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

Abstract

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 [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 [Math. Models Methods Appl. Sci., 27:1871-1928, 2017].

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• A new first-order formulation of the Einstein equations exploiting analogies with electrodynamics
• Two-stage fourth-order accurate time discretizations for 1D and 2D special relativistic hydrodynamics
• Second-order accurate BGK schemes for the special relativistic hydrodynamics with the Synge equation of state
• Provably Physical-Constraint-Preserving Discontinuous Galerkin Methods for Multidimensional Relativistic MHD Equations
• A physical-constraints-preserving genuinely multidimensional HLL scheme for the special relativistic hydrodynamics