High-order Numerical Schemes For High-speed Flows

A numerical scheme with high order of accuracy is necessary to resolve small length scales in flow transition and turbulence processes. However, numerical simulation for shock-boundary layer interaction, shock-acoustic interaction, porous media flow and multiple phase flow, among others, also require a numerical scheme that can successfully capture discontinuities. To accomplish this, it is essential that an effective shock/discontinuity detector is implemented to reduce damping of physically important high-frequency waves.In this work, two high-order shock capturing schemes - the Weighted Essentially Non-Oscillatory (WENO) scheme and the Weighted Compact Scheme (WCS) - are investigated. Based on this analysis, a shock/discontinuity detector is developed. Results show that the detector is robust and is capable of detecting strong, weak and oblique shocks or discontinuities.