Comparative Study of Sub-grid Scale Models with High Order Flux Reconstruction Method for Turbulent Flows

Although implicit large eddy simulation (ILES) with the high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) method has been shown to produce adequate results for many flow problems, under-resolved LES such as wall-modeled LES (WMLES) often needs other means such as solution limiting or filtering to achieve stability. Shock-capturing limiters often introduce too much numerical dissipation which can degrade the resolution of small-scale turbulence. In the present study, we explore the use of sub-grid scale (SGS) models in the context of the FR/CPR method to improve the robustness and accuracy of under resolved LES.We compare the performance of three SGS models: the static Smagorinsky model, the Vreman model, and the wall-adapting local eddy-viscosity (WALE) model. The models are implemented in the unstructured grid LES solver called hpMusic based on the high-order FR/CPR method. The Taylor-Green vortex and the fully developed turbulent channel flow are employed to evaluate the performance of the SGS models through comparison with results from direct numerical simulation.