On Numerical Shock Instability of Low Diffusion Shock-Capturing Schemes

Low diffusion shock-capturing schemes are known to produce numerical shock anomalies in hypersonic flow computations. In the current study, we conduct a stability analysis of the Roe approach. It has been found that the shock instability can be effectively suppressed if enough entropy production can be guaranteed inside the numerical shock structure. To improve the robustness of the Roe solver, a modification is proposed to enforce enough entropy production of the numerical flux function. Numerical results show that the proposed scheme is quite robust against shock instabilities.