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

TL;DR

This paper develops and analyzes physical-constraints-preserving schemes for multi-dimensional special relativistic magnetohydrodynamics with a general equation of state on complex meshes, extending previous work limited to ideal EOS and Cartesian grids.

Contribution

It introduces a rigorous analysis of PCP schemes with Lax-Friedrichs flux on general meshes for relativistic MHD with a general EOS, including new convex decomposition and divergence-free conditions.

Findings

Established PCP property under general mesh conditions

Linked PCP to a discrete divergence-free condition

Extended analysis to non-ideal equations 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].