Journal of Computational Physics, ISSN 0021-9991, 12/2019, Volume 398, p. 108899

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2012, Volume 231, Issue 22, pp. 7476 - 7503

In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at...

Conservation laws | Multidimensional Riemann solvers | MHD | HLL | HLLC | Higher order Godunov schemes | Euler equations | HYPERBOLIC SYSTEMS | DIVERGENCE-FREE CONDITION | EQUATIONS | HIGH-ORDER | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | CONSTRAINED TRANSPORT METHOD | GAS-DYNAMICS | IDEAL MAGNETOHYDRODYNAMICS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GODUNOV-TYPE METHODS | Environmental law

Conservation laws | Multidimensional Riemann solvers | MHD | HLL | HLLC | Higher order Godunov schemes | Euler equations | HYPERBOLIC SYSTEMS | DIVERGENCE-FREE CONDITION | EQUATIONS | HIGH-ORDER | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | CONSTRAINED TRANSPORT METHOD | GAS-DYNAMICS | IDEAL MAGNETOHYDRODYNAMICS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GODUNOV-TYPE METHODS | Environmental law

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2014, Volume 277, pp. 163 - 200

Multidimensional Riemann solvers have been formulated recently by the author (Balsara, 2010, 2012) . They operate at the vertices of a two-dimensional mesh,...

Conservation laws | Multidimensional Riemann solvers | Higher order schemes | ADER | WENO | Multidimensional riemann solvers | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | RELATIVISTIC MAGNETOHYDRODYNAMICS | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSPLIT GODUNOV METHOD | IDEAL MHD | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | EULER EQUATIONS | Environmental law

Conservation laws | Multidimensional Riemann solvers | Higher order schemes | ADER | WENO | Multidimensional riemann solvers | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | RELATIVISTIC MAGNETOHYDRODYNAMICS | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSPLIT GODUNOV METHOD | IDEAL MHD | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | EULER EQUATIONS | Environmental law

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2017, Volume 346, p. 25

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional...

Fluid mechanics | Boundary value problems | Magnetohydrodynamics | Computational fluid dynamics | Analogue | Approximations | Fluid flow | Hydrodynamics | Conservation laws | Finite element method | Solvers | Mathematical models | Galerkin method | Hyperbolic systems | Riemann solver | Self-similarity

Fluid mechanics | Boundary value problems | Magnetohydrodynamics | Computational fluid dynamics | Analogue | Approximations | Fluid flow | Hydrodynamics | Conservation laws | Finite element method | Solvers | Mathematical models | Galerkin method | Hyperbolic systems | Riemann solver | Self-similarity

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 05/2017, Volume 336, p. 104

In this paper we focus on the numerical solution of the induction equation using Runge–Kutta Discontinuous Galerkin (RKDG)-like schemes that are globally...

Reconstruction | Systems stability | Magnetohydrodynamics | Divergence | Propagation | Stability analysis | Studies | Conservation laws | Algorithms | Wave propagation | Solvers | Runge-Kutta method | Galerkin method | Magnetic fields | Two dimensional analysis | Riemann solver | Magnetic properties

Reconstruction | Systems stability | Magnetohydrodynamics | Divergence | Propagation | Stability analysis | Studies | Conservation laws | Algorithms | Wave propagation | Solvers | Runge-Kutta method | Galerkin method | Magnetic fields | Two dimensional analysis | Riemann solver | Magnetic properties

Journal Article

6.
Full Text
Multidimensional HLLE Riemann solver: Application to Euler and magnetohydrodynamic flows

Journal of Computational Physics, ISSN 0021-9991, 2010, Volume 229, Issue 6, pp. 1970 - 1993

In this work we present a general strategy for constructing multidimensional HLLE Riemann solvers, with particular attention paid to detailing the...

Conservation laws | MHD | Multidimensional | Euler | Riemann solvers | DIVERGENCE-FREE CONDITION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | DIFFERENCE-SCHEMES | MHD EQUATIONS | PHYSICS, MATHEMATICAL | GAS-DYNAMICS | IDEAL MAGNETOHYDRODYNAMICS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GODUNOV-TYPE METHODS | HYPERBOLIC CONSERVATION-LAWS | Environmental law

Conservation laws | MHD | Multidimensional | Euler | Riemann solvers | DIVERGENCE-FREE CONDITION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | DIFFERENCE-SCHEMES | MHD EQUATIONS | PHYSICS, MATHEMATICAL | GAS-DYNAMICS | IDEAL MAGNETOHYDRODYNAMICS | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GODUNOV-TYPE METHODS | HYPERBOLIC CONSERVATION-LAWS | Environmental law

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 09/2012, Volume 231, Issue 22, pp. 7504 - 7517

Several computational problems in science and engineering are stringent enough that maintaining positivity of density and pressure can become a problem. We...

Reconstruction | Magnetohydrodynamics | Positivity | WENO | Hydrodynamics | Higher order Godunov schemes | ADER | EFFICIENT IMPLEMENTATION | HYPERBOLIC SYSTEMS | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | MULTIDIMENSIONAL RIEMANN PROBLEM | IDEAL MAGNETOHYDRODYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | EULER EQUATIONS | Fluid dynamics | Specific gravity | Computational fluid dynamics | Fluid flow | MHD | Density | Preserving

Reconstruction | Magnetohydrodynamics | Positivity | WENO | Hydrodynamics | Higher order Godunov schemes | ADER | EFFICIENT IMPLEMENTATION | HYPERBOLIC SYSTEMS | ESSENTIALLY NONOSCILLATORY SCHEMES | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | MULTIDIMENSIONAL RIEMANN PROBLEM | IDEAL MAGNETOHYDRODYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | EULER EQUATIONS | Fluid dynamics | Specific gravity | Computational fluid dynamics | Fluid flow | MHD | Density | Preserving

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 08/2015, Volume 295, pp. 1 - 23

In this paper we build on our prior work on multidimensional Riemann solvers by detailing the construction of a three-dimensional HLL Riemann solver. As with...

Hyperbolic conservation laws | Multidimensional HLL Riemann solver | Euler equations | Higher order Godunov schemes | MHD equations | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | CONSTRAINED TRANSPORT | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LINEAR HYPERBOLIC SYSTEMS | UNSPLIT GODUNOV METHOD | IDEAL MHD | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Environmental law | Magnetohydrodynamics | Construction | Accuracy | MHD | Mathematical models | Fluxes | Riemann solver | Three dimensional

Hyperbolic conservation laws | Multidimensional HLL Riemann solver | Euler equations | Higher order Godunov schemes | MHD equations | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | PHYSICS, MATHEMATICAL | CONSTRAINED TRANSPORT | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LINEAR HYPERBOLIC SYSTEMS | UNSPLIT GODUNOV METHOD | IDEAL MHD | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Environmental law | Magnetohydrodynamics | Construction | Accuracy | MHD | Mathematical models | Fluxes | Riemann solver | Three dimensional

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 08/2009, Volume 228, Issue 14, pp. 5040 - 5056

In a pair of earlier papers the author showed the importance of divergence-free reconstruction in adaptive mesh refinement problems for magnetohydrodynamics...

Reconstruction | WENO schemes | Magnetohydrodynamics | Numerical methods | NUMERICAL MAGNETOHYDRODYNAMICS | EFFICIENT IMPLEMENTATION | ISOTHERMAL MAGNETOHYDRODYNAMICS | POLARIZED ALFVEN WAVES | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | CONSTRAINED TRANSPORT METHOD | IDEAL MAGNETOHYDRODYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Fluid dynamics | Magnetic fields | Analysis | Design engineering | Accuracy | Computational fluid dynamics | Fluid flow | MHD | Runge-Kutta method | Physics - Computational Physics

Reconstruction | WENO schemes | Magnetohydrodynamics | Numerical methods | NUMERICAL MAGNETOHYDRODYNAMICS | EFFICIENT IMPLEMENTATION | ISOTHERMAL MAGNETOHYDRODYNAMICS | POLARIZED ALFVEN WAVES | HIGH-ORDER | PHYSICS, MATHEMATICAL | SHOCK-CAPTURING SCHEMES | CONSTRAINED TRANSPORT METHOD | IDEAL MAGNETOHYDRODYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Fluid dynamics | Magnetic fields | Analysis | Design engineering | Accuracy | Computational fluid dynamics | Fluid flow | MHD | Runge-Kutta method | Physics - Computational Physics

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 01/2016, Volume 304, pp. 275 - 319

In this paper a new, and formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of...

Well-balanced scheme for single and two-layer shallow water equations | Path-conservative HLLEM Riemann solver | Conservation laws and general hyperbolic PDE with non-conservative terms | RMHD/MHD equations and nonlinear elasticity | Resolution of linearly degenerate intermediate waves | Euler equations with real equation of state and multiphase flows | COMPRESSIBLE 2-PHASE FLOW | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | RELATIVISTIC MAGNETOHYDRODYNAMICS | STRUCTURED MESHES | SHALLOW-WATER EQUATIONS | SOURCE TERMS | PDE with non-conservative terms | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GODUNOV-TYPE METHODS | Conservation laws and general hyperbolic | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Conservatism | Analysis | Fluid dynamics | Environmental law | Nonlinear dynamics | Magnetohydrodynamics | Computation | Mathematical analysis | Mathematical models | Entropy | Dynamical systems | Riemann solver | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MAGNETOHYDRODYNAMICS | TWO-PHASE FLOW | LAYERS | ELASTICITY | EIGENVALUES | NONLINEAR PROBLEMS | EIGENVECTORS | CONSERVATION LAWS | EQUATIONS OF STATE | FLOW MODELS | MULTIPHASE FLOW | ENTROPY

Well-balanced scheme for single and two-layer shallow water equations | Path-conservative HLLEM Riemann solver | Conservation laws and general hyperbolic PDE with non-conservative terms | RMHD/MHD equations and nonlinear elasticity | Resolution of linearly degenerate intermediate waves | Euler equations with real equation of state and multiphase flows | COMPRESSIBLE 2-PHASE FLOW | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | RELATIVISTIC MAGNETOHYDRODYNAMICS | STRUCTURED MESHES | SHALLOW-WATER EQUATIONS | SOURCE TERMS | PDE with non-conservative terms | GAS-DYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GODUNOV-TYPE METHODS | Conservation laws and general hyperbolic | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Conservatism | Analysis | Fluid dynamics | Environmental law | Nonlinear dynamics | Magnetohydrodynamics | Computation | Mathematical analysis | Mathematical models | Entropy | Dynamical systems | Riemann solver | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MAGNETOHYDRODYNAMICS | TWO-PHASE FLOW | LAYERS | ELASTICITY | EIGENVALUES | NONLINEAR PROBLEMS | EIGENVECTORS | CONSERVATION LAWS | EQUATIONS OF STATE | FLOW MODELS | MULTIPHASE FLOW | ENTROPY

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 11/2019, p. 109062

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 03/2014, Volume 261, pp. 172 - 208

The goal of this paper is to formulate genuinely multidimensional HLL and HLLC Riemann solvers for unstructured meshes by extending our prior papers on the...

High order schemes | Multidimensional Riemann solvers | ADER | WENO | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | FINITE-VOLUME | GAS-DYNAMICS | IDEAL MAGNETOHYDRODYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MAGNETOHYDRODYNAMIC FLOWS | GODUNOV-TYPE METHODS | HYPERBOLIC CONSERVATION-LAWS | Fluid dynamics | MHD | Paper | Magnetohydrodynamics | Fluxes | Computation | Riemann solver | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Two dimensional

High order schemes | Multidimensional Riemann solvers | ADER | WENO | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | DIFFERENCE-SCHEMES | PHYSICS, MATHEMATICAL | FINITE-VOLUME | GAS-DYNAMICS | IDEAL MAGNETOHYDRODYNAMICS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MAGNETOHYDRODYNAMIC FLOWS | GODUNOV-TYPE METHODS | HYPERBOLIC CONSERVATION-LAWS | Fluid dynamics | MHD | Paper | Magnetohydrodynamics | Fluxes | Computation | Riemann solver | Computational fluid dynamics | Mathematical analysis | Fluid flow | Mathematical models | Two dimensional

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2019, Volume 398, p. 1

In this work we present a conservative WENO Adaptive Order (AO) reconstruction operator applied to an explicit one-step Arbitrary-Lagrangian-Eulerian (ALE)...

Reconstructed DG schemes | [formula omitted] schemes | Arbitrary-Lagrangian-Eulerian (ALE) | WENO-AO reconstruction | High order of accuracy in space and time | Moving unstructured meshes | TRIANGULAR MESHES | COMPRESSIBLE FLOWS | TETRAHEDRAL MESHES | DISCONTINUOUS GALERKIN METHOD | PNPM schemes | PHYSICS, MATHEMATICAL | NONCONSERVATIVE HYPERBOLIC SYSTEMS | FORCE SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ELEMENT METHODS | CONSERVATION-LAWS | NEUMANN STABILITY ANALYSIS | WENO AO reconstruction | FINITE-VOLUME SCHEMES | Reconstruction | Computational fluid dynamics | Fluid flow | Conservation | Straight lines | Finite volume method | Hydrodynamics | Fluxes | Evolutionary algorithms | Accuracy | Mathematical analysis | Spacetime | Polynomials | Galerkin method | Time integration

Reconstructed DG schemes | [formula omitted] schemes | Arbitrary-Lagrangian-Eulerian (ALE) | WENO-AO reconstruction | High order of accuracy in space and time | Moving unstructured meshes | TRIANGULAR MESHES | COMPRESSIBLE FLOWS | TETRAHEDRAL MESHES | DISCONTINUOUS GALERKIN METHOD | PNPM schemes | PHYSICS, MATHEMATICAL | NONCONSERVATIVE HYPERBOLIC SYSTEMS | FORCE SCHEMES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ELEMENT METHODS | CONSERVATION-LAWS | NEUMANN STABILITY ANALYSIS | WENO AO reconstruction | FINITE-VOLUME SCHEMES | Reconstruction | Computational fluid dynamics | Fluid flow | Conservation | Straight lines | Finite volume method | Hydrodynamics | Fluxes | Evolutionary algorithms | Accuracy | Mathematical analysis | Spacetime | Polynomials | Galerkin method | Time integration

Journal Article

Computers & Fluids, ISSN 0045-7930, 10/2017, Volume 156, p. 220

In this paper, a family of high-order space-time polynomials in the context of continuous and discontinuous Galerkin methods is proposed. The resulting...

Studies | Construction | Degrees of freedom | Mathematical analysis | Finite volume method | Polynomials | Galerkin method | Fluxes | Derivatives

Studies | Construction | Degrees of freedom | Mathematical analysis | Finite volume method | Polynomials | Galerkin method | Fluxes | Derivatives

Journal Article

15.
Full Text
Second-Order-accurate Schemes for Magnetohydrodynamics with Divergence-free Reconstruction

The Astrophysical Journal Supplement Series, ISSN 0067-0049, 03/2004, Volume 151, Issue 1, pp. 149 - 184

While working on an adaptive mesh refinement (AMR) scheme for divergence-free magnetohydrodynamics (MHD), Balsara discovered a unique strategy for the...

MHD | Methods: numerical | EFFICIENT IMPLEMENTATION | VARIATION DIMINISHING SCHEME | RIEMANN SOLVER | ADAPTIVE MESH REFINEMENT | RADIATION MAGNETOHYDRODYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | SHOCK-CAPTURING SCHEMES | IDEAL MAGNETOHYDRODYNAMICS | ASTRONOMY & ASTROPHYSICS | methods : numerical | CONSERVATION-LAWS | Physics - Cosmology and Nongalactic Astrophysics | Physics - Earth and Planetary Astrophysics | Physics - Instrumentation and Methods for Astrophysics | Physics - High Energy Astrophysical Phenomena | Physics - Solar and Stellar Astrophysics | Physics - Astrophysics of Galaxies

MHD | Methods: numerical | EFFICIENT IMPLEMENTATION | VARIATION DIMINISHING SCHEME | RIEMANN SOLVER | ADAPTIVE MESH REFINEMENT | RADIATION MAGNETOHYDRODYNAMICS | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | SHOCK-CAPTURING SCHEMES | IDEAL MAGNETOHYDRODYNAMICS | ASTRONOMY & ASTROPHYSICS | methods : numerical | CONSERVATION-LAWS | Physics - Cosmology and Nongalactic Astrophysics | Physics - Earth and Planetary Astrophysics | Physics - Instrumentation and Methods for Astrophysics | Physics - High Energy Astrophysical Phenomena | Physics - Solar and Stellar Astrophysics | Physics - Astrophysics of Galaxies

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2018, Volume 354, p. 613

The Finite Difference Time Domain (FDTD) scheme has served the computational electrodynamics community very well and part of its success stems from its ability...

Magnetic induction | Electrodynamics | Preservation | Finite difference time domain method | Time domain analysis | Aerodynamics | Maxwell's equations | Thermodynamics | Computation | Magnetic permeability | Solvers | Staggering | Runge-Kutta method | Linear equations | Fields (mathematics) | Computer algebra | Permittivity | Riemann solver | Material properties | Finite difference method

Magnetic induction | Electrodynamics | Preservation | Finite difference time domain method | Time domain analysis | Aerodynamics | Maxwell's equations | Thermodynamics | Computation | Magnetic permeability | Solvers | Staggering | Runge-Kutta method | Linear equations | Fields (mathematics) | Computer algebra | Permittivity | Riemann solver | Material properties | Finite difference method

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2018, Volume 354, pp. 613 - 645

The Finite Difference Time Domain (FDTD) scheme has served the computational electrodynamics community very well and part of its success stems from its ability...

Computational electrodynamics | Higher order | Multidimensional Riemann solvers | Maxwell equations | Godunov schemes | Involution constraint | Algebra | Permeability

Computational electrodynamics | Higher order | Multidimensional Riemann solvers | Maxwell equations | Godunov schemes | Involution constraint | Algebra | Permeability

Journal Article