High order WENO scheme based on HLL-HLLC solver and its application

HLL-HLLC is one kind of schemes which are suitable for a large range of Ma number. It can overcome the shock instability phenomena which may happen to HLLC scheme while keeping low dissipation. The proposed HLL-HLLC scheme is coupled with finite difference type of high order WENO schemes based on characteristic variables to evaluate the inviscid numerical flux in a high order. Meanwhile, a set of fully conservative 4th-order central difference schemes are utilized to deal with the viscous terms. In this way, high order numerical methodologies for RANS are established. Four classical test cases are simulated to validate the proposed schemes: hypersonic flow over blunt body, transonic flow over ONERA M6 wing, transonic flow over DLR F6-WB configuration and DLR F6-WBNP complex configuration. The performances of two WENO variations are investigated. What's more, the free parameter for WENO schemes is proposed in complex fluid simulations to strengthen the convergence rate. Numerical results show that: high order schemes could capture the shock sharply and give a more accurate location of strong shocks; furthermore, much more flow details could be distinguished. The proposed high order schemes are robust enough to satisfy the needs of engineering.