Towards Accurate And Robust Shock-Capturing Schemes For Hypersonic Flow Computations

The high speed flow problems usually involve complex flow phenomena, such as strong shock waves, shear layers, shock/shock interactions, shock wave/boundary layer interactions, vortices and separated flows. Prediction of these problems requires robust, efficient and accurate numerical methods. This article focuses on the dissipative mechanism and shock stability of upwind schemes in boundary layer and around the normal shock respectively. The numerical conditions for upwind schemes to accurately resolve boundary layers and robustly capture strong shock waves are proposed respectively based on both theoretical and experimental analysis. These conditions are considered to be very useful for analyzing numerical dissipation and shock instability of upwind methods. Furthermore, we even give detail guides about how to modify a numerical scheme with diffusive behavior and poor robustness into a boundary-layer resolving and carbuncle-free one. Then, a robust and accurate upwind scheme called HLLEM-S is proposed. Numerical results for massive carefully chosen test problems are investigated to demonstrate the accuracy and robustness of the proposed scheme. Comparative results with several popular upwind schemes show that the new method has good performance on accuracy, robustness, convergence and complex geometry adaptability which are considered to be crucial for hypersonic flow computations.