An HLLC Riemann solver for magneto-hydrodynamics

This paper extends a class of approximate Riemann solvers devised by Harten, Lax and van Leer (HLL) for Euler equations of hydrodynamics to magneto-hydrodynamics (MHD) equations. In particular, we extend the two-state HLLC (HLL for contact wave) construction of Toro, Spruce and Speares to MHD equations. We derive a set of HLLC middle states that satisfies the conservation laws. Numerical examples are given to demonstrate that the new MHD-HLLC solver can achieve high numerical resolution, especially for resolving contact discontinuity. In addition, this new solver maintains a high computational efficiency when compared to Roe’s approximate Riemann solver.