research-article

Entropy Stable Finite Volume Scheme for Ideal Compressible MHD on 2-D Cartesian Meshes

Authors:

Praveen Chandrashekar,

Christian KlingenbergAuthors Info & Claims

SIAM Journal on Numerical Analysis, Volume 54, Issue 2

Pages 1313 - 1340

https://doi.org/10.1137/15M1013626

Published: 01 January 2016 Publication History

Abstract

We present a finite volume scheme for ideal compressible magnetohydrodynamic (MHD) equations on two-dimensional Cartesian meshes. The semidiscrete scheme is constructed to be entropy stable by using the symmetrized version of the equations as introduced by Godunov. We first construct an entropy conservative scheme for which sufficient condition is given and we also derive a numerical flux satisfying this condition. Second, following a standard procedure, we make the scheme entropy stable by adding dissipative flux terms using jumps in entropy variables. A semi-discrete high resolution scheme is constructed that preserves the entropy stability of the first order scheme. We demonstrate the robustness of this new scheme on several standard MHD test cases.

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cover image SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Volume 54, Issue 2

DOI:10.1137/sjnaam.54.2

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© 2016, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2016

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Singh CYadav ABhoriya DKumar HBalsara D(2025)Entropy Stable Finite Difference Schemes for Chew, Goldberger and Low Anisotropic Plasma Flow EquationsJournal of Scientific Computing10.1007/s10915-024-02763-3102:2Online publication date: 6-Jan-2025
https://dl.acm.org/doi/10.1007/s10915-024-02763-3
Boscheri WLoubère RBraeunig JMaire P(2024)A geometrically and thermodynamically compatible finite volume scheme for continuum mechanics on unstructured polygonal meshesJournal of Computational Physics10.1016/j.jcp.2024.112957507:COnline publication date: 15-Jun-2024
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Zampa EBusto SDumbser M(2024)A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limitingApplied Numerical Mathematics10.1016/j.apnum.2024.01.014198:C(346-374)Online publication date: 25-Jun-2024
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Abgrall RBusto SDumbser M(2023)A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanicsApplied Mathematics and Computation10.1016/j.amc.2022.127629440:COnline publication date: 1-Mar-2023
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Bhoriya DBiswas BKumar HChandrashekhar P(2023)Entropy Stable Discontinuous Galerkin Schemes for Two-Fluid Relativistic Plasma Flow EquationsJournal of Scientific Computing10.1007/s10915-023-02387-z97:3Online publication date: 6-Nov-2023
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