Parameter-free shock detector and high order hybrid algorithm for shock/complex flowfield interaction

In order to accurately simulate the interaction of shock wave/complex flows, hybrid schemes combining a compact scheme and weighted essentially non-oscillatory(WENO) scheme are beneficial, in particular due to the high order low dissipation schemes used in smooth regions. For a hybrid scheme, there are two key issues, one is how to detect the discontinuity, the other is how to choose the high order low dissipation scheme to ensure the accuracy, robustness and efficiency. In this paper, a shock detecting method without any artificial parameter is proposed using the definition of the derivative. Based on this shock detecting method, a high order accuracy low dissipation shock-capturing algorithm is constructed. Numerical examples show that the shock detecting method and the hybrid algorithm are accurate, efficient and robust.