Grid Convergence Properties of Wall-Modeled Large Eddy Simulations in the Asymptotic Regime

Abstract

Abstract This study explores the grid convergence properties of wall-modeled large eddy simulation (WMLES) solutions as the large eddy simulation (LES) grid approaches the direct numerical simulation (DNS) grid. This aspect of WMLES is fundamental but has not been previously investigated or documented. We investigate two types of grid refinements: one where the LES/wall-model matching location is fixed at an off-wall grid point, and another where the matching location is fixed at a specific distance from the wall. In both cases, we refine the LES grid simultaneously in all three Cartesian directions, with grid resolution ranging from typical LES resolution to typical DNS resolution. Our focus is on examining the mean flow and turbulent kinetic energy (TKE) as the grid refines. While the turbulence statistics consistently converge toward the DNS solution, we observe nonmonotonic convergence in the mean flow statistics. We show that improving the grid resolution does not necessarily enhance the accuracy of the mean flow predictions. Specifically, we identify a negative log layer mismatch when the LES/wall-model matching location lies below the logarithmic layer, regardless of grid resolution and matching location. Finally, we demonstrate that the nonmonotonic convergence of the mean flow can lead to misleading conclusions from grid convergence studies of WMLES.