Low Mach number effect in simulation of high Mach number flow

In the last decades, Godunov schemes are among the most successful methods in simulating compressible flows involving shock waves and discontinuities [18]. Godunov schemes utilize the solution of an Riemann solver at the face of computational cells as the numerical flux to introduce sufficient numerical dissipation [5]. However, some low-dissipation Godunov schemes, such as those with Roe flux, may suffer from numerical instabilities at the strong shock front, known as the carbuncle phenomena, when simulating multi-dimensional high Mach number flows [15].