The Exact Solution of the Riemann Problem in Relativistic MHD

TL;DR

This paper presents an exact analytical solution to the Riemann problem in special relativistic MHD, providing a comprehensive test case for numerical codes in relativistic plasma simulations.

Contribution

It offers a general solution framework for the Riemann problem in relativistic MHD, including special cases with fewer waves, enhancing testing and validation of numerical methods.

Findings

Solution covers three-wave and seven-wave cases

Provides a benchmark for relativistic MHD codes

Enhances accuracy in numerical simulations of relativistic plasmas

Abstract

We discuss the procedure for the exact solution of the Riemann problem in special relativistic magnetohydrodynamics (MHD). We consider both initial states leading to a set of only three waves analogous to the ones in relativistic hydrodynamics, as well as generic initial states leading to the full set of seven MHD waves. Because of its generality, the solution presented here could serve as an important test for those numerical codes solving the MHD equations in relativistic regimes.