Paper Info
Title
Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations
Abstract
This paper presents entropy symmetrization and high-order accurate entropy stable schemes for the relativistic magnetohydrodynamic (RMHD) equations. It is shown that the conservative RMHD equations are not symmetrizable and do not admit a thermodynamic entropy pair. To address this issue, a symmetrizable RMHD system, equipped with a convex thermodynamic entropy pair, is first proposed by adding a source term into the equations, providing an analogue to the nonrelativistic Godunov-Powell system. Arbitrarily high-order accurate entropy stable finite difference schemes are developed on Cartesian meshes based on the symmetrizable RMHD system. The crucial ingredients of these schemes include (i) affordable explicit entropy conservative fluxes which are technically derived through carefully selected parameter variables, (ii) a special high-order discretization of the source term in the symmetrizable RMHD system, and (iii) suitable high-order dissipative operators based on essentially nonoscillatory reconstruction to ensure the entropy stability. Several numerical tests demonstrate the accuracy and robustness of the proposed entropy stable schemes.
Year
DOI
Venue
2020
10.1137/19M1275590
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
DocType
Volume
relativistic magnetohydrodynamics,symmetrizable,entropy conservative,entropy stable,high-order accuracy
Journal
42
Issue
ISSN
Citations 
4
1064-8275
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Wu Kailiang100.68
Chi-Wang Shu24053540.35