Resolution-induced inhomogeneity in large-eddy simulations

Non-uniform spatial filters do not commute with spatial differentiation, introducing additional terms in the filtered Navier–Stokes equations known as commutator errors, often neglected in Large Eddy Simulation (LES) on non-uniform grids. Stokes Flow Regularization (SFR) extends spatial filtering to derive LES equations with desirable properties even under non-uniform resolution. The resolved continuity equation enforces a divergence-free velocity field, and the effect of resolution variation in the momentum equation is collapsed into a residual stress tensor to be modeled. In the uniform case, the resolved velocity corresponds to a Gaussian-filtered field. For non-uniform LES resolution, SFR requires solving diffusion equations to obtain consistent resolved velocity and residual stress tensor fields from DNS. This enables a priori analysis and supports dynamic SGS models that include resolution effects without test filtering. We demonstrate resolution-induced inhomogeneity using coarsened DNS of homogeneous isotropic turbulence (with and without a uniform mean flow) and discuss implications for LES modeling.