Numerical discretization and subgrid‐scale model effects on large‐eddy simulations of a stable boundary layer

Abstract

Aspects of a large‐eddy simulation (LES) model performance are investigated in simulations of a moderately stable boundary layer. The LES utilizes the constant‐coefficient Smagorinsky–Lilly subgrid‐scale (SGS) closure. Three model parameters are considered: grid spacing, SGS model constant and order of accuracy (resolving power) of the advection discretization. Second‐, fourth‐ and sixth‐order fully conservative non‐dissipative advection schemes are examined. All three model parameters considered significantly affect the LES results. Depending on the value of the model constant, two main error‐producing mechanisms are identified. For high values of the model constant, spurious turbulence collapse, either during the short period of model spin‐up, or for the entire simulation duration, is observed. Even though this spurious model characteristic was previously documented, and perhaps expected for low‐resolution simulations, it depends on the order of the advection discretization, implying a significant discretization and SGS closure interaction. For low values of the model constant, numerical discretization errors dominate, leading to accumulation of energy at small scales and over‐prediction of the magnitude of the surface heat flux. Differences in potential temperature profiles are well correlated with the surface heat flux. Overall, the fourth‐ and sixth‐order schemes perform significantly better than the second‐order scheme. The differences between the fourth‐ and sixth‐order schemes are relatively small and the increased computational expense of the sixth‐order scheme may not be effective in most applications, at least for the low‐order statistics considered in this study. Even though the results of the Smagorinsky–Lilly closure show persistent dependence on all model parameters examined, for several parameter combinations the differences with respect to a reference simulation are small. Thus, in contrast to the conclusions of previous studies, the closure can accurately capture moderately stable flows.