Self-Similar-Structure–Based All-Speed Genuinely Two-Dimensional Riemann Solver

Abstract

In this study, the low-speed asymptotic analysis of the Multidimensional, Self-Similar, Strongly Interacting, Consistent with the Second-Order Moment (MuSIC2) scheme in the low-speed limit is conducted. Based on such analysis, a controlling function is employed to control the numerical dissipation in the momentum equations at low speeds, and the All-Speed MuSIC2 (AMuSIC2) scheme is proposed in curvilinear coordinates. Systematic numerical tests are illustrated. The one-dimensional cases show that the AMuSIC2 scheme is capable of accurately capturing one-dimensional shocks, expansion waves, and contact discontinuities. The two-dimensional odd–even decoupling case indicates that the AMuSIC2 scheme is robust against the unphysical shock anomaly in capturing strong shocks. The spherical blast wave case indicates that the AMuSIC2 scheme improves the traditional one-dimensional Riemann solvers’ mesh imprinting phenomenon as the MuSIC2 scheme. The two-dimensional inviscid flow over the NACA0012 airfoil case and the low-speed Gresho vortex case suggest that the AMuSIC2 scheme improves the MuSCI2 scheme’s accuracy at low speeds remarkably. The turbulent flow over the flat plate case and the turbulent flow past the NACA4412 airfoil case also suggest that the AMuSIC2 scheme has a much higher level of accuracy at low speeds than its counterpart.