New Shock Detector and Improved Control Function for Shock-boundary Layer Interaction

Standard compact scheme or upwind compact scheme have high order accuracy and high resolution, but cannot capture the shock without oscillations. In this paper, modified compact scheme is developed by using an effective shock detector to block upwinding compact scheme to cross the shock, a control function, and an adaptive scheme which uses some WENO flux near the shock. The new scheme makes the original upwinding compact scheme able to capture the shock sharper than WENO and, more important, keep high order accuracy and high resolution in the smooth area which is particularly important for shock, shock boundary layer interaction and shock acoustic interaction. The scheme is robust and has no case-related coefficients.