A robustness-enhanced method for Riemann solver

The appearance of shock anomaly is a major unsolved problem for some low diffusion schemes when simulating the hypersonic flow. In this paper, a simple method is proposed to enhance the robustness of the low diffusion schemes to overcome the shock anomaly. The main idea of this method is adding an appropriate extra term to the original low diffusion schemes without influencing the accuracy in aerodynamic heating prediction. This extra term is derived from the difference between the flux splitting scheme (FVS) and the advection upstream splitting method+ (AUSM+). Adding this term to three low diffusion schemes, seven typical numerical tests are conducted to examine the capability of those schemes. Numerical results show that the three new schemes turn out to be carbuncle-free and shock-stable without losing their original accuracy in prediction of aerodynamic heating, validating the feasibility and reliability of the proposed method.