Dynamic wall-modeling for LES of shock/boundary-layer interacting separated flow at high Reynolds number

We present a new dynamic procedure for non-equilibrium wall-modeling in large-eddy simulation (LES) at arbitrarily high Reynolds numbers. The proposed dynamic non-equilibrium wall-model is based on the methods that model the wall shear stress directly, and solves the full RANS equations in the wall-model layer. We first show how the existing non-equilibrium wall-model becomes inaccurate at high Reynolds number and then propose an improved method which solves this issue. The improvement stems directly from reasoning about how the turbulence length scale changes with wall distance in the inertial sublayer and the resolution-characteristics of numerical methods. The proposed method is shown to accurately predict both equilibrium boundary layers and non-equilibrium shock-induced separated boundary layer at very high Reynolds number, with both realistic instantaneous turbulent structures and accurate statistics (skin friction and turbulence quantities) without the use of ad hoc corrections, something that existing non-equilibrium wall-models fail to do robustly.