A Riemann solver for the two-dimensional MHD equations

Abstract

This paper presents how the equations of magnetohydrodynamics (MHD) in primitive form should be written in conservative form with the inclusion of a divergence source along with a divergence wave and how a physically correct sonic fix can be embedded directly in the fluxes. The numerical scheme was applied to a blast wave problem in which a circular energetic plasma is released in a free and magnetized medium with a reflected wall. The results show that the method with the new sonic fix can handle the divergence condition on the magnetic field and produces an almost uniform shock compression in all directions, resolving the shocks and discontinuities rather sharply. © 1997 John Wiley & Sons, Ltd.