Assessment of Low-Dissipative Shock-Capturing Schemes for the Compressible Taylor–Green Vortex

Abstract

Interactions between shock waves and turbulence are ubiquitous in high-speed flows of practical aeronautical interest. Recent advances in computational power have made implicit large-eddy simulation and direct numerical simulation feasible tools for investigating the underlying physical mechanisms involved. However, numerical methods for shock capturing introduce high levels of numerical dissipation to the whole flowfield, making them a poor choice for resolving the small scales of turbulence. In this work, the efficacy of a selection of low-dissipative and hybrid weighted and targeted essentially nonoscillatory (WENO/TENO) shock-capturing methods is assessed. An extension of the classic subsonic Taylor–Green vortex problem is presented up to Mach 1.25, where compressibility and dilatational dissipation become important. The presence of strong shock waves is demonstrated, and the shock waves merge and interact with one another to form complex shock systems. A supersonic test case is then specified, using a Reynolds number of 1600 to ensure a wide range of scales is present to test the numerical schemes. Low-dissipative TENO schemes are found to offer substantial improvements in resolution over established WENO methods for a comparable computational cost.