Optimization and Application of the HLLC Riemann Solver

The entropy fix of the HLLC Riemann solver for the general equation of state was studied. Based on HLL and HLLC Riemann solvers' trait and the upwind characteristic, the idea of the HLL Riemann solver was used to overcome the sonic fix in the sonic rarefaction wave. Motivied by Olieinik's entropy condition, some threshold values were defined to kill the sonic fix, which can be used in the ALE methods for the multimaterial problems. Numerical experiments support the Modified HLLC Riemann solver.