The HLLEM scheme is a popular numerical method for computing the convective fluxes in the Euler equations and the Navier–Stokes equations due to its accuracy and positivity-preserving. However, it still has two defects. One is the numerical instability, such as the carbuncle phenomenon, in computations involving multidimensional strong shock waves; the other is the non-physical results caused by accuracy issues in computations of low Mach number flows. In the engineering field, high Mach number flows with strong shock waves and low Mach number...
