Development of an accurate and robust HLLC-type Riemann solver for all Mach number flows

Due to its positivity-preserving, entropy condition satisfying and easy extension to other types of hyperbolic equations, the HLLC scheme has become a popular Riemann solver to calculate numerical fluxes. However, there are two drawbacks needed to be tackled before it becomes an impeccable flux solver for various compressible flows: one is the numerical instability in calculating multidimensional strong shock waves; The other is the failure to converge to the desired limit solution in calculating low Mach number flows approaching the incompressible limit. In the current work, the shock instability of the HLLC scheme is cured by simply modifying the nonlinear wave speeds and a hybrid strategy is adopted for accurate calculations of contact waves and rarefaction waves. In addition, the performance of the HLLC scheme in simulating low Mach number flows is improved by controlling the excessive numerical dissipation in momentum equations under low-speed flow regime. The excellent performance of the proposed scheme for simulating flow problems across high and low Mach numbers are demonstrated by a suit of canonical numerical test cases.