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This paper presents entropy symmetrization and high-order accurate entropystable schemes for the relativistic magnetohydrodynamic (RMHD) equations. It isshown that the conservative RMHD equations are not symmetrizable and do notadmit a thermodynamic entropy pair. To address this issue, a symmetrizable RMHDsystem, equipped with a convex thermodynamic entropy pair, is proposed byadding a source term into the equations, providing an analogue to thenon-relativistic Godunov--Powell system. Arbitrarily high-order accurateentropy stable finite difference schemes are developed on Cartesian meshesbased on the symmetrizable RMHD system. The crucial ingredients of theseschemes include (i) affordable explicit entropy conservative fluxes which aretechnically derived through carefully selected parameter variables, (ii) aspecial high-order discretization of the source term in the symmetrizable RMHDsystem, and (iii) suitable high-order dissipative operators based onessentially non-oscillatory reconstruction to ensure the entropy stability.Several numerical tests demonstrate the accuracy and robustness of the proposedentropy stable schemes.

Entropy Symmetrization and High-Order Accurate Entropy Stable Numerical Schemes for Relativistic MHD Equations