An HLLC Riemann Solver for

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 satis¯es the conservation laws. Numerical examples are given to demonstrate that the new MHD-HLLC solver can achieve high numer-ical resolution, especially for resolving contact discontinuity. In addition, this new solver maintains a high computational e±ciency when compared to Roe's approxi-mate Riemann solver