The MHLLE (Multidimensional Harten, Lax, van Leer and Einfeldt) scheme, which is a genuinely multidimensional Riemann solver proposed by Balsara, encounters the accuracy problem at low speeds because it is built upon the compressible Euler equations. In order to overcome this problem, asymptotic analysis on the MHLLE scheme is conducted in this study. Based on the asymptotic analysis, a novel multidimensional Riemann solver called MHLLELS (Multidimensional Harten, Lax, van Leer and Einfeldt scheme for Low Speeds) for curvilinear coordinates is proposed. Systematic numerical cases, including 2d inviscid NACA (National Advisory Committee for Aeronautics) 0012 airfoil, Gresho vortex problem, separated flows around a circular cylinder (M_∞ = 0.01), turbulent flow over a flat plate, turbulent flow past a NACA0012 airfoil, turbulent flow past a backward facing step, and spherical blast wave, are carried out. Results indicate that the MHLLELS scheme proposed in this study improves the MHLLE scheme’s accuracy at low speeds remarkably, while it is with a high resolution in multidimensional cases. It is promising to be widely used in both scholar and engineering areas.

MHLLE（多维 Harten、Lax、van Leer 和 Einfeldt）方案是 Balsara 提出的真正的多维黎曼求解器，在低速时遇到精度问题，因为它建立在可压缩的欧拉方程上。为了克服这个问题，本研究对MHLLE方案进行了渐近分析。基于渐近分析，提出了一种新的曲线坐标多维黎曼求解器，称为 MHLLELS（多维 Harten、Lax、van Leer 和 Einfeldt 低速方案）。系统数值案例，包括 2d 无粘性 NACA（国家航空咨询委员会）0012 翼型、Gresho 涡问题、围绕圆柱体的分离流 ( M _∞ = 0.01)、平板上的湍流、NACA0012 翼型的湍流、逆向台阶的湍流和球形冲击波。结果表明，本研究提出的MHLLELS方案在低速下显着提高了MHLLE方案的精度，而在多维情况下具有较高的分辨率。它有望在学术和工程领域得到广泛应用。