High-Order Adaptive Dissipation Scheme Based on Vortex Recognition for Compressible Turbulence Flow

In the numerical simulation of compressible turbulence involving shock waves, accurately capturing the intricate vortex structures and robustly computing the shock wave are imperative. Employing a high-order scheme with adaptive dissipation characteristics proves to be an efficient approach in distinguishing small-scale vortex structures with precision while capturing discontinuities. However, differentiating between small-scale vortex structures and discontinuities during calculations has been a key challenge. This paper introduces a high-order adaptive dissipation central-upwind weighted compact nonlinear scheme based on vortex recognition (named as WCNS-CU-Ω), that is capable of physically distinguishing shock waves and small-scale vortex structures in the high wave number region by identifying vortices within the flow field, thereby enabling adaptive control of numerical dissipation for interpolation schemes. A variety of cases involving Euler, N-S even RANS equations are tested to verify the performance of the WCNS-CU-Ω scheme. It was found that this new scheme exhibits excellent small-scale resolution and robustness in capturing shock waves. As a result, it can be applied more broadly to numerical simulations of compressible turbulence.