Exact Solver and Uniqueness Conditions for Riemann Problems of Ideal Magnetohydrodynamics

Abstract

This paper presents the technical details necessary to implement an exact solver for the Riemann problem of magnetohydrodynamics (MHD) and investigates the uniqueness of MHD\Riemann solutions. The formulation of the solver results in a nonlinear algebraic 5 x 5 system of equations which has to be solved numerically. The equations of MHD form a non-strict hyperbolic system with non-convex fluxfunction. Thus special care is needed for possible non-regular waves, like compound waves or overcompressive shocks. The structure of the Hugoniot loci will be demonstrated and the non-regularity discussed. Several non-regular intermediate waves could be taken into account inside the solver. The non-strictness of the MHD system causes the Riemann problem also to be not unique. By virtue of the structure of the Hugoniot loci it follows, however, that the degree of freedom is reduced in the case of a non-regular solution. From this, uniqueness conditions for the Riemann problem of MHD are deduced.