Subgrid-Scale Models for Large-Eddy Simulations of Shock-Boundary-Layer Interactions

Direct numerical simulation and large-eddy simulation of a flat-plate supersonic turbulent boundary layer interacting with an oblique incident shock wave are conducted for a priori and a posteriori assessments of subgrid-scale models. The incident shock is strong enough to generate a marginal separation in the boundary layer near the interaction region providing the subgrid-scale models with a nontrivial challenge. The governing equations for direct numerical simulation and large-eddy simulation are solved by a new seventh-order monotonicity-preserving scheme for inviscid fluxes and a sixth-order compact finite-difference scheme for the viscous terms. The effect of subgrid-scale stress term on the resolved velocity field is shown to be significant and shock-dependent. The subgrid-scale models tested include the mixed-time-scale model, the dynamic Smagorinsky model, the dynamic mixed model and a new dynamic model termed the compressible serial-decomposition model. A priori analysis indicate that the new dynamic model is more accurate than other subgrid-scale closures. A posteriori tests also indicate better predictions of direct numerical simulation results by the large-eddy simulation employing the compressible serial-decomposition model.