On subgrid models and filter operations in large eddy simulations

Large eddy simulations use a subgrid model, which is characterized by a len gth scale that is often related to the scale of the computational mesh by a numerical constant, C-s. Mason and Callen argued that this subgrid model a nd its length scale define and impose the filter operation of the simulatio n. They saw C-s as a measure of numerical accuracy. Others have sought to l ink the filter operation to the computational mesh and have viewed C-s as n eeding determination for correct implementation. Here tests with a high res olution of 224 X 224 X 200 grid points are found to confirm Mason and Calle n's view. These simulations are also used together with lower-resolution si mulations to illustrate the degree of convergence achieved. Some erroneous features of the simulations are identified through this test. For the case of buoyant convection, the buoyancy dependence of the subgrid model is further examined. Most available subgrid models allow for buoyancy fluxes changing the level of the subgrid energy but only allow stable buoy ancy gradients to modify the subgrid length scale-a reduction in this case. In contrast to most applications, it has been suggested that for a fixed f ilter operation, the subgrid length scale should always have a buoyancy dep endence and should increase, in a finite way, with unstable buoyant transfe r. Here an examination of spectral behavior in high-resolution simulations supports such an approach and shows that the model with the buoyancy-depend ent length scale is indeed consistent with a fixed filter operation. The mo re conventional models are shown to have less satisfactory behavior.