On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

被引：0
作者：
Kailiang Wu
Huazhong Tang
机构：
[1] The Ohio State University,Department of mathematics
[2] Peking University,HEDPS, CAPT and LMAM, School of Mathematical Sciences
[3] Xiangtan University,School of Mathematics and Computational Science
来源：
Zeitschrift für angewandte Mathematik und Physik | 2018年 / 69卷
关键词：
Relativistic magnetohydrodynamics; Equation of state; Physical-constraints-preserving schemes; Admissible state set; Convexity; Generalized Lax–Friedrichs splitting; Discrete divergence-free condition; 65N30; 76M10; 76Y05;
D O I：
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摘要：
The paper studies the physical-constraints-preserving (PCP) schemes for multi-dimensional special relativistic magnetohydrodynamics with a general equation of state (EOS) on more general meshes. It is an extension of the work (Wu and Tang in Math. Models Methods Appl. Sci. 27:1871–1928, 2017) which focuses on the ideal EOS and uniform Cartesian meshes. The general EOS without a special expression poses some additional difficulties in discussing the mathematical properties of admissible state set with the physical constraints on the fluid velocity, density and pressure. Rigorous analyses are provided for the PCP property of finite volume or discontinuous Galerkin schemes with the Lax–Friedrichs (LxF)-type flux on a general mesh with non-self-intersecting polytopes. Those are built on a more general form of generalized LxF splitting property and a different convex decomposition technique. It is shown in theory that the PCP property is closely connected with a discrete divergence-free condition, which is proposed on the general mesh and milder than that in Wu and Tang (2017).
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