Assessment of low-dissipative shock-capturing schemes for transitional and turbulent shock interactions

摘要

Interactions between Shockwaves and turbulence are ubiquitous in high-speed flows of practical aeronautical interest. Recent advances in computational power have made implicit large eddy simulation (iLES) and direct numerical simulation (DNS) feasible tools for investigating the underlying physical mechanisms involved. The success of tackling these problems depends however on contrasting requirements of the applied numerical schemes. Shock-capturing schemes stabilise the solution by adding numerical dissipation in the vicinity of flow discontinuities, but have the detrimental effect of damping small-scale turbulence. In this work the efficacy of a selection of low-dissipative and hybrid shock-capturing methods is assessed in a finite-difference framework, for transitional and turbulent flows with shocks. The classic Taylor-Green vortex problem at Re = 1600 is extended to a range of Mach numbers up to Mach 1.25, where compressibility and dilatational dissipation become important. Secondly, the shock-induced transition of a flat-plate laminar boundary layer with upstream disturbances is investigated for an oblique shock reflection with initial deflection θ = 2.5° at Mach 1.5. Low-dissipative Targeted Essentially Non-Oscillatory (TENO) schemes are found to offer improved resolution and reduced grid requirements at a comparable cost compared to conventional Weighted Essentially Non-Oscillatory (WENO) schemes. Low-dissipative schemes however are found to exhibit increased numerical oscillations in the vicinity of shocks unless the scheme weights are carefully chosen.