Low-Speed Modification for the Genuinely Multidimensional Harten, Lax, van Leer and Einfeldt Scheme in Curvilinear Coordinates

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.