Abstract: The HLLC Riemann solver for magnetohydrodynamics (MHD) numerical simulation was previously developed based on the HLLC solver for hydrodynamics (HD). The inclusion of magnetic field leads to extra characteristic waves, leading to an inconsistency problem of the jump condition across the contact discontinuity. Usually, for the magnetic field, the single HLL intermediate state is used to replace the two HLLC intermediate states to achieve conservation and computational stability, at the cost of insufficient simulation accuracy for tangential discontinuity. In this paper, the previously developed HLLC solver is modified to deal with MHD tangential discontinuities accurately and satisfy the Toro condition. Based on different numerical tests, such as the time-dependent simulation of one-dimensional shocktube, tangential discontinuities, and the global MHD simulation of Earth's magnetosphere, we compare the numerical results of the modified HLLC solver with those of the standard HLLC and HLLD solvers. The results indicate that the modified HLLC solver has better capture accuracy for tangential discontinuities than the standard HLLC solver, and reaches the accuracy of HLLD solver in some situations.

Key words: Magnetohydrodynamics, Riemann solver, HLLC, tangential discontinuities