A physical length-scale for LES of turbulent flow

The fundamental assumption underlying large-eddy simulations (LES) is that the large, energy-carrying, eddies are resolved, while only the smaller eddies are modeled. An implication of this assumption is that the filter-width Δ, the length scale that separates the resolved from the unresolved eddies, should be a fraction of the integral scale, which is characteristic of the large eddies. In practice, however, the filter width is taken to be proportional to the grid size, h. This approach is generally legitimate, since the grid is usually refined where the important turbulence scales are smaller; it presents, however, two problems. First, rapid variations of the mesh (especially in methods that use local mesh refinement) may cause commutation and aliasing errors, and unphysical results (Vanella et al., 2008). Second, it requires knowledge, on the part of the user, on the characteristics of turbulence; in complex flows it may not be possible to predict the turbulence behavior a priori