Enhanced approximate Riemann solvers for all-Mach number flows using anti-diffusion coefficients

This paper compares the Harten–Lax–Leer–Einfeldt Modified (HLLEM) and Harten–Lax–Leer Convective Pressure Split (HLL-CPS) schemes for Euler equations and proposes improvements for all-Mach number flows. Enhancements to the HLLEM scheme involve adding anti-diffusion terms in the face normal direction and modifying anti-diffusion coefficients for linearly degenerate waves near shocks. The HLL-CPS scheme is improved by adjusting anti-diffusion coefficients for the face normal direction and linearly degenerate waves. Matrix stability, linear perturbation, and asymptotic analyses demonstrate the robustness of the proposed schemes and their ability to capture low Mach flow features. Numerical tests confirm that the schemes are free from shock instabilities at high speeds and accurately resolve low Mach number flow features.