSs) with ridges of the forward finite-time Lyapunov exponent (FTLE) field and to identify attracting LCSs with ridges of the backward FTLE. However, we show that, in two-dimensional incompressible flows, also attracting LCSs appear as ridges of the forward FTLE field. This raises the issue of the characterization of attracting LCSs using a forward finite-time Lyapunov analysis. To this end, we extend recent results regarding the relationship between forward and backward maximal and minimal FTLEs, to both the whole finite-time Lyapunov spectrum and to stretch directions. This is accomplished by considering the singular value decomposition (SVD) of the linearized flow map. By virtue of geometrical insights from the SVD, we provide characterizations of attracting LCSs in forward time for two geometric approaches to hyperbolic LCSs. We apply these results to the attracting FTLE ridge of the incompressible saddle flow. PMID:26328582
Attracting Lagrangian coherent structures on Riemannian manifolds
NASA Astrophysics Data System (ADS)
Karrasch, Daniel
2015-08-01
It is a wide-spread convention to identify repelling Lagrangian Coherent Structures (LCSs) with ridges of the forward finite-time Lyapunov exponent (FTLE) field and to identify attracting LCSs with ridges of the backward FTLE. However, we show that, in two-dimensional incompressible flows, also attracting LCSs appear as ridges of the forward FTLE field. This raises the issue of the characterization of attracting LCSs using a forward finite-time Lyapunov analysis. To this end, we extend recent results regarding the relationship between forward and backward maximal and minimal FTLEs, to both the whole finite-time Lyapunov spectrum and to stretch directions. This is accomplished by considering the singular value decomposition (SVD) of the linearized flow map. By virtue of geometrical insights from the SVD, we provide characterizations of attracting LCSs in forward time for two geometric approaches to hyperbolic LCSs. We apply these results to the attracting FTLE ridge of the incompressible saddle flow.
One Model of Singular Relativistic Lagrangian
NASA Astrophysics Data System (ADS)
Laserra, E.; Strianese, M.; Pavlotsky, I. P.
The so-called no-interaction theorem of D.G. Currie, T.F. Jordan, E.C. Sudarshan, H. Leutwyler, G. Marmo and N. Mukunda makes it possible to construct relativistic quasiclassical particle dynamics in the post-Galilean approximation only. It is obtained that in this approximation the Lagrangians are singular on some surfaces of the phase space. These peculiarities have different physical and mathematical nature from the ones studied by P.M.A. Dirac, where Hessians vanish in the whole phase-space. The dynamical properties are essentially peculiar on the studied singular surfaces. These properties, in our opinion, can be related with some physical phenomena. In the present paper the general situation is first described. As the whole problem is large and difficult we examined in detail just typical one- and two-dimensional models in the second part of the paper.
Validation of a Lagrangian particle model
NASA Astrophysics Data System (ADS)
Brzozowska, Lucyna
2013-05-01
In this paper a custom-developed model of dispersion of pollutants is presented. The proposed approach is based on both a Lagrangian particle model and an urban-scale diagnostic model of the air velocity field. Both models constitute a part of an operational air quality assessment system. The proposed model is validated by comparing its computed results with the results of measurements obtained in a wind tunnel reflecting conditions of the Mock Urban Setting Test (MUST) experiment. Commonly used measures of errors and model concordance are employed and the results obtained are additionally compared with those obtained by other authors for CFD and non-CFD class models. The obtained results indicate that the validity of the model presented in this paper is acceptable.
LSPRAY-II: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2004-01-01
LSPRAY-II is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-II, we have advanced the state-of-the-art in spray computations in several important ways.
An extended Lagrangian method for subsonic flows
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing; Loh, Ching Y.
1992-01-01
It is well known that fluid motion can be specified by either the Eulerian of Lagrangian description. Most of Computational Fluid Dynamics (CFD) developments over the last three decades have been based on the Eulerian description and considerable progress has been made. In particular, the upwind methods, inspired and guided by the work of Gudonov, have met with many successes in dealing with complex flows, especially where discontinuities exist. However, this shock capturing property has proven to be accurate only when the discontinuity is aligned with one of the grid lines since most upwind methods are strictly formulated in 1-D framework and only formally extended to multi-dimensions. Consequently, the attractive property of crisp resolution of these discontinuities is lost and research on genuine multi-dimensional approach has just been undertaken by several leading researchers. Nevertheless they are still based on the Eulerian description.
LSPRAY-V: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2015-01-01
LSPRAY-V is a Lagrangian spray solver developed for application with unstructured grids and massively parallel computers. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray encountered over a wide range of operating conditions in modern aircraft engine development. It could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-V, we have advanced the state-of-the-art in spray computations in several important ways.
Lagrangian coherent structures in the Gulf Stream
NASA Astrophysics Data System (ADS)
Liu, Yi; Wilson, Chris; Green, Melissa
2015-11-01
Finite-time Lyapunov exponent (FTLE) is calculated to identify Lagrangian coherent structures in the Gulf Stream region. The velocity fields are determined using the geostrophic velocities derived from satellite altimetry data. The coherent structures in and around the Gulf Stream are delineated by the both positive and negative FTLE ridges, and represent boundaries between dynamically distinct regions that are important to investigate transport and mixing processes in the ocean. Alternating positive and negative FTLE ridge patterns are found to line the meandering jet, which indicate the regions of entrainment and detrainment along the jet. Results compare well with the Bower kinematic model of a meandering jet, although it is clear that the kinematic model is an over-simplification of the jet dynamics, and studying the dynamics of vortex interaction with the jet is important for understanding fluid transfer in the Gulf Stream region.
LSPRAY-III: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2008-01-01
LSPRAY-III is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray because of its importance in aerospace application. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers. With the development of LSPRAY-III, we have advanced the state-of-the-art in spray computations in several important ways.
Lagrangian coherent structures and plasma transport processes
NASA Astrophysics Data System (ADS)
Falessi, M. V.; Pegoraro, F.; Schep, T. J.
2015-10-01
> A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom, the Poincaré map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers, i.e. a trajectory cannot cross such boundaries throughout the evolution of the system. Lagrangian coherent structures generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.
Lagrangian statistics of light particles in turbulence
NASA Astrophysics Data System (ADS)
Mercado, Julián Martínez; Prakash, Vivek N.; Tagawa, Yoshiyuki; Sun, Chao; Lohse, Detlef; (International CollaborationTurbulence Research)
2012-05-01
We study the Lagrangian velocity and acceleration statistics of light particles (micro-bubbles in water) in homogeneous isotropic turbulence. Micro-bubbles with a diameter db = 340 μm and Stokes number from 0.02 to 0.09 are dispersed in a turbulent water tunnel operated at Taylor-Reynolds numbers (Reλ) ranging from 160 to 265. We reconstruct the bubble trajectories by employing three-dimensional particle tracking velocimetry. It is found that the probability density functions (PDFs) of the micro-bubble acceleration show a highly non-Gaussian behavior with flatness values in the range 23 to 30. The acceleration flatness values show an increasing trend with Reλ, consistent with previous experiments [G. Voth, A. La Porta, A. M. Crawford, J. Alexander, and E. Bodenschatz, "Measurement of particle accelerations in fully developed turbulence," J. Fluid Mech. 469, 121 (2002)], 10.1017/S0022112002001842 and numerics [T. Ishihara, Y. Kaneda, M. Yokokawa, K. Itakura, and A. Uno, "Small-scale statistics in highresolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics," J. Fluid Mech. 592, 335 (2007)], 10.1017/S0022112007008531. These acceleration PDFs show a higher intermittency compared to tracers [S. Ayyalasomayajula, Z. Warhaft, and L. R. Collins, "Modeling inertial particle acceleration statistics in isotropic turbulence," Phys. Fluids. 20, 095104 (2008)], 10.1063/1.2976174 and heavy particles [S. Ayyalasomayajula, A. Gylfason, L. R. Collins, E. Bodenschatz, and Z. Warhaft, "Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence," Phys. Rev. Lett. 97, 144507 (2006)], 10.1103/PhysRevLett.97.144507 in wind tunnel experiments. In addition, the micro-bubble acceleration autocorrelation function decorrelates slower with increasing Reλ. We also compare our results with experiments in von Kármán flows and point-particle direct numerical simulations with periodic
Transitory Transport Between Lagrangian Coherent Structures
NASA Astrophysics Data System (ADS)
Mosovsky, B. A.; Meiss, J. D.
2011-12-01
In recent years, the geophysical and dynamical systems communities have developed numerous novel techniques for identifying structures that remain coherent in the Lagrangian sense in aperiodic time-dependent flows. The existence and persistence of these structures is intimately tied to the dynamical time scales of the flow, and as such, they can lend valuable insight into finite-time transport and mixing processes. Geophysical examples in the recent literature include eddy interaction and transport across ocean currents, transport of water-borne pollutants off the coast of California, and mixing and transport within the stratospheric polar vortex. However, in many cases the identification of the coherent structures themselves is a difficult task, making any further quantification of transport between them over a finite time interval either prohibitively expensive or imprecise. In this talk we consider transitory systems, those that experience time-dependent behavior only on a compact interval in time, and present a method for rigorously quantifying transport between Lagrangian coherent structures over this transition interval. In the systems we consider, this transport is effected by the exchange of "lobes" of fluid particles resulting from the intersection of the invariant manifolds bounding the coherent structures. We provide a method for computing the volumes of these lobes that relies on knowing only the trajectories at the intersections of the manifolds, and we present, as applications of our theory, a 2D rotating double-gyre flow and a 3D transitory version of the classical Arnold-Beltrami-Childress (ABC) flow. These flows can be viewed as simplified kinematic descriptions of eddy-eddy interactions and three-dimensional turbulence, respectively. For the 2D case, we compare our results to a common technique employing finite-time Lyapunov exponents, and discuss the benefits and limitations of both methods.
Lagrangian tracing of Sahelian Sudan moisture sources
NASA Astrophysics Data System (ADS)
Salih, Abubakr A. M.; Zhang, Qiong; Tjernström, Michael
2013-04-01
Sahelian Sudan, 10° to 16°N, is an arid to semi-arid zone that separates the Saharan to the north and the wet Savannah to the south. The region is characterized by, relatively, limited water resources, and hence has a high dependency on the annual rainfall. According to the latest IPCC report, regions that have such limited water resources are highly vulnerable to the ongoing climate change and variability. Taking into account that the agriculture is the main economical activity, the variability in annual rainfall is of direct soci-economical relevance. Similar to the rest of the African Sahel, the rainy season, June through September, across Sahelian Sudan is connected to the annual march of the Intertropical Convergence Zone (ITCZ). However, there still a limited understanding of the actual sources of moisture that supplies this region with water vapor during the rainy season. Broadly speaking, the Atlantic, the Congo rain forest, the Read Sea and the Indian Ocean are the main potential sources. In this study we use Lagrangian tracing technique to indentify the sources of moisture of Sahelian Sudan and attempt quantifying their contribution to the total annual moisture convergence. For this we utilized output from the Lagrangian trajectory model FLEXPART driven by the meteorological fields from the European Center for Medium range Weather Forecast ERA-interim for period of ten years 2000 to 2009. We trace back, for ten days each mass element to indentify the source region. The models also accounts for precipitation and moisture uptakes through the course of the transport of the air parcel from source to destination. Identifying the sources of moisture is of great importance, and can help in two connected directions. First, identifying sources of moisture will help in understanding the variability and will provide insight about the drought causes and mechanisms. Second, revealing the moisture sources would enhance ongoing efforts in seasonal forecasting.
Hybrid N-order Lagrangian interpolation Eulerian-Lagrangian method for salinity calculation
NASA Astrophysics Data System (ADS)
Wu, Yan-cheng; Zhu, Shou-xian; Zhou, Lin; You, Xiao-bao; Zhang, Wen-jing
2016-04-01
The Eulerian-Lagrangian method (ELM) has been used by many ocean models as the solution of the advection equation, but the numerical error caused by interpolation imposes restriction on its accuracy. In the present study, hybrid N-order Lagrangian interpolation ELM (LiELM) is put forward in which the N-order Lagrangian interpolation is used at first, then the lower order Lagrangian interpolation is applied in the points where the interpolation results are abnormally higher or lower. The calculation results of a step-shaped salinity advection model are analyzed, which show that higher order ( N=3-8) LiELM can reduce the mean numerical error of salinity calculation, but the numerical oscillation error is still significant. Even number order LiELM makes larger numerical oscillation error than its adjacent odd number order LiELM. Hybrid N-order LiELM can remove numerical oscillation, and it significantly reduces the mean numerical error when N is even and the current is in fixed direction, while it makes less effect on mean numerical error when N is odd or the current direction changes periodically. Hybrid odd number order LiELM makes less mean numerical error than its adjacent even number order LiELM when the current is in the fixed direction, while the mean numerical error decreases as N increases when the current direction changes periodically, so odd number of N may be better for application. Among various types of Hybrid N-order LiELM, the scheme reducing N-order directly to 1st-order may be the optimal for synthetic selection of accuracy and computational efficiency.
The Cauchy-Lagrangian method for numerical analysis of Euler flow
NASA Astrophysics Data System (ADS)
Podvigina, O.; Zheligovsky, V.; Frisch, U.
2016-02-01
A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle, only limited spatial smoothness of the initial data. Efficient generation of high-order time-Taylor coefficients is made possible by a recurrence relation that follows from the Cauchy invariants formulation of the Euler equation (Zheligovsky and Frisch, 2014 [44]). Truncated time-Taylor series of very high order allow the use of time steps vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the accuracy of the solution. Tests performed on the two-dimensional Euler equation indicate that the Cauchy-Lagrangian method is more - and occasionally much more - efficient and less prone to instability than Eulerian Runge-Kutta methods, and less prone to rapid growth of rounding errors than the high-order Eulerian time-Taylor algorithm. We also develop tools of analysis adapted to the Cauchy-Lagrangian method, such as the monitoring of the radius of convergence of the time-Taylor series. Certain other fluid equations can be handled similarly.
Lagrangian analysis. Modern tool of the dynamics of solids
NASA Astrophysics Data System (ADS)
Cagnoux, J.; Chartagnac, P.; Hereil, P.; Perez, M.; Seaman, L.
Lagrangian specificity of the required measurements is assured by the fact that a transducer enclosed within a solid material is necessarily linked in motion to the particles of the material which surround it. This Lagrangian instrumentation is described in the second chapter. The authors are concerned with the techniques considered today to be the most effective. These are, for stress : piezoresistive gauges (50 Ω and low impedance) and piezoelectric techniques (PVF2 gauges, quartz transducers) ; and for particle velocity : electromagnetic gauges, VISAR and IDL Doppler laser interferometers. In each case both the physical principles as well as techniques of use are set out in detail. For the most part, the authors use their own experience to describe the calibration of these instrumentation systems and to compare their characteristics : measurement range, response time, accuracy, useful recording time, detection area... These characteristics should be taken into account by the physicist when he has to choose the instrumentation systems best adapted to the Lagrangian analysis he intends to apply to any given material. The discussion at the end of chapter 2 should guide his choice both for plane and spherical one-dimensional motions. The third chapter examines to what extent the accuracy of Lagrangian analysis is affected by the accuracies of the numerical analysis methods and experimental techniques. By means of a discussion of different cases of analysis, the authors want to make the reader aware of the different kinds of sources of errors that may be encountered. This work brings up to date the state of studies on Lagrangian analysis methods based on a wide review of bibliographical sources together with the contribution made to research in this field by the four authors themselves in the course of the last ten years. Le formage des métaux par explosif, la consolidation dynamique des poudres, la balistique terminale, l'abattage des roches par explosif, sont autant d
NASA Astrophysics Data System (ADS)
Diggs, Angela; Balachandar, Sivaramakrishnan
2015-06-01
The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Eulerian Projection (EP) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Lagrangian Projection (LP) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, EP methods are used in multiphase flow, but sub-grid resolution can be obtained through use of LP methods. By evaluating the total error and its components we compare the performance of EP and LP methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities. Most importantly, we will show that such careful attention to numerical methodologies is needed in order to capture complex shock interaction with a bed of particles. Supported by U.S. Department of Defense SMART Program and the U.S. Department of Energy PSAAP-II program under Contract No. DE-NA0002378.
NASA Astrophysics Data System (ADS)
Young, D. L.; Tsai, C. H.; Wu, C. S.
2015-11-01
An alternative vector potential formulation is used to solve the Navier-Stokes (N-S) equations in 3D incompressible viscous flow problems with and without through-flow boundaries. Difficulties of the vector potential formulation include the implementation of boundary conditions for through-flow boundaries and the numerical treatment of fourth-order partial differential equations. The advantages on the other hand are the automatic satisfaction of the continuity equation; and pressure is decoupled from the velocity. The objective of this paper is to introduce the appropriate gauge and boundary conditions on the vector potential formulation by a localized meshless method. To handle the divergence-free property, a Coulomb gauge condition is enforced on the vector potential to ensure its existence and uniqueness mathematically. We further improve the algorithm to through-flow problems for the boundary conditions of vector potential by introducing the concept of Stokes' theorem. Based on this innovation, there is no need to include an additional variable to tackle the through-flow fields. This process will greatly simplify the imposition of boundary conditions by the vector potential approach. Under certain conditions, the coupled fourth-order partial differential equations can be easily solved by using this meshless local differential quadrature (LDQ) method. Due to the LDQ capability to deal with the high order differential equations, this algorithm is very attractive to solve this fourth-order vector potential formulation for the N-S equations as comparing to the conventional numerical schemes such as finite element or finite difference methods. The proposed vector potential formulation is simpler and has improved accuracy and efficiency compared to other pressure-free or pressure-coupled algorithms. This investigation can be regarded as the first complete study to obtain the N-S solutions by vector potential formulation through a LDQ method. Two classic 3D benchmark
Lagrangian analysis of hemodynamics data from FSI simulation
Duvernois, Vincent; Marsden, Alison L.; Shadden, Shawn C.
2013-01-01
We present the computation of Lagrangian-based flow characterization measures for time-dependent, deformable-wall, finite-element blood flow simulations. Applicability of the algorithm is demonstrated in a fluid–structure interaction simulation of blood flow through a total cavopulmonary connection (Fontan procedure), and results are compared with a rigid-vessel simulation. Specifically, we report on several important Lagrangian-based measures including flow distributions, finite-time Lyapunov exponent fields, particle residence time, and exposure time calculations. Overall, strong similarity in Lagrangian measures of the flow between deformable and rigid-vessel models was observed. PMID:23559551
Constructing the Lagrangian in the Eulerian coordinate for relativistic hydrodynamics
NASA Astrophysics Data System (ADS)
Chiueh, Tzihong
1994-02-01
The Lorentz-covariant Lagrangian for an ideal relativistic flow is constructed in the Eulerian coordinate. In contrast to the Lagrangian of nonrelativistic flows in the Eulerian formulation, for which the continuity equation is required to be externally imposed as a constraint [Mittag, Stephen, and Yourgrau, in Variational Principles in Dynamics .ul and Quantum Theory, edited by W. Yourgrau and X. Mandelstam (Dover, New York, 1968)], this Lorentz-covariant Lagrangian automatically yields the continuity equation as well as the equation of state. In addition, the relativistic generalization of the Bernoulli equation can also be derived from the present formulation.
An implicit Lagrangian lattice Boltzmann method for the compressible flows
NASA Astrophysics Data System (ADS)
Yan, Guangwu; Dong, Yinfeng; Liu, Yanhong
2006-08-01
In this paper, we propose a new Lagrangian lattice Boltzmann method (LBM) for simulating the compressible flows. The new scheme simulates fluid flows based on the displacement distribution functions. The compressible flows, such as shock waves and contact discontinuities are modelled by using Lagrangian LBM. In this model, we select the element in the Lagrangian coordinate to satisfy the basic fluid laws. This model is a simpler version than the corresponding Eulerian coordinates, because the convection term of the Euler equations disappears. The numerical simulations conform to classical results.
Two-dimensional Lagrangian simulation of suspended sediment
Schoellhamer, David H.
1988-01-01
A two-dimensional laterally averaged model for suspended sediment transport in steady gradually varied flow that is based on the Lagrangian reference frame is presented. The layered Lagrangian 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 Lagrangian 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.
Lagrangian tracing of Sahelian Sudan moisture sources
NASA Astrophysics Data System (ADS)
Salih, Abubakr A. M.; Zhang, Qiong; Tjernström, Michael
2015-07-01
The Sahelian Sudan is an arid to semiarid region that depends on the seasonal rainfall as the main source of water, but its rainfall has large interannual variability. Such dry regions usually have their main moisture sources elsewhere; thus, the rainfall variability is directly related to the moisture transport. This study seeks to identify source regions of water vapor for Sahelian Sudan during the monsoon period, from July to September. We have used the Lagrangian trajectory model FLEXPART driven by ERA-Interim reanalysis for the time period 1998 to 2008. The results show that most of the air masses that reach this region during the monsoon period have their major origins over the Arabian Peninsula, Central Africa, or are associated with the tropical easterly jet. Flow associated with Intertropical Convergence Zone contributes almost half of the total precipitated water; most of it comes from Central Africa. This suggests that moisture recycling is the major contributor, compared to Oceanic sources. The flows from the northeast (Arabian Peninsula and north Asia) and east (Horn of Africa and north Indian Ocean) contribute about one third of the precipitated water. The rest of precipitated water comes from the Mediterranean, subtropical Atlantic, and western Sahel, all with smaller contribution. Our results also indicate that different subregions of Sahelian Sudan have different moisture sources. Such result needs to be taken into account in seasonal forecasting practices.
Top marine predators track Lagrangian coherent structures
Tew Kai, Emilie; Rossi, Vincent; Sudre, Joel; Weimerskirch, Henri; Lopez, Cristobal; Hernandez-Garcia, Emilio; Marsac, Francis; Garçon, Veronique
2009-01-01
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel. PMID:19416811
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).
Lagrangian particle model for multiphase flows
Tartakovsky, Alexandre M.; Ferris, Kim F.; Meakin, Paul
2009-10-01
A Lagrangian particle model for multiphase multicomponent fluid flow, based on smoothed particle hydrodynamics (SPH), was developed and used to simulate the flow of an emulsion consisting of bubbles of a non-wetting liquid surrounded by a wetting liquid. In SPH simulations, fluids are represented by sets of particles that are used as discretization points to solve the Navier-Stokes fluid dynamics equations. In the multiphase multicomponent SPH model, a modified van der Waals equation of state is used to close the system of flow equations. The combination of the momentum conservation equation with the van der Waals equation of state results in a particle equation of motion in which the total force acting on each particle consists of many-body repulsive and viscous forces, two-body (particle-particle) attractive forces, and body forces such as gravitational forces. Similarly to molecular dynamics, for a given fluid component the combination of repulsive and attractive forces causes a phase separation. The surface tension at liquid-liquid interfaces is imposed through component dependent attractive forces. The wetting behavior of the fluids is controlled by phase dependent attractive interactions between the fluid particles and stationary particles that represent the solid phase. The dynamics of fluids away from interface is governed by purely hydrodynamic forces. Comparison with analytical solutions for static conditions and relatively simple flows demonstrates the accuracy of the SPH model.
Top marine predators track Lagrangian coherent structures.
Tew Kai, Emilie; Rossi, Vincent; Sudre, Joel; Weimerskirch, Henri; Lopez, Cristobal; Hernandez-Garcia, Emilio; Marsac, Francis; Garçon, Veronique
2009-05-19
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel. PMID:19416811
Using Lagrangian perturbation theory for precision cosmology
Sugiyama, Naonori S.
2014-06-10
We explore the Lagrangian perturbation theory (LPT) at one-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in this theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the one-loop solution in LPT to the two-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the two-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at k = 0.2 h Mpc{sup –1} and z = 0.35 to better than 2%.
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
NASA Astrophysics Data System (ADS)
Iglesias, David; Marrero, Juan C.; de Diego, David Martín; Martínez, Eduardo
2008-06-01
This paper studies the construction of geometric integrators for nonholonomic systems. We develop a formalism for nonholonomic discrete Euler Lagrange equations in a setting that permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).
LSPRAY-IV: A Lagrangian Spray Module
NASA Technical Reports Server (NTRS)
Raju, M. S.
2012-01-01
LSPRAY-IV is a Lagrangian spray solver developed for application with parallel computing and unstructured grids. It is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo Probability Density Function (PDF) solvers. The solver accommodates the use of an unstructured mesh with mixed elements of either triangular, quadrilateral, and/or tetrahedral type for the gas flow grid representation. It is mainly designed to predict the flow, thermal and transport properties of a rapidly vaporizing spray. Some important research areas covered as a part of the code development are: (1) the extension of combined CFD/scalar-Monte- Carlo-PDF method to spray modeling, (2) the multi-component liquid spray modeling, and (3) the assessment of various atomization models used in spray calculations. The current version contains the extension to the modeling of superheated sprays. The manual provides the user with an understanding of various models involved in the spray formulation, its code structure and solution algorithm, and various other issues related to parallelization and its coupling with other solvers.
One-loop effective lagrangians after matching
NASA Astrophysics Data System (ADS)
del Aguila, F.; Kunszt, Z.; Santiago, J.
2016-05-01
We discuss the limitations of the covariant derivative expansion prescription advocated to compute the one-loop Standard Model (SM) effective lagrangian when the heavy fields couple linearly to the SM. In particular, one-loop contributions resulting from the exchange of both heavy and light fields must be explicitly taken into account through matching because the proposed functional approach alone does not account for them. We review a simple case with a heavy scalar singlet of charge -1 to illustrate the argument. As two other examples where this matching is needed and this functional method gives a vanishing result, up to renormalization of the heavy sector parameters, we re-evaluate the one-loop corrections to the T-parameter due to a heavy scalar triplet with vanishing hypercharge coupling to the Brout-Englert-Higgs boson and to a heavy vector-like quark singlet of charged 2 / 3 mixing with the top quark, respectively. In all cases we make use of a new code for matching fundamental and effective theories in models with arbitrary heavy field additions.
Lagrangian based methods for coherent structure detection
Allshouse, Michael R.; Peacock, Thomas
2015-09-15
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows.
Lagrangian based methods for coherent structure detection.
Allshouse, Michael R; Peacock, Thomas
2015-09-01
There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. PMID:26428570
Lagrangian Hydrocode Simulations of Tsunamigenic, Subaerial Landslides
NASA Astrophysics Data System (ADS)
Schwaiger, H. F.; Parsons, J.; Higman, B.
2006-12-01
The interaction of debris flows, both subaqueous and subaerial, with bodies of water can produce tsunamis with a locally devastating impact. When debris flows begin above the water surface, the impact can produce a large air cavity, significantly increasing the effective volume of water displaced and complicating efforts to model the resulting tsunami. Because grid-based, Eulerian numerical methods have an inherent difficulty tracking material boundaries, we have implemented a particle-based, Lagrangian model (Smoothed Particle Hydrodynamics). The use of a particle model removes the common numerical difficulties associated with large deformation, multi-phase flows such as the numerical diffusion of material boundaries. We treat the debris flow as an incompressible, viscous fluid and the body of water as inviscid. Other rheologies of the debris flow (Mohr-Coulomb or Bingham plastic) can be included through the use of a non-linear viscosity. We apply this model to study the 1958 Lituya Bay landslide and resulting tsunami. Our simulation results compare favorably with field observations as well as a scaled laboratory experiment and a numerical study using an AMR Eulerian compressible fluid model.
Construction of Lagrangians and Hamiltonians from the Equation of Motion
ERIC Educational Resources Information Center
Yan, C. C.
1978-01-01
Demonstrates that infinitely many Lagrangians and Hamiltonians can be constructed from a given equation of motion. Points out the lack of an established criterion for making a proper selection. (Author/GA)
Lagrangian statistics in forced two-dimensional turbulence
NASA Astrophysics Data System (ADS)
Kamps, Oliver; Friedrich, Rudolf
2007-11-01
In recent years the Lagrangian description of turbulent flows has attracted much interest from the experimental point of view and as well is in the focus of numerical and analytical investigations. We present detailed numerical investigations of Lagrangian tracer particles in the inverse energy cascade of two-dimensional turbulence. In the first part we focus on the shape and scaling properties of the probability distribution functions for the velocity increments and compare them to the Eulerian case and the increment statistics in three dimensions. Motivated by our observations we address the important question of translating increment statistics from one frame of reference to the other [1]. To reveal the underlying physical mechanism we determine numerically the involved transition probabilities. In this way we shed light on the source of Lagrangian intermittency.[1ex] [1] R. Friedrich, R. Grauer, H. Hohmann, O. Kamps, A Corrsin type approximation for Lagrangian fluid Turbulence , arXiv:0705.3132
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-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 Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics
NASA Astrophysics Data System (ADS)
Webb, G. M.; Anco, S. C.
2016-02-01
The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian 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 Lagrangian 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 Lagrangian 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 Lagrangian 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 Lagrangian energy conservation law with respect to the Lagrangian 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.
The augmented Lagrangian method for parameter estimation in elliptic systems
NASA Technical Reports Server (NTRS)
Ito, Kazufumi; Kunisch, Karl
1990-01-01
In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.
Renormalizing Operator-Stable Lagrangian Velocities for Microbial Dynamics Simulations
NASA Astrophysics Data System (ADS)
Cushman, J. H.; Park, M.
2008-05-01
In previous works we've developed upscaling methodologies for stable Levy Lagrangian velocities in fractal media. The renormalization tools were generalized central limit theorems which are equivalent to a renormalization group approach. Here we extend these ides to operator-stable Lagrangian velocities and apply the results to microbial dynamics in multi-scale geologic formations. Renormalized Fokker-Planck equations are presented at each scale.
Eulerian and Lagrangian statistics in fully developed rotating turbulent flows.
NASA Astrophysics Data System (ADS)
Biferale, Luca; Bonaccorso, Fabio; Mazzitelli, Irene; Lanotte, Alessandra; Perlekar, Prasad; Musacchio, Stefano; Hinsberg, Michel; Toschi, Federico
2015-11-01
We present results concerning both Eulerian and Lagrangian statistics for turbulent under rotation at small and large Rossby numbers. Concerning the Eulerian statistics we discuss the effects of the presence of strong coherent large-scale vortical structures on the small-scale statistics. Concerning Lagrangian properties, we discuss the effects of preferential sampling at changing the inertial properties of the particles also due to the centrifugal and Coriolis forces. Supported by the ERC AdG NewTURB num. 339032.
Construction of an effective Yang-Mills Lagrangian with manifest BCJ duality
NASA Astrophysics Data System (ADS)
Tolotti, Mathias; Weinzierl, Stefan
2013-07-01
The BCJ decomposition is a highly non-trivial property of gauge theories. In this paper we systematically construct an effective Lagrangian, whose Feynman rules automatically produce the BCJ numerators. The effective Lagrangian contains non-local terms. The difference between the standard Yang-Mills Lagrangian and the effective Lagrangian simplifies to zero.
Parallelisation of the Lagrangian atmospheric dispersion model NAME
NASA Astrophysics Data System (ADS)
Müller, Eike H.; Ford, Rupert; Hort, Matthew C.; Huggett, Lois; Riley, Graham; Thomson, David J.
2013-12-01
The NAME Atmospheric Dispersion Model is a Lagrangian particle model used by the Met Office to predict the propagation and spread of pollutants in the atmosphere. The model is routinely used in emergency response applications, where it is important to obtain results as quickly as possible. This requirement for a short runtime and the increase in core number of commonly available CPUs, such as the Intel Xeon series, has motivated the parallelisation of NAME in the OPENMP shared memory framework. In this work we describe the implementation of this parallelisation strategy in NAME and discuss the performance of the model for different setups. Due to the independence of the model particles, the parallelisation of the main compute intensive loops is relatively straightforward. The random number generator for modelling sub-grid scale turbulent motion needs to be adapted to ensure that different particles use independent sets of random numbers. We find that on Intel Xeon X5680 CPUs the model shows very good strong scaling up to 12 cores in a realistic emergency response application for predicting the dispersion of volcanic ash in the North Atlantic airspace. We implemented a mechanism for asynchronous reading of meteorological data from disk and demonstrate how this can reduce the runtime if disk access plays a significant role in a model run. To explore the performance on different chip architectures we also ported the part of the code which is used for calculating the gamma dose from a cloud of radioactive particles to a graphics processing unit (GPU) using CUDA-C. We were able to demonstrate a significant speedup of around one order of magnitude relative to the serial CPU version.
Second-order parametrized-post-Newtonian Lagrangian
Benacquista, M.J. )
1992-02-15
A many-body Lagrangian to second post-Newtonian order using an extension of the parametrized-post-Newtonian (PPN) formalism is introduced and the properties of new parameters are explored. A parametrized gauge transformation is developed to permit comparison with theories of gravity in a variety of different coordinate systems. A procedure to impose Lorentz invariance on a general second-order post-Newtonian Lagrangian is developed. The Lagrangian is then constrained to possess Lorentz invariance and a Lorentz-invariant'' gauge is introduced. The constrained Lagrangian is found to be described by ten new second-order PPN parameters. When the Lagrangian is further constrained to describe theories of gravity for which test particles move along geodesics, one of the ten new parameters is given entirely in terms of first-order PPN parameters, leaving only nine PPN parameters to describe the second-order gravitational interaction. A metric'' gauge is introduced which allows the metric to be easily found from the Lagrangian and is shown to reduce to the gauge associated with the canonical formalism of Arnowitt, Deser, and Misner when the general-relativity values of the PPN parameters are used.
An Efficient Augmented Lagrangian Method for Statistical X-Ray CT Image Reconstruction
Li, Jiaojiao; Niu, Shanzhou; Huang, Jing; Bian, Zhaoying; Feng, Qianjin; Yu, Gaohang; Liang, Zhengrong; Chen, Wufan; Ma, Jianhua
2015-01-01
Statistical iterative reconstruction (SIR) for X-ray computed tomography (CT) under the penalized weighted least-squares criteria can yield significant gains over conventional analytical reconstruction from the noisy measurement. However, due to the nonlinear expression of the objective function, most exiting algorithms related to the SIR unavoidably suffer from heavy computation load and slow convergence rate, especially when an edge-preserving or sparsity-based penalty or regularization is incorporated. In this work, to address abovementioned issues of the general algorithms related to the SIR, we propose an adaptive nonmonotone alternating direction algorithm in the framework of augmented Lagrangian multiplier method, which is termed as “ALM-ANAD”. The algorithm effectively combines an alternating direction technique with an adaptive nonmonotone line search to minimize the augmented Lagrangian function at each iteration. To evaluate the present ALM-ANAD algorithm, both qualitative and quantitative studies were conducted by using digital and physical phantoms. Experimental results show that the present ALM-ANAD algorithm can achieve noticeable gains over the classical nonlinear conjugate gradient algorithm and state-of-the-art split Bregman algorithm in terms of noise reduction, contrast-to-noise ratio, convergence rate, and universal quality index metrics. PMID:26495975
Redshift distortions of clustering: a Lagrangian approach.
NASA Astrophysics Data System (ADS)
Hivon, E.; Bouchet, F. R.; Colombi, S.; Juszkiewicz, R.
1995-06-01
We study the effects of peculiar velocities on statistical measures of galaxy clustering. These effects occur when distances to the galaxies are estimated from their redshifts. It is assumed that the clustering pattern results from the gravitational instability of initially Gaussian, small-amplitude perturbations of a Friedman-Lemaitre cosmological model. Explicit expressions are given for an arbitrary density parameter {OMEGA} of the model, both when the cosmological constant, {LAMBDA}, is zero, and when the model is spatially flat, {OMEGA}+ {LAMBDA}/3H^2^ =1. Kaiser (1987) had analyzed the redshift distortion of the two-point correlation function. This function determines the variance of the density field distribution function and can be computed using linear perturbation theory. We show here how to compute higher order moments in redshift space, paying special attention to the skewness, or third moment of the density field, and its Fourier space counterpart, the bispectrum. This calls for a weakly non-linear analysis. We rely on a perturbative expansion of particle trajectories in Lagrangian coordinates, using the formalism introduced by Moutarde et al. (1991) and further developed by Bouchet et al. (1992, 1994). This formalism extends to higher orders the Zel'dovich first order (i.e. linear) solution (1970). The lowest non-vanishing contribution to the skewness comes from the first and second-order terms in perturbation theory. Therefore, using Zel'dovich approximation would not be self-consistent and would yield inaccurate results. We show that a physically consistent and quantitatively accurate analysis of the growth skewness in redshift space can be obtained from second-order Lagrangian theory. With practical applications to redshift surveys in mind, we also study the effects of spatial smoothing of the evolved density field. The necessary formalism was developed by Juszkiewicz & Bouchet (1991) and Juszkiewicz et al. (1993a). Here we give the first complete
Lagrangian volume deformations around simulated galaxies
NASA Astrophysics Data System (ADS)
Robles, S.; Domínguez-Tenreiro, R.; Oñorbe, J.; Martínez-Serrano, F. J.
2015-07-01
We present a detailed analysis of the local evolution of 206 Lagrangian Volumes (LVs) selected at high redshift around galaxy seeds, identified in a large-volume Λ cold dark matter (ΛCDM) hydrodynamical simulation. The LVs have a mass range of 1-1500 × 1010 M⊙. We follow the dynamical evolution of the density field inside these initially spherical LVs from z = 10 up to zlow = 0.05, witnessing highly non-linear, anisotropic mass rearrangements within them, leading to the emergence of the local cosmic web (CW). These mass arrangements have been analysed in terms of the reduced inertia tensor I_{ij}^r, focusing on the evolution of the principal axes of inertia and their corresponding eigendirections, and paying particular attention to the times when the evolution of these two structural elements declines. In addition, mass and component effects along this process have also been investigated. We have found that deformations are led by dark matter dynamics and they transform most of the initially spherical LVs into prolate shapes, i.e. filamentary structures. An analysis of the individual freezing-out time distributions for shapes and eigendirections shows that first most of the LVs fix their three axes of symmetry (like a skeleton) early on, while accretion flows towards them still continue. Very remarkably, we have found that more massive LVs fix their skeleton earlier on than less massive ones. We briefly discuss the astrophysical implications our findings could have, including the galaxy mass-morphology relation and the effects on the galaxy-galaxy merger parameter space, among others.
Development of a Lagrangian-Lagrangian methodology to predict brownout dust clouds
NASA Astrophysics Data System (ADS)
Syal, Monica
A Lagrangian-Lagrangian dust cloud simulation methodology has been developed to help better understand the complicated two-phase nature of the rotorcraft brownout problem. Brownout conditions occur when rotorcraft land or take off from ground surfaces covered with loose sediment such as sand and dust, which decreases the pilot's visibility of the ground and poses a serious safety of flight risk. The present work involved the development of a comprehensive, computationally efficient three-dimensional sediment tracking method for dilute, low Reynolds number Stokes-type flows. The flow field generated by a helicopter rotor in ground effect operations over a mobile sediment bed was modeled by using an inviscid, incompressible, Lagrangian free-vortex method, coupled to a viscous semi-empirical approximation for the boundary layer flow near the ground. A new threshold model for the onset of sediment mobility was developed by including the effects of unsteady pressure forces that are induced in vortically dominated rotor flows, which can significantly alter the threshold conditions for particle motion. Other important aspects of particle mobility and uplift in such vortically driven dust flows were also modeled, including bombardment effects when previously suspended particles impact the bed and eject new particles. Bombardment effects were shown to be a particularly significant contributor to the mobilization and eventual suspension of large quantities of smaller-sized dust particles, which tend to remain suspended. A numerically efficient Lagrangian particle tracking methodology was developed where individual particle or clusters of particles were tracked in the flow. To this end, a multi-step, second-order accurate time-marching scheme was developed to solve the numerically stiff equations that govern the dynamics of particle motion. The stability and accuracy of this scheme was examined and matched to the characteristics of free-vortex method. One-way coupling of the
Lewis, Robert Michael (College of William and Mary, Williamsburg, VA); Torczon, Virginia Joanne (College of William and Mary, Williamsburg, VA); Kolda, Tamara Gibson
2006-08-01
We consider the solution of nonlinear programs in the case where derivatives of the objective function and nonlinear constraints are unavailable. To solve such problems, we propose an adaptation of a method due to Conn, Gould, Sartenaer, and Toint that proceeds by approximately minimizing a succession of linearly constrained augmented Lagrangians. Our modification is to use a derivative-free generating set direct search algorithm to solve the linearly constrained subproblems. The stopping criterion proposed by Conn, Gould, Sartenaer and Toint for the approximate solution of the subproblems requires explicit knowledge of derivatives. Such information is presumed absent in the generating set search method we employ. Instead, we show that stationarity results for linearly constrained generating set search methods provide a derivative-free stopping criterion, based on a step-length control parameter, that is sufficient to preserve the convergence properties of the original augmented Lagrangian algorithm.
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
NASA Astrophysics Data System (ADS)
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
Evolutionary geometry of Lagrangian structures in a transitional boundary layer
NASA Astrophysics Data System (ADS)
Zheng, Wenjie; Yang, Yue; Chen, Shiyi
2016-03-01
We report a geometric study of Lagrangian structures in a weakly compressible, spatially evolving transitional boundary layer at the Mach number 0.7. The Lagrangian structures in the transition process are extracted from the Lagrangian scalar field by a sliding window filter at a sequence of reference times. The multi-scale and multi-directional geometric analysis is applied to characterize the geometry of spatially evolving Lagrangian structures, including the averaged inclination and sweep angles at different scales ranging from one half of the boundary layer thickness to several viscous length scales. Here, the inclination angle is on the plane of the streamwise and wall-normal directions, and the sweep angle is on the plane of the streamwise and spanwise directions. In general, the averaged inclination angle is increased and the sweep angle is decreased with the reference time. The variation of the angles for large-scale structures is smaller than that for small-scale structures. Before the transition, the averaged inclination and sweep angles are only slightly altered for all the scales. As the transition occurs, averaged inclination angles increase and sweep angles decrease rapidly for small-scale structures. In the late transitional stage, the averaged inclination angle of small-scale structures with 30 viscous length scales is approximately 42°, and the averaged sweep angle in the logarithm law region is approximately 30°. Additionally, the geometry of Lagrangian structures in transitional boundary layer flow is compared with that in the fully developed turbulent channel flow.
Coupled Eulerian/Lagrangian Simulation for Overpressure Structural Response
NASA Astrophysics Data System (ADS)
Lloyd, Andrew; Pan, Hua; Miller, David; Cogar, John
2011-06-01
Accurately modeling blast dynamics is critical in the assessment of structures subjected to blast loading. The current industry standard for modeling blast effects in Lagrangian based Finite Element simulations is CONWEP; tabulated pressure data taken directly from blast events. CONWEP is limited, however, and may not always be physically representative of the blast/structural interaction that occurs in the field. Eulerian hydrocodes provide advantages over CONWEP in that they can capture shock front interaction and model blast surface interfaces with fidelity due to the presence of the working fluid. Eulerian codes, however, break down over larger time scales; whereas, Lagrangian modeling allows for discrete finite elements with definable boundary interfaces that can be tracked out to longer time scales. Hence, a hybrid approach that couples the Eulerian blast modeling with Lagrangian system dynamics is necessary. The objective of this paper is to demonstrate improvements in overpressure structural response modeling using a Coupled Eulerian/Lagrangian algorithm implemented in VelodyneTM. Velodyne results using the Coupled Eulerian/Lagrangian algorithm are compared to results from Eulerian hydrocode simulations and Velodyne simulations using the CONWEP algorithm.
Users manual for a one-dimensional Lagrangian transport model
Schoellhamer, D.H.; Jobson, H.E.
1986-01-01
A Users Manual for the Lagrangian Transport Model (LTM) is presented. The LTM uses Lagrangian calculations that are based on a reference frame moving with the river flow. The Lagrangian reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used 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)
Traveling between the Lagrangian points and the Earth
NASA Astrophysics Data System (ADS)
Antonio, F. B. A.
1994-11-01
This paper is concerned with trajectories to transfer a spacecraft between the Lagrangian points and the Earth. The Lagrangian points have important applications in astronautics, since they are equilibrium points of the equation of motion and very good candidates to locate a satellite or a space station. The planar circular restricted three-body problem in two dimensions is used as the model for the Earth-Moon system, and Lamaitre regularization is used to avoid singularities during the numerical integration required to solve the Lambert's three-body problem. Relations with previous results are shown, specially with: (1) transfers between the Lagrangian points and the Moon, (2) search for the absolute minimum delta V transfer between the Earth and the Moon, and (3) use of L(sub 1), as a node for lunar exploration.
Coherent Lagrangian vortices in three-dimensional unsteady flows
NASA Astrophysics Data System (ADS)
Blazevski, Daniel; Haller, George
2014-05-01
Detecting barriers to, and facilitators of, transport is a fundamental problem in studying the behavior of Lagrangian trajectories in a fluid. A recent extension of two-dimensional results provides transport barriers in 3D flows as locally most attracting, repelling or shearing surfaces. This provides an objective definition of a Lagrangian vortex boundary as an outermost member of a family of most shearing cylindrical material surfaces. The detection of such a 3D vortex boundary yields an accurate estimate on the volume the vortex transports. We compute 3D Lagrangian vortices in kinematic models, and also use a global circulation model to extract sharp boundaries for coherent three-dimensional Agulhas rings in the South Atlantic.
Lagrangian and Hamiltonian constraints for guiding-center Hamiltonian theories
Tronko, Natalia; Brizard, Alain J.
2015-11-15
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 Lagrangian constraints that have not been explored before. A new first-order term appearing in the guiding-center phase-space Lagrangian 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 Lagrangian constraint on the guiding-center Hamiltonian yields a natural interpretation for its higher-order corrections.
Measurement of Lagrangian velocity in fully developed turbulence.
Mordant, N; Metz, P; Michel, O; Pinton, J F
2001-11-19
We have developed a new experimental technique to measure the Lagrangian velocity of tracer particles in a turbulent flow, based on ultrasonic Doppler tracking. This method yields a direct access to the velocity of a single particle at a turbulent Reynolds number R(lambda) = 740, with two decades of time resolution, below the Lagrangian correlation time. We observe that the Lagrangian velocity spectrum has a Lorentzian form E(L)(omega) = u(2)(rms)T(L)/[1+(T(L)omega)(2)], in agreement with a Kolmogorov-like scaling in the inertial range. The probability density functions of the velocity time increments display an intermittency which is more pronounced than that of the corresponding Eulerian spatial increments. PMID:11736341
Lagrangian statistics and flow topology in forced 2-D turbulence
Kadoch, B.; Del-Castillo-Negrete, Diego B; Bos, W.J.T.; Schneider, Kai
2011-01-01
A study of the relationship between Lagrangian 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 Lagrangian 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 Lagrangian 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 Lagrangian 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 Lagrangian acceleration in forced turbulence show a comparable level of intermittency in both the periodic and the bounded domains. The conditional pdfs of the Lagrangian curvature are characterized, in all cases, by self-similar power-law behavior with a decay exponent of order - 2.
A Discrete Lagrangian Algorithm for Optimal Routing Problems
Kosmas, O. T.; Vlachos, D. S.; Simos, T. E.
2008-11-06
The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.
de Sitter group and Einstein-Hilbert Lagrangian
Mahato, Prasanta
2004-12-15
Axial-vector torsion in the Einstein-Cartan space U{sub 4} is considered here. By picking a particular term from the SO(4,1) Pontryagin density and then modifying it in a SO(3,1) invariant way, we get a Lagrangian density with Lagrange multipliers. Then considering torsion and torsionless connection as independent fields, it has been found that {kappa} and {lambda} of Einstein-Hilbert Lagrangian, appear as integration constants in such a way that {kappa} has been found to be linked with the topological Nieh-Yan density of U{sub 4} space.
A Lagrangian study of eddies in the ocean
NASA Astrophysics Data System (ADS)
Prants, Sergey V.
2016-05-01
A brief review of our results on the application of the Lagrangian approach to study observed and simulated eddies in the ocean is presented. It is shown by a few examples of mesoscale vortex structures in the North Western Pacific how to compute and analyze maps of specific Lagrangian indicators in order to study the birth, formation, evolution, metamorphoses and death of ocean eddies. The examples involve two-dimensional eddies observed in satellitederived velocity fields in the deep ocean and three-dimensional ones simulated in a regional numerical model of circulation with a high resolution.
Some properties of constraints in theories with degenerate Lagrangians
Nesterenko, V.V.; Chervyakov, A.M.
1986-01-01
The Poisson brackets of the primary constraints are expressed by means of linear differential operators in terms of Lagrangian constraints. In the framework of the Lagrangian formalism the authors propose a sufficient criterion for existence in the theory of second class constraints. It is shown that invariance of the action with respect to transformations with arbitrary functions of the time leads to primary constraints that are in involution with one another and with the canonical Hamiltonian, at least in the weak sense. It follows from the analysis of the functional arbitrariness in the solutions of the Hamilton equations that such primary constraints must be first-class constraints.
Generalized extended Lagrangian Born-Oppenheimer molecular dynamics
Niklasson, Anders M. N. Cawkwell, Marc J.
2014-10-28
Extended Lagrangian 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 Lagrangian 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.
A thermobaric instability of Lagrangian vertical coordinate ocean models
NASA Astrophysics Data System (ADS)
Hallberg, Robert
Lagrangian- (and isopycnic-) vertical coordinate ocean models are subject to an exponentially growing numerical instability in weakly stratified regions when thermobaricity is not accurately compensated. Inaccurate compensation for compressibility in the pressure gradient terms leads to pressure gradient truncation errors (due to the vertical discretization) that can drive the Lagrangian coordinate surfaces to reinforce these errors. It is possible to avoid this instability while using the full non-linear equation of state for seawater by using an optimal alternate discretization of the pressure gradient terms and extracting a slowly spatially varying reference compressibility that approximates the compressibility of the ocean's mean state.
Lagrangian satellites of Tethys and Dione. II - Theory of motion
NASA Astrophysics Data System (ADS)
Oberti, P.
1990-02-01
Numerical simulations of the motion of Tethys and Dione's Lagrangian satellites have been fitted to the observations collected from 1980 to 1985. From these experiments, amplitudes and periods of different perturbations due to the Lagrangian satellite environment have been estimated, and the accuracy of a basic analytical model of the motion have been tested. This model has then been modified to take the most important perturbation into account, and the constants of the motion have been fitted to the observations. The resulting theory provides positions differing from those observed by about 0.5 arcsec for Telesto and Calypso, and less for Helen, primarily due to observation uncertainties.
Spectral-clustering approach to Lagrangian vortex detection
NASA Astrophysics Data System (ADS)
Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George
2016-06-01
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 Lagrangian 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 Lagrangian vortices in several two- and three-dimensional flows.
A Spectral Clustering Approach to Lagrangian Vortex Detection
NASA Astrophysics Data System (ADS)
Hadjighasem, Alireza; Karrasch, Daniel; Teramoto, Hiroshi; Haller, George
2015-11-01
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 Lagrangian 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 Lagrangian vortices in several two- and three-dimensional flows.
On Lagrangian stochastic modelling of material transport in oceanic gyres
NASA Astrophysics Data System (ADS)
Reynolds, A. M.
2002-11-01
The introduction of ‘spin’ into second-order Lagrangian stochastic models (LSM) for stationary turbulence with broken reflectional symmetry is shown to result in the prediction of super-diffusive transport at intermediate times and the occurrence of anomalously large normal diffusion at later times. These characteristic features of material transport in oceanic gyres cannot be reproduced by two-dimensional first-order LSM. A correspondence is established between high-dimensional, low-order LSM and lower-dimensional, higher-order LSM. It is found that time-dependent spin statistics allow for the coexistence of rotating particle trajectories and non-oscillatory Lagrangian velocity autocorrelation functions.
Lagrangian Analysis of Kerguelen's Naturally Iron-fertilised Phytoplankton Bloom
NASA Astrophysics Data System (ADS)
Della Penna, A.; Trull, T. W.; Grenier, M.; Wotherspoon, S.; Johnson, C.; De Monte, S.; d'Ovidio, F.
2015-12-01
The role of iron as a limiting micro-nutrient for primary production in High Nutrient Low Chlorophyll regions has been highlighted by paleoceanography, artificial fertilisation experiments and observed naturally fertilised systems. Examples of natural fertilisation have suggested that (sub-)mesoscale (1-100 km, days-months) horizontal transport modulates and structures the spatial and temporal extent of iron enrichment, phytoplankton production and biogeography. Here we combine different satellite products (altimetry, ocean color, PHYSAT), in-situ sampling, drifting floats and autonomous profilers to analyse the naturally iron-fertilised phytoplankton bloom of the Kerguelen region (Southern Ocean). Considering the Kerguelen Plateau as the main local source of iron, we compute two Lagrangian diagnostics: the "age" - how long before a water parcel has touched the plateau- and the "origin" - the latitude where a water parcel has left the plateau. First, we verify that these altimetry-defined diagnostics' spatial patterns -computed using geostrophic and Ekman corrected velocity fields- are coherent with the ones structuring the trajectories of more than 100 drifters and that trends in surface Chlorophyll (Chl) present an overall agreement with total column content (yet with ~2-3x differences in dynamic ranges likely due to the varying presence of Chl below the mixed layer). Second, assuming a first-order removal, we fit "age" with iron measurements and we estimate removal rates for bloom and abiotic conditions of respectively 0.058 and 0.041 1/d. Then, we relate "age" and "origin" with locations of high Chl concentrations and diatom-dominance. We find out that locations of high Chl concentration correspond to water parcels that have recently left the plateau. Furthermore, general additive models reveal that recently enriched waters are more likely to present a diatom dominance. However, the expected exponential fit varies within the geographic domain suggesting that
Lipsius, Kai; Wilhelm, Ralf; Richter, Otto; Schmalstieg, Klaus Jürgen; Schiemann, Joachim
2006-01-01
Modeling pollen dispersal to predict cross-pollination is of great importance for the ongoing discussion of adventitious presence of genetically modified material in food and feed. Two different modeling approaches for pollen dispersal were used to simulate two years of data for the rate of cross-pollination of non-GM maize (Zea mays (L.)) fields by pollen from a central 1 ha transgenic field. The models combine the processes of wind pollen dispersal (transport) and pollen competition. Both models used for the simulation of pollen dispersal were Lagrangian approaches: a stochastic particle Lagrange model and a Lagrangian transfer function model. Both modeling approaches proved to be appropriate for the simulation of the cross-pollination rates. However, model performance differed significantly between years. We considered different complexity in meteorological input data. Predictions compare well with experimental results for all simplification steps, except that systematic deviations occurred when only main wind direction was used. Concluding, it can be pointed out that both models might be adapted to other pollen dispersal experiments of different crops and plot sizes, when wind direction statistics are available. However, calibration of certain model parameters is necessary. PMID:17445511
Functional approach to derivative expansion of the effective Lagrangian
Zuk, J.A.
1985-11-15
We present a new functional method for calculating higher-derivative terms in the one-loop effective Lagrangian for multicomponent scalar field theories. The general results we obtain are illustrated with explicit calculations for the O(n)-invariant phi/sup 4/ theory.
Lagrangian Approach to Study Catalytic Fluidized Bed Reactors
NASA Astrophysics Data System (ADS)
Madi, Hossein; Hossein Madi Team; Marcelo Kaufman Rechulski Collaboration; Christian Ludwig Collaboration; Tilman Schildhauer Collaboration
2013-03-01
Lagrangian 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 Lagrangian approach. A fluidized bed methanation employed in the production of Synthetic Natural Gas from wood was chosen as the case study. The Lagrangian 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 Lagrangian 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)
A Lagrangian form for the T - Ω formulation
NASA Astrophysics Data System (ADS)
Vinsard, Gérard; Dufour, Stéphane; Saatdjian, Esteban
2016-03-01
A Lagrangian form for the T - Ω formulation using the Rayleigh function to take into account Joule losses is presented. Its use gives an interesting insight when calculating induced currents in non simply connected regions. Contribution to the topical issue "Numelec 2015 - Elected submissions", edited by Adel Razek
Using Lagrangian Coherent Structures to understand coastal water quality
NASA Astrophysics Data System (ADS)
Fiorentino, L. A.; Olascoaga, M. J.; Reniers, A.; Feng, Z.; Beron-Vera, F. J.; MacMahan, J. H.
2012-09-01
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 Lagrangian circulation. Specifically, we reveal Lagrangian Coherent Structures (LCSs), i.e., distinguished material curves which shape global mixing patterns and thus act as skeletons of the Lagrangian 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 Lagrangian 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.
Connections between chiral Lagrangians and QCD sum-rules
NASA Astrophysics Data System (ADS)
Fariborz, Amir H.; Pokraka, A.; Steele, T. G.
2016-01-01
In this paper, it is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g. quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet a0(980)-a0(1450) system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors lead to a remarkable agreement between the quark condensates in QCD and the mesonic vacuum expectation values that induce spontaneous chiral symmetry breaking in chiral Lagrangians. This concrete example shows a clear sensitivity to the underlying a0-system mixing angle, illustrating the value of this methodology in extensions to more complicated mesonic systems.
The complete HEFT Lagrangian after the LHC Run I
NASA Astrophysics Data System (ADS)
Brivio, I.; Gonzalez-Fraile, J.; Gonzalez-Garcia, M. C.; Merlo, L.
2016-07-01
The complete effective chiral Lagrangian for a dynamical Higgs is presented and constrained by means of a global analysis including electroweak precision data together with Higgs and triple gauge-boson coupling data from the LHC Run I. The operators' basis up to next-to-leading order in the expansion consists of 148 (188 considering right-handed neutrinos) flavour universal terms and it is presented here making explicit the custodial nature of the operators. This effective Lagrangian provides the most general description of the physical Higgs couplings once the electroweak symmetry is assumed, and it allows for deviations from the SU(2)_L doublet nature of the Standard Model Higgs. The comparison with the effective linear Lagrangian constructed with an exact SU(2)_L doublet Higgs and considering operators with at most canonical dimension six is presented. A promising strategy to disentangle the two descriptions consists in analysing (i) anomalous signals present only in the chiral Lagrangian and not expected in the linear one, that are potentially relevant for LHC searches, and (ii) decorrelation effects between observables that are predicted to be correlated in the linear case and not in the chiral one. The global analysis presented here, which includes several kinematic distributions, is crucial for reducing the allowed parameter space and for controlling the correlations between parameters. This improves previous studies aimed at investigating the Higgs Nature and the origin of the electroweak symmetry breaking.
The Hilbert-Schmidt Lagrangian Grassmannian in infinite dimension
NASA Astrophysics Data System (ADS)
López Galván, Manuel
2016-01-01
In this paper we study the action of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator in the Lagrangian Grassmannian manifold. We prove several geometric properties using the quotient norm in the tangent spaces. We determinate the geodesic curves of this structure and we study the completeness of the corresponding geodesic distance.
Singular Lagrangians. Classical dynamics and quantization. Lectures for young scientists
NASA Astrophysics Data System (ADS)
Nesterenko, V. V.; Chervyakov, A. M.
The lectures are devoted to the classical and quantum dynamics of the systems described by singular (or degenerate) Lagrangians. The complete set of the Hamiltonian constraints is constructed in the framework of the Lagrangian formalism. The equations of motion in the phase space are derived by taking into account all the constraints in the theory. It is proved that the dynamic on the physical submanifold of the phase space has the Hamiltonian form. On lectures the second Noether theorem is widely used. On its basis the properties of the Poisson brackets of the primary constraints are investigated and the invariance of the Lagrangian constraints during evolution is proved. The setting of the Cauchy problem in the theories with singular Lagrangians is discussed. The quantization of the systems with constraints is carried out by the functional integration in the phase space. There is considered the most general case of the first class and the second class constraints with an explicit time dependence. The gauge conditions may be noninvoluntary and time dependent. The material is illustrated by some examples (relativistic point particle, relativistic string, electromagnetic field, and Yang-Mills fields).
Simultaneous temperature and velocity Lagrangian measurements in turbulent thermal convection
NASA Astrophysics Data System (ADS)
Liot, O.; Seychelles, F.; Zonta, F.; Chibbaro, S.; Coudarchet, T.; Gasteuil, Y.; Pinton, J.-F.; Salort, J.; Chillà, F.
2016-05-01
We report joint Lagrangian velocity and temperature measurements in turbulent thermal convection. Measurements are performed using an improved version (extended autonomy) of the neutrally-buoyant instrumented particle that was used by to performed experiments in a parallelepipedic Rayleigh-Benard cell. The temperature signal is obtained from a RFtransmitter. Simultaneously, we determine particle's position and velocity with one camera, which grants access to the Lagrangian heat flux. Due to the extended autonomy of the present particle, we obtain well converged temperature and velocity statistics, as well as pseudo-eulerian maps of velocity and heat flux. Present experimental results have also been compared with the results obtained by a corresponding campaign of Direct Numerical Simulations and Lagrangian Tracking of massless tracers. The comparison between experimental and numerical results show the accuracy and reliability of our experimental measurements. Finally, the analysis of lagrangian velocity and temperature frequency spectra is shown and discussed. In particular, we observe that temperature spectra exhibit an anomalous f^2.5 frequency scaling, likely representing the ubiquitous passive and active scalar behavior of temperature
Analysis of the Lagrangian path structures in fluid turbulence
NASA Astrophysics Data System (ADS)
Wang, Lipo
2014-04-01
Because in the Lagrangian frame the time scale separation has a stronger Reynolds number dependence than the length scale case in the Eulerian frame, it is more difficult to reveal inertial range scaling laws, as predicted from dimensional arguments. The present work introduces a newly defined trajectory segment structure to tentatively understand Lagrangian statistics. When a fluid particle evolves in space, its Lagrangian trajectory encounters regions of different dynamics, which can be characterized by the magnitude of material acceleration, i.e., |a|, in certain time span. The extrema of |a| are considered as the representative markers along the Lagrangian trajectories. A trajectory segment is defined as the part bounded by two adjacent extrema of |a|. The time difference and magnitude of the velocity difference at the two ends of each segment are chosen as the characteristic parameters. It shows that such structure reveals interesting turbulence physics, such as the scaling of the structure function and the quantitative description of the time scale. The corresponding explanation and analysis of flow physics are provided as well to improve the understanding of some remaining challenging issues.
Lagrangian fluid dynamics using the Voronoi-Delauanay mesh
Dukowicz, J.K.
1981-01-01
A Lagrangian technique for numerical fluid dynamics is described. This technique makes use of the Voronoi mesh to efficiently locate new neighbors, and it uses the dual (Delaunay) triangulation to define computational cells. This removes all topological restrictions and facilitates the solution of problems containing interfaces and multiple materials. To improve computational accuracy a mesh smoothing procedure is employed.
Lagrangian Predictive Skill Assessment for the Deepwater Horizon Spill
NASA Astrophysics Data System (ADS)
Lipphardt, B. L.; Huntley, H. S.; Sulman, M.; Kirwan, A. D.
2011-12-01
The explosion and sinking of the Deepwater Horizon drilling platform produced enormous human, ecological, and economic impacts. At the same time this disaster provided an unprecedented amount of Lagrangian information on ocean processes, including a large number of surface and near-surface drifters deployed in the northeastern Gulf of Mexico as well as remotely sensed images of the surface oil slick. In addition several global and regional ocean model predictions were used to forecast the spill movements. These models generally exhibited large variations in the mesoscale flow near the Deepwater Horizon site, even though they all assimilated similar sets of ocean observations. This provides a unique opportunity to thoroughly assess model Lagrangian predictive skill. Here, the predictive skill of one model, a regional implementation of the Hybrid Coordinate Ocean Model (HYCOM), is evaluated using data from more than 80 drifter trajectories in the northern Gulf of Mexico. These trajectories are compared with maps of Lagrangian coherent structures, computed from near-surface model velocities, to determine whether the observations are consistent with the larger scale transport structure predicted by the model. We also discuss new metrics to assess model Lagrangian predictive skill of the plume movement.
Conditions for the existence of a Lagrangian in field theory
Farias, J.R.
1982-12-15
The necessary and sufficient conditions for a given set of n second-order field equations to be derivable from a variational principle of Hamilton's type were derived recently by Santilli. An alternative form is given which makes practical verification less tedious, and permits a direct construction of the Lagrangian.
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
Combining the Monotonic Lagrangian Grid with a Direct Simulation Monte Carlo Model
NASA Astrophysics Data System (ADS)
Cybyk, Bohdan Z.; Oran, Elaine S.; Boris, Jay P.; Anderson, John D.
1995-12-01
Using the monotonic Lagrangian grid (MLG) as a data structure in the direct simulation Monte Carlo (DSMC) methodology produces an approach that automatically adjusts grid resolution to time-varying densities in the flow. The MLG algorithm is an algorithm for tracking and sorting moving particles, and it has a monotonic data structure for indexing and storing the physical attributes of the particles. The DSMC method is a direct particle simulation technique widely used in predicting rarefied flows of dilute gases. Monotonicity features of the MLG ensure that particles close in physical space are stored in adjacent array locations so that particle interactions may be restricted to a "template" of near neighbors. The MLG templates provide a time-varying grid network that automatically adapts to local number densities within the flowfield. Computational advantages and disadvantages of this new implementation are demonstrated by a series of test problems.
A Lagrangian scheme for time-dependent ionization in simulations of astrophysical plasmas
NASA Astrophysics Data System (ADS)
Shen, C.; Raymond, J. C.; Murphy, N. A.; Lin, J.
2015-09-01
Time-dependent ionization is important in astrophysical environments where the thermodynamical time scale is shorter than the ionization or recombination time scales. In this work, we report a FORTRAN program that performs fast non-equilibrium ionization calculations in post-processing based on hydrodynamics(HD) or magnetohydrodynamics(MHD) simulation results. Using HD or MHD simulation results, we track the movement of plasma in a Lagrangian framework, and obtain the evolutionary history of temperature and electron density. The time-dependent ionization equations are then solved by the Eigenvalue method. For any complex temperature and electron density histories, we introduce an adaptive time-step strategy to improve the computational efficiency. Our tests show that this program has advantages of high numerical stability and high accuracy. In addition, it is also easy to extend this solver to other HD and MHD simulations. This code is freely available for download from the Web.
An extended-Lagrangian scheme for charge equilibration in reactive molecular dynamics simulations
NASA Astrophysics Data System (ADS)
Nomura, Ken-ichi; Small, Patrick E.; Kalia, Rajiv K.; Nakano, Aiichiro; Vashishta, Priya
2015-07-01
Reactive molecular dynamics (RMD) simulations describe chemical reactions at orders-of-magnitude faster computing speed compared with quantum molecular dynamics (QMD) simulations. A major computational bottleneck of RMD is charge-equilibration (QEq) calculation to describe charge transfer between atoms. Here, we eliminate the speed-limiting iterative minimization of the Coulombic energy in QEq calculation by adapting an extended-Lagrangian scheme that was recently proposed in the context of QMD simulations, Souvatzis and Niklasson (2014). The resulting XRMD simulation code drastically improves energy conservation compared with our previous RMD code, Nomura et al. (2008), while substantially reducing the time-to-solution. The XRMD code has been implemented on parallel computers based on spatial decomposition, achieving a weak-scaling parallel efficiency of 0.977 on 786,432 IBM Blue Gene/Q cores for a 67.6 billion-atom system.
Decentralised consensus for multiple Lagrangian systems based on event-triggered strategy
NASA Astrophysics Data System (ADS)
Liu, Xiangdong; Du, Changkun; Lu, Pingli; Yang, Dapeng
2016-06-01
This paper considers the decentralised event-triggered consensus problem for multi-agent systems with Lagrangian dynamics under undirected graphs. First, a distributed, leaderless, and event-triggered consensus control algorithm is presented based on the definition of generalised positions and velocities for all agents. There is only one triggering function for both the generalised positions and velocities and no Zeno behaviour exhibited under the proposed consensus strategy. Second, an adaptive event-triggered consensus control algorithm is proposed for such multi-agent systems with unknown constant parameters. Third, based on sliding-mode method, an event-triggered consensus control algorithm is considered for the case with external disturbance. Finally, simulation results are given to illustrate the theoretical results.
Li, Wu
1994-12-31
We study differentiable exact penalty functions, depending only on x, derived from Hestenes-Powell-Rockafellar`s quadratic augmented Lagrangian function for a minimization problem with two-sided inequality constraints by using Fletcher`s Lagrangian multiplier estimate. We also consider new penalty functions, depending only on the Lagrangian multiplier, derived from the augmented Lagrangian function. These penalty functions are particularly useful for quadratic programming problems.
A compatible Lagrangian hydrodynamic scheme for multicomponent flows with mixing
Chang, Chong; Stagg, Alan K
2012-01-01
We present a Lagrangian time integration scheme and compatible discretization for total energy conservation in multicomponent mixing simulations. Mixing behavior results from relative motion between species. Species velocities are determined by solving species momentum equations in a Lagrangian manner. Included in the species momentum equations are species artificial viscosity (since each species can undergo compression) and inter-species momentum exchange. Thermal energy for each species is also solved, including compression work and thermal dissipation caused by momentum exchange. The present procedure is applicable to mixing of an arbitrary number of species that may not be in pressure or temperature equilibrium. A traditional staggered stencil has been adopted to describe motion of each species. The computational mesh for the mixture is constructed in a Lagrangian manner using the mass-averaged mixture velocity. Species momentum equations are solved at the vertices of the mesh, and temporary species meshes are constructed and advanced in time using the resulting species velocities. Following the Lagrangian step, species quantities are advected (mapped) from the species meshes to the mixture mesh. Momentum exchange between species introduces work that must be included in an energy-conserving discretization scheme. This work has to be transformed to dissipation in order to effect a net change in species thermal energy. The dissipation between interacting species pairs is obtained by combining the momentum exchange work. The dissipation is then distributed to the species involved using a distribution factor based on species specific heats. The resulting compatible discretization scheme provides total energy conservation of the whole mixture. In addition, the numerical scheme includes conservative local energy exchange between species in mixture. Due to the relatively large species interaction coefficients, both the species momenta and energies are calculated
Ames, Thomas L.; Farnsworth, Grant V.; Ketcheson, David Isaac; Robinson, Allen Conrad
2009-09-01
The modeling of solids is most naturally placed within a Lagrangian framework because it requires constitutive models which depend on knowledge of the original material orientations and subsequent deformations. Detailed kinematic information is needed to ensure material frame indifference which is captured through the deformation gradient F. Such information can be tracked easily in a Lagrangian code. Unfortunately, not all problems can be easily modeled using Lagrangian concepts due to severe distortions in the underlying motion. Either a Lagrangian/Eulerian or a pure Eulerian modeling framework must be introduced. We discuss and contrast several Lagrangian/Eulerian approaches for keeping track of the details of material kinematics.