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 instabi...
