A five-wave HLL Riemann solver for relativistic MHD

TL;DR

This paper introduces a five-wave Riemann solver tailored for ideal relativistic magnetohydrodynamics, extending previous non-relativistic methods to improve accuracy in complex plasma simulations.

Contribution

It develops a novel five-wave Riemann solver for relativistic MHD, incorporating the effects of relativistic discontinuities and providing a more precise alternative to existing solvers.

Findings

Significantly improves accuracy over HLL and HLLC solvers.

Validated through one-dimensional tests and multidimensional applications.

Proper closure achieved by solving a nonlinear scalar equation for total pressure.

Abstract

We present a five-wave Riemann solver for the equations of ideal relativistic magnetohydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi and Kusano for the equations of ideal MHD. The solution to the Riemann problem is approximated by a five wave pattern, comprised of two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a nonlinear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular HLL solver or the recently proposed HLLC schemes.