A Godunov-type scheme for relativistic magnetohydrodynamics

Abstract

The basic properties of relativistic magnetohydrodynamics, as a hyperbolic system of quasi-linear conservation laws, are discussed. These are then used to develop a multidimensional Godunov-type numerical scheme that enforces the magnetic flux conservation. This scheme is based on linear Riemann solvers and has second-order accuracy in smooth regions. The results of thorough test calculations demonstrate that the scheme is robust and can cope with truly ultrarelativistic problems.