A non-equilibrium wall-model for LES of shock/boundary layer interaction at high Reynolds number

A dynamic non-equilibrium wall-model for large-eddy simulation at arbitrarily high Reynolds numbers is proposed and validated on a equilibrium boundary layer and a shock /boundary-layer interaction problem. The proposed method 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 model approximately dynamically matches the total stresses and heat fluxes at the matching location and also accounts for the physics that the unresolved stresses and heat fluxes are increased in the wall-normal direction toward the wall in the inner-layer wall-model. The resulting method is shown to accurately predict both equilibrium and non-equilibrium (separated) boundary layers at a very high Reynolds number, with both realistic instantaneous fields and accurate statistics (both skin friction and turbulence quantities), something that existing non-equilibrium wall-models fail to do robustly.