SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2006, Volume 44, Issue 1, pp. 300 - 321

The goal of this paper is to provide a theoretical framework allowing one to extend some general concepts related to the numerical approximation of 1-d...

Conservation laws | Approximation | Mathematical functions | Entropy | Godunov method | Numerical schemes | Borel measures | Cauchy problem | Curves | Well-balanced schemes | Approximate Riemann solvers | Finite volume method | Roe methods | Relaxation methods | Godunov methods | Nonconservative products | High order methods | approximate Riemann solvers | DEFINITION | MATHEMATICS, APPLIED | well-balanced schemes | high order methods | WEAK STABILITY | EQUATIONS | WELL-BALANCED SCHEME | finite volume method | FORMULATION | KINETIC SCHEME | SOURCE TERMS | PRODUCTS | nonconservative products | CONSERVATION-LAWS | relaxation methods

Conservation laws | Approximation | Mathematical functions | Entropy | Godunov method | Numerical schemes | Borel measures | Cauchy problem | Curves | Well-balanced schemes | Approximate Riemann solvers | Finite volume method | Roe methods | Relaxation methods | Godunov methods | Nonconservative products | High order methods | approximate Riemann solvers | DEFINITION | MATHEMATICS, APPLIED | well-balanced schemes | high order methods | WEAK STABILITY | EQUATIONS | WELL-BALANCED SCHEME | finite volume method | FORMULATION | KINETIC SCHEME | SOURCE TERMS | PRODUCTS | nonconservative products | CONSERVATION-LAWS | relaxation methods

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 04/2019, Volume 382, pp. 1 - 26

In this work, we consider the discretization of nonlinear hyperbolic systems in nonconservative form with the high-order discontinuous Galerkin spectral...

Discontinuous Galerkin method | Nonconservative hyperbolic systems | Two-phase flows | Entropy stable schemes | Summation-by-parts | BAER-NUNZIATO EQUATIONS | IDEAL COMPRESSIBLE MHD | MODEL | PHYSICS, MATHEMATICAL | LARGE TIME STEPS | WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SPLIT-FORM | ROBUST | QUADRATURE | FINITE-VOLUME SCHEMES | Two phase flow | Maximum principle | Entropy | Stability analysis | Fluxes | Euler-Lagrange equation | Conservation laws | Interpolation | Robustness (mathematics) | Discretization | Interface stability | Spectral element method | Runge-Kutta method | Mathematical models | Galerkin method | Nonlinear systems | Hyperbolic systems | Mechanics | Engineering Sciences | Fluids mechanics

Discontinuous Galerkin method | Nonconservative hyperbolic systems | Two-phase flows | Entropy stable schemes | Summation-by-parts | BAER-NUNZIATO EQUATIONS | IDEAL COMPRESSIBLE MHD | MODEL | PHYSICS, MATHEMATICAL | LARGE TIME STEPS | WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SPLIT-FORM | ROBUST | QUADRATURE | FINITE-VOLUME SCHEMES | Two phase flow | Maximum principle | Entropy | Stability analysis | Fluxes | Euler-Lagrange equation | Conservation laws | Interpolation | Robustness (mathematics) | Discretization | Interface stability | Spectral element method | Runge-Kutta method | Mathematical models | Galerkin method | Nonlinear systems | Hyperbolic systems | Mechanics | Engineering Sciences | Fluids mechanics

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2012, Volume 34, Issue 5, pp. B523 - B558

In this work we present a new approach to the construction of high order finite volume central schemes on staggered grids for general hyperbolic systems,...

Well-balanced schemes | Nonconservative hyperbolic systems | Runge-kutta methods | Central schemes | High order accuracy | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | high order accuracy | WENO SCHEMES | well-balanced schemes | RECONSTRUCTION | Runge Kutta methods | SHALLOW-WATER EQUATIONS | HIGH-ORDER EXTENSIONS | central schemes | nonconservative hyperbolic systems | ERROR | FINITE-VOLUME SCHEMES

Well-balanced schemes | Nonconservative hyperbolic systems | Runge-kutta methods | Central schemes | High order accuracy | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | high order accuracy | WENO SCHEMES | well-balanced schemes | RECONSTRUCTION | Runge Kutta methods | SHALLOW-WATER EQUATIONS | HIGH-ORDER EXTENSIONS | central schemes | nonconservative hyperbolic systems | ERROR | FINITE-VOLUME SCHEMES

Journal Article

Communications in Computational Physics, ISSN 1815-2406, 04/2017, Volume 21, Issue 4, pp. 913 - 946

We propose here a class of numerical schemes for the approximation of weak solutions to nonlinear hyperbolic systems in nonconservative form-the notion of...

discrete scheme | complex fluid dynamics | nonconservative system | Nonlinear hyperbolic | controlled dissipation | NUMERICAL-METHODS | KINETIC RELATIONS | EXISTENCE | PHYSICS, MATHEMATICAL | NONCLASSICAL SHOCKS | WAVES | MODELS | PRODUCTS | ERROR | CONSERVATION-LAWS

discrete scheme | complex fluid dynamics | nonconservative system | Nonlinear hyperbolic | controlled dissipation | NUMERICAL-METHODS | KINETIC RELATIONS | EXISTENCE | PHYSICS, MATHEMATICAL | NONCLASSICAL SHOCKS | WAVES | MODELS | PRODUCTS | ERROR | CONSERVATION-LAWS

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 4/2009, Volume 39, Issue 1, pp. 67 - 114

This paper is concerned with the development of well-balanced high order Roe methods for two-dimensional nonconservative hyperbolic systems. In particular, we...

Source terms | Computational Mathematics and Numerical Analysis | 2d Nonconservative hyperbolic systems | Mathematical and Computational Physics | Mathematics | Nonconservative products | Conservation laws | Algorithms | Appl.Mathematics/Computational Methods of Engineering | Geophysical flows | Shallow water systems | Generalized Roe schemes | Finite volume schemes | Two-layer problems | MATHEMATICS, APPLIED | RECONSTRUCTION | PROPERTY | EQUATIONS | WELL-BALANCED SCHEME | SHALLOW-WATER SYSTEMS | PRODUCTS | CONSERVATION-LAWS | FLUXES | FINITE-VOLUME SCHEMES | Environmental law | Two dimensional | Computation | Shallow water | Hyperbolic systems | Consistency

Source terms | Computational Mathematics and Numerical Analysis | 2d Nonconservative hyperbolic systems | Mathematical and Computational Physics | Mathematics | Nonconservative products | Conservation laws | Algorithms | Appl.Mathematics/Computational Methods of Engineering | Geophysical flows | Shallow water systems | Generalized Roe schemes | Finite volume schemes | Two-layer problems | MATHEMATICS, APPLIED | RECONSTRUCTION | PROPERTY | EQUATIONS | WELL-BALANCED SCHEME | SHALLOW-WATER SYSTEMS | PRODUCTS | CONSERVATION-LAWS | FLUXES | FINITE-VOLUME SCHEMES | Environmental law | Two dimensional | Computation | Shallow water | Hyperbolic systems | Consistency

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2013, Volume 51, Issue 3, pp. 1371 - 1391

The vanishing viscosity limit of nonconservative hyperbolic systems depends heavily on the specific form of the viscosity. Numerical approximations, such as...

Viscosity | Conservation laws | Shallow water equations | Line segments | Approximation | Entropy | Godunov method | Numerical schemes | Shallow water | Cauchy problem | Entropy conservative schemes | Nonconservative hyperbolic systems | Scheme | Entropy stable | Two-layer shallow water system | MATHEMATICS, APPLIED | two-layer shallow water system | entropy stable scheme | nonconservative hyperbolic systems | ERROR | entropy conservative schemes | SHALLOW-WATER EQUATIONS | Operators | Discretization | Robustness | Diffusion | Hyperbolic systems

Viscosity | Conservation laws | Shallow water equations | Line segments | Approximation | Entropy | Godunov method | Numerical schemes | Shallow water | Cauchy problem | Entropy conservative schemes | Nonconservative hyperbolic systems | Scheme | Entropy stable | Two-layer shallow water system | MATHEMATICS, APPLIED | two-layer shallow water system | entropy stable scheme | nonconservative hyperbolic systems | ERROR | entropy conservative schemes | SHALLOW-WATER EQUATIONS | Operators | Discretization | Robustness | Diffusion | Hyperbolic systems

Journal Article

Computers and Fluids, ISSN 0045-7930, 06/2018, Volume 169, pp. 10 - 22

It is well known, thanks to Laxâ€“Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and...

Nonconservative formulation | Euler equations | Fluid dynamics | Residual distribution | Multiphase flow systems | Conservation | RELAXATION-PROJECTION METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | COMPRESSIBLE FLOWS | MESHES | RESIDUAL DISTRIBUTION SCHEMES

Nonconservative formulation | Euler equations | Fluid dynamics | Residual distribution | Multiphase flow systems | Conservation | RELAXATION-PROJECTION METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | COMPRESSIBLE FLOWS | MESHES | RESIDUAL DISTRIBUTION SCHEMES

Journal Article

Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 07/2006, Volume 75, Issue 255, pp. 1103 - 1134

This paper is concerned with the development of high order methods for the numerical approximation of one-dimensional nonconservative hyperbolic systems. In...

Conservation laws | Interpolation | Approximation | Eigenvalues | Mathematical functions | Numerical schemes | Shallow water | Curves | Linearization | Cauchy problem | High order schemes | Well-balanced schemes | Weighted ENO | Shallow-water systems | Roe methods | Nonconservative products | Hyperbolic systems | MATHEMATICS, APPLIED | high order schemes | WENO SCHEMES | well-balanced schemes | ENO | WELL-BALANCED SCHEME | weighted ENO | SOURCE TERMS | LAWS | shallow-water systems | nonconservative products | hyperbolic systems | EXACT CONSERVATION PROPERTY

Conservation laws | Interpolation | Approximation | Eigenvalues | Mathematical functions | Numerical schemes | Shallow water | Curves | Linearization | Cauchy problem | High order schemes | Well-balanced schemes | Weighted ENO | Shallow-water systems | Roe methods | Nonconservative products | Hyperbolic systems | MATHEMATICS, APPLIED | high order schemes | WENO SCHEMES | well-balanced schemes | ENO | WELL-BALANCED SCHEME | weighted ENO | SOURCE TERMS | LAWS | shallow-water systems | nonconservative products | hyperbolic systems | EXACT CONSERVATION PROPERTY

Journal Article

ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 1/2007, Volume 41, Issue 1, pp. 169 - 185

This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The theory developed by Dal...

Approximate Riemann solvers | Nonconservative hyperbolic systems | Godunov method | Well-balancing | approximate Riemann solvers | SOURCE TERMS | DEFINITION | MATHEMATICS, APPLIED | well-balancing | nonconservative hyperbolic systems | WELL-BALANCED SCHEME | CONSERVATION-LAWS

Approximate Riemann solvers | Nonconservative hyperbolic systems | Godunov method | Well-balancing | approximate Riemann solvers | SOURCE TERMS | DEFINITION | MATHEMATICS, APPLIED | well-balancing | nonconservative hyperbolic systems | WELL-BALANCED SCHEME | CONSERVATION-LAWS

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2008, Volume 227, Issue 3, pp. 1887 - 1922

We present space- and spaceâ€“time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in...

Nonconservative products | Numerical fluxes | Two-phase flows | Arbitrary Lagrangian Eulerian (ALE) formulation | Discontinuous Galerkin finite element methods | PACS-47.55.-t | PACS-47.85.Dh | MSC-65M60 | PACS-02.60.Cb | MSC-35L67 | PACS-02.70.Dh | MSC-35L65 | MSC-35L60 | MSC-76M10 | 2-FLUID MODEL | RIEMANN SOLVER | discontinuous Galerkin finite element methods | arbitrary Lagrangian Eulerian (ALE) formulation | FLUX | PHYSICS, MATHEMATICAL | numerical fluxes | SOURCE TERMS | AVALANCHE | SHALLOW-WATER SYSTEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | PRODUCTS | two-phase flows | nonconservative products | FLOWS | SCHEMES | Finite element method | Analysis | Methods | SPACE-TIME | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | PARTIAL DIFFERENTIAL EQUATIONS | TOPOGRAPHY | MULTIPHASE FLOW | TWO-PHASE FLOW | FINITE ELEMENT METHOD | LAGRANGIAN FUNCTION | WATER

Nonconservative products | Numerical fluxes | Two-phase flows | Arbitrary Lagrangian Eulerian (ALE) formulation | Discontinuous Galerkin finite element methods | PACS-47.55.-t | PACS-47.85.Dh | MSC-65M60 | PACS-02.60.Cb | MSC-35L67 | PACS-02.70.Dh | MSC-35L65 | MSC-35L60 | MSC-76M10 | 2-FLUID MODEL | RIEMANN SOLVER | discontinuous Galerkin finite element methods | arbitrary Lagrangian Eulerian (ALE) formulation | FLUX | PHYSICS, MATHEMATICAL | numerical fluxes | SOURCE TERMS | AVALANCHE | SHALLOW-WATER SYSTEMS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | PRODUCTS | two-phase flows | nonconservative products | FLOWS | SCHEMES | Finite element method | Analysis | Methods | SPACE-TIME | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | PARTIAL DIFFERENTIAL EQUATIONS | TOPOGRAPHY | MULTIPHASE FLOW | TWO-PHASE FLOW | FINITE ELEMENT METHOD | LAGRANGIAN FUNCTION | WATER

Journal Article

ESAIM: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, 9/2004, Volume 38, Issue 5, pp. 821 - 852

This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to...

Source terms | Well-balanced schemes | Nonconservative hyperbolic systems | Shallow-water systems | Roe method | MATHEMATICS, APPLIED | well-balanced schemes | EQUATIONS | IRREGULAR GEOMETRY | FORMULATION | RIEMANN PROBLEM | SCHEME | shallow-water systems | PRODUCTS | nonconservative hyperbolic systems | source terms | CHANNELS | CONSERVATION-LAWS

Source terms | Well-balanced schemes | Nonconservative hyperbolic systems | Shallow-water systems | Roe method | MATHEMATICS, APPLIED | well-balanced schemes | EQUATIONS | IRREGULAR GEOMETRY | FORMULATION | RIEMANN PROBLEM | SCHEME | shallow-water systems | PRODUCTS | nonconservative hyperbolic systems | source terms | CHANNELS | CONSERVATION-LAWS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 01/2016, Volume 272, pp. 385 - 402

â€¢Unsplit implementation of hyperbolic divergence cleaningâ€¢Galilean invariant hyperbolic divergence cleaning (= Powell+GLM)â€¢Via Roe-linearization full control...

Generalized Lagrange multiplier | Shallow water MHD | Finite-volume schemes | Divergence cleaning | Nonconservative PDE | MATHEMATICS, APPLIED | SOLVERS | MHD EQUATIONS | NonconseNative PDE | CONSTRAINED TRANSPORT METHOD | IDEAL MHD | SYSTEMS | CONSERVATION-LAWS | FLOWS | Fluid dynamics

Generalized Lagrange multiplier | Shallow water MHD | Finite-volume schemes | Divergence cleaning | Nonconservative PDE | MATHEMATICS, APPLIED | SOLVERS | MHD EQUATIONS | NonconseNative PDE | CONSTRAINED TRANSPORT METHOD | IDEAL MHD | SYSTEMS | CONSERVATION-LAWS | FLOWS | Fluid dynamics

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 10/2012, Volume 75, Issue 15, pp. 5933 - 5960

This research explores the initial-boundary value problem for the 2Ã—2 hyperbolic systems of balance laws whose sources are the time-dependent and contain the...

Modified Lax method | Nonlinear balance laws | Generalized Glimm scheme | Perturbed boundary Riemann problem | Initial-boundary value problem | Hyperbolic integro-differential systems | [formula omitted]-systems | Entropy solution | Perturbed Riemann problem | p-systems | EXISTENCE | MATHEMATICS, APPLIED | NONCONSERVATIVE FORM | VARIATIONAL WAVE-EQUATION | ENTROPY SOLUTIONS | MATHEMATICS | CONSERVATION-LAWS | WEAK SOLUTIONS | TIME-PERIODIC SOLUTIONS

Modified Lax method | Nonlinear balance laws | Generalized Glimm scheme | Perturbed boundary Riemann problem | Initial-boundary value problem | Hyperbolic integro-differential systems | [formula omitted]-systems | Entropy solution | Perturbed Riemann problem | p-systems | EXISTENCE | MATHEMATICS, APPLIED | NONCONSERVATIVE FORM | VARIATIONAL WAVE-EQUATION | ENTROPY SOLUTIONS | MATHEMATICS | CONSERVATION-LAWS | WEAK SOLUTIONS | TIME-PERIODIC SOLUTIONS

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 7/2011, Volume 48, Issue 1, pp. 141 - 163

We present a new kind of high-order reconstruction operator of polynomial type, which is used in combination with the scheme presented in Castro et al. (J....

Computational Mathematics and Numerical Analysis | Nonconservative hyperbolic systems | Algorithms | High-order schemes | Theoretical, Mathematical and Computational Physics | Well-balanced | GPUs | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Shallow water | Finite volume methods | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | ORDER | CONSERVATION-LAWS | FLOWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Reconstruction | Shallow water equations | Operators | Computation | Central processing units | Two dimensional | Hyperbolic systems

Computational Mathematics and Numerical Analysis | Nonconservative hyperbolic systems | Algorithms | High-order schemes | Theoretical, Mathematical and Computational Physics | Well-balanced | GPUs | Appl.Mathematics/Computational Methods of Engineering | Mathematics | Shallow water | Finite volume methods | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | ORDER | CONSERVATION-LAWS | FLOWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Reconstruction | Shallow water equations | Operators | Computation | Central processing units | Two dimensional | Hyperbolic systems

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2000, Volume 39, Issue 9, pp. 135 - 159

We propose a way to construct robust numerical schemes for the computations of numerical solutions of one- and two-dimensional hyperbolic systems of balance...

Conservation laws | Source terms | Nonconservative products | Balanced scheme | MATHEMATICS, APPLIED | GODUNOV | conservation laws | RIEMANN SOLVER | EQUATIONS | nonconservative products | ROE | source terms | balanced scheme | FLOWS

Conservation laws | Source terms | Nonconservative products | Balanced scheme | MATHEMATICS, APPLIED | GODUNOV | conservation laws | RIEMANN SOLVER | EQUATIONS | nonconservative products | ROE | source terms | balanced scheme | FLOWS

Journal Article

Computers and Fluids, ISSN 0045-7930, 08/2016, Volume 134-135, pp. 111 - 129

â€¢High order cell-centered ADER-WENO ALE schemes for nonlinear hyperelasticity (GPR model).â€¢Thermodynamically compatible symmetric hyperbolic formulation of...

Hyperbolic conservation laws with stiff source terms and non-conservative products | Unified first order hyperbolic formulation of continuum mechanics | Symmetric-hyperbolic Godunov-Peshkov-Romenski model (GPR model) of nonlinear hyperelasticity | Viscous heat conducting fluids and nonlinear elasto-plastic solids | High order direct Arbitrary-Lagrangian-Eulerian finite volume schemes | High order ADER-WENO schemes on moving unstructured meshes | TRIANGULAR MESHES | High order direct | TETRAHEDRAL MESHES | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | Arbitrary-Lagrangian-Eulerian finite volume schemes | NONCONSERVATIVE HYPERBOLIC SYSTEMS | Godunov-Peshkov-Romenski model (GPR model) of nonlinear hyperelasticity | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONTINUUM-MECHANICS | Symmetric-hyperbolic | BALANCE LAWS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | DIFFUSE INTERFACE MODEL | Thermodynamics | Mechanical engineering | Analysis | Environmental law | Finite element method | Reconstruction | Numerical analysis | Mathematical analysis | Nonlinearity | Mathematical models | Continuum mechanics | Navier-Stokes equations | Numerical Analysis | Analysis of PDEs | Mathematics

Hyperbolic conservation laws with stiff source terms and non-conservative products | Unified first order hyperbolic formulation of continuum mechanics | Symmetric-hyperbolic Godunov-Peshkov-Romenski model (GPR model) of nonlinear hyperelasticity | Viscous heat conducting fluids and nonlinear elasto-plastic solids | High order direct Arbitrary-Lagrangian-Eulerian finite volume schemes | High order ADER-WENO schemes on moving unstructured meshes | TRIANGULAR MESHES | High order direct | TETRAHEDRAL MESHES | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | Arbitrary-Lagrangian-Eulerian finite volume schemes | NONCONSERVATIVE HYPERBOLIC SYSTEMS | Godunov-Peshkov-Romenski model (GPR model) of nonlinear hyperelasticity | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | CONTINUUM-MECHANICS | Symmetric-hyperbolic | BALANCE LAWS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | DIFFUSE INTERFACE MODEL | Thermodynamics | Mechanical engineering | Analysis | Environmental law | Finite element method | Reconstruction | Numerical analysis | Mathematical analysis | Nonlinearity | Mathematical models | Continuum mechanics | Navier-Stokes equations | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

Journal of Computational Science, ISSN 1877-7503, 01/2013, Volume 4, Issue 1-2, pp. 111 - 124

â–º Nonconservative hyperbolic systems. â–º Dal Masoâ€“LeFlochâ€“Murat path theory. â–º Numerical approximation of non-conservative systems. Attempts to define weak...

Laxâ€“Friedrichs scheme | Godunov scheme | Nonconservative product | Finite volume schemes | Hyperbolic systems | Lax-Friedrichs scheme | RIEMANN SOLVER | EQUATIONS | MODEL | SHOCK-WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ERROR | COMPUTER SCIENCE, THEORY & METHODS | FLOWS | SCHEMES

Laxâ€“Friedrichs scheme | Godunov scheme | Nonconservative product | Finite volume schemes | Hyperbolic systems | Lax-Friedrichs scheme | RIEMANN SOLVER | EQUATIONS | MODEL | SHOCK-WAVES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ERROR | COMPUTER SCIENCE, THEORY & METHODS | FLOWS | SCHEMES

Journal Article

Multiscale Modeling and Simulation, ISSN 1540-3459, 2011, Volume 9, Issue 3, pp. 1253 - 1275

The Vicsek model is a very popular individual based model which describes collective behavior among animal societies. A large-scale limit of the Vicsek model...

Relaxation | Nonconservative equation | Individual based model | Splitting scheme | Geometric constraint | Hyperbolic systems | nonconservative equation | splitting scheme | individual based model | PARTICLE | relaxation | CONTINUUM-LIMIT | geometric constraint | MODEL | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOTION | PHASE-TRANSITION | MOVEMENT | hyperbolic systems

Relaxation | Nonconservative equation | Individual based model | Splitting scheme | Geometric constraint | Hyperbolic systems | nonconservative equation | splitting scheme | individual based model | PARTICLE | relaxation | CONTINUUM-LIMIT | geometric constraint | MODEL | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MOTION | PHASE-TRANSITION | MOVEMENT | hyperbolic systems

Journal Article