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

At first glance, grid convergence and wall modeling appear to be competing objectives that require reconciliation in inherently underresolved wall-modeled large-eddy simulation (LES). The understanding of which flow quantities can converge at typical wall-modeled LES resolution, as well as what parameters of wall models affect the convergence trend, is currently limited. Motivated by the attached eddy theory and drawing analogy to the explicitly filtered LES, we propose that the convergence path of wall-modeled LES, and potentially its final converged state, are directly influenced by the extent of the wall-modeled region (or the wall-model matching height). Specifically, the onset of convergence is expected to occur at coarser grid resolutions when larger extents of the wall-modeled region are employed. To investigate this hypothesis, numerical experiments are conducted on canonical turbulent channel flow, a three-dimensional turbulent boundary layer with a rotating freestream velocity vector and turbulent channel flow subject to a sudden imposition of spanwise pressure gradient. The focus is on analyzing the convergence trend of the mean wall-shear stress, mean velocity, and turbulence intensity. The obtained results provide compelling evidence supporting the idea for mean-flow quantities. However, it is observed that turbulence intensity convergence is slower compared to the mean quantities, and no clear dependence on the extent of the wall-modeled region is evident. An explanation of the divergent grid convergence behaviors for mean and turbulence statistics is provided, based on the attached eddy hypothesis. Lastly, we discuss some initial considerations regarding the variation or fixation of the wall-modeled extent during grid convergence. These thoughts shed light on potential strategies to enhance the convergence and interpretation of wall-modeled LES. •Grid convergence and wall modeling are mutually competing objectives at first Glance.•The extent of the wall-modeled region is shown to control the convergence path of wall-modeled LES.•Conditions of convergence for the mean flow and Reynolds stresses are discussed.