A Critical Assessment of the Smagorinsky Model and a New Approach to Large-Eddy Simulations

The Smagorinsky model for the large-eddy simulation of turbulence is critically assessed from a basic theoretical standpoint. It is shown that this model does not respond properly to the coarsening of the mesh because of its incorrect dependence on the dimensional mesh size. Rather, it is the dimensionless ratio of the computational mesh size to the Kolmogorov length scale that determines how well resolved a computation is and should be used to parameterize subgrid scale models. Furthermore, the Smagorinsky model has no dependence on rotational strains and depends improperly on the irrotational strain rate invariants. These facts tend to explain why the Smagorinsky constant is not in reality a constant in applications. An entirely new methodology for large-eddy simulations that is suitable for complex geometries is proposed that eliminates these deficiencies. In this new approach to large-eddy simulations, subgrid scale models go continuously to Reynolds stress models in the coarse meshinfinite Reynolds number limit.