An Improved Blending Formulation for Wall-Modeled Large-Eddy Simulations

For high-Reynolds-numbers wall-bounded flows, large-eddy simulation (LES) combined with a wall stress model (WSM) is frequently used. The mean velocity of turbulent boundary layers at high-Reynolds-numbers follows a logarithmic distribution near the wall. However, in LES of high-Reynolds-number wallbounded flows, an overshoot of the mean velocity gradient near the wall is often reported. Many attempts have tried to suppress this overshoot of mean velocity gradient. However, a successful explanation on the relationship between the mean velocity gradient and flow properties, accounting for effects of subgrid-scale model, numerical scheme, and grid set-up has not yet been reported. In the current study, we elaborate a relationship between the mean shear and its budgets for the case of wall-modeled LES.We show that the overshoot of the mean shear is not necessarily caused by over-dissipation, as often reported in literature. Moreover, we proposed a novel hybrid scheme for the Smagorinsky model, where the model coefficient is determined dynamically near the wall, based on the relationship between the desired logarithmic mean shear and the SGS terms composing the bulk of the budgets for the mean shear. The normal Smagorinsky model is then employed far away from the wall. We show that this new model successfully yields the desired logarithmic velocity distribution near the wall.