A hybrid multidimensional Riemann solver to couple self-similar method with MULTV method for complex flows

Abstract

Since proposed, the self-similarity variables based genuinely multidimensional Riemann solver is attracting more attentions due to its high resolution in multidimensional complex flows. However, it needs numerous logical operations in supersonic cases, which limit the method’s applicability in engineering problems greatly. In order to overcome this defect, a hybrid multidimensional Riemann solver, called HMTHS (Hybrid of MulTv and multidimensional HLL scheme based on Self-similar structures), is proposed. It simulates the strongly interacting zone by adopting the MHLLES (Multidimensional Harten-Lax-van Leer-Eifeldt scheme based on Self-similar structures) scheme at subsonic speeds, which is with a high resolution by considering the second moment in the similarity variables. Also, it adopts the MULTV (Multidimensional Toro and Vasquez) scheme, which is with a high resolution in capturing discontinuities, to simulate the flux at supersonic speeds. Systematic numerical experiments, including both one-dimensional cases and two-dimensional cases, are conducted. One-dimensional moving contact discontinuity case and sod shock tube case suggest that HMTHS can accurately capture one-dimensional expansion waves, shock waves, and linear contact discontinuities. Two-dimensional cases, such as the double Mach reflection case, the supersonic shock / boundary layer interaction case, the hypersonic flow over the cylinder case, and the hypersonic viscous flow over the double-ellipsoid case, indicate that the HMTHS scheme is with a high resolution in simulating multidimensional complex flows. Therefore, it is promising to be widely applied in both scholar and engineering areas.