On the grid convergence in wall-modeled large-eddy simulation

Wall modeled large-eddy simulation (WMLES) has become a popular computational tool for high Reynolds number turbulent flows, as it achieves a balance between cost and accuracy. However, grid convergence in WMLES has not been well understood due to the conflicting objectives of grid convergence and use of increasingly coarse near-wall grids for wall modeling. In this work, we propose that the extent of the wall-modeled region critically affects the convergence behavior of WMLES. For a fixed extent of the wall-modeled region, once the turbulence scales are well resolved at the location where the LES data are sampled, the wall-model input is likely unchanged with further grid refinements, leading to the converged model output (wall stress) and therefore convergence in WMLES. This proposition is being examined in a turbulent channel flow and a three dimensional turbulent boundary layer with a rotating freestream velocity vector. We suspect that the extent of the wall-modeled region plays a role similar to the filter size in the explicitly filtered LES, dictating the resolution at which the WMLES converges and the error therein. In this scenario, WMLES would tend to converge at a coarser grid resolution when the wall-model region extends further away from the wall.