This paper compares the HLLEM and 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.

翻译：本文比较了适用于欧拉方程的HLLEM与HLL-CPS格式，并提出了针对全马赫数流动的改进方案。HLLEM格式的增强包括在面法向添加抗扩散项，并针对激波附近的线性退化波修正抗扩散系数。HLL-CPS格式的改进则通过调整面法向及线性退化波的抗扩散系数实现。矩阵稳定性分析、线性扰动分析与渐近分析证明了所提格式的鲁棒性及其捕捉低马赫流动特征的能力。数值试验证实，该系列格式在高速条件下无激波不稳定性，并能精确解析低马赫数流动特征。