Effects of Discretization of Smagorinsky–Lilly Subgrid Scale Model on Large-Eddy Simulation of Stable Boundary Layers

Large-eddy simulation (LES) models are sensitive to numerical discretization because of the large fraction of resolved turbulent energy (>80%) and the strong non-linear interactions between resolved-scale fields with the turbulence subgrid scale (SGS) model. The effects of the Smagorinsky–Lilly SGS model discretization are investigated. Three finite difference schemes are compared. Second-, fourth-, and sixth-order centered difference schemes are used to approximate the spatial derivatives of the SGS model. In the LES of homogeneous isotropic turbulence (HIT), including (non-isotropic) turbulent mixing of a passive scalar, no differences are observed with respect to the SGS model discretization. The HIT LES results are validated against a direct numerical simulation, which resolves all flow scales and does not include an SGS model. In the LES of a moderately stable atmospheric boundary layer, the LES results depend on the SGS discretization for coarse grid resolutions. The second-order scheme performs better at coarse resolutions compared to higher-order schemes. Overall, it is found that higher-order discretizations of the Smagorinsky–Lilly model are not beneficial compared to the second-order scheme.