We have clearly shown in the former chapters the advantages of the spectral eddy-viscosity models with, in particular, the possibility of accounting for local or semilocal effects in the neighborhood of the cutoff. More details on this point may be found in Sagaut, which contains many advanced aspects on LES modeling. However, in most industrial or environmental applications, the complexity of the computational domain prohibits the use of spectral methods. One thus has to deal with numerical codes written in physical space and employing finite-volume or finite-differences methods often with unstructured grids. This last point will not be considered in this book, although it is crucial for practical applications. We will present, however, simulations on orthogonal grids of mesh size varying in direction and location and sometimes in curvilinear geometry. This chapter will mainly be devoted to models of the structure-function family with applications to isotropic turbulence, free-shear and separated flows, and boundary layers. We will also present in less detail alternative models such as the dynamic structure-function model, hyperviscosity model, mixed structure-function/hyperviscous model, and the mixed model.

Structure-function model

Formalism

The structure-function (SF) model is an attempt to go beyond the Smagorinsky model while keeping in physical space the same scalings as in spectral eddy-viscosity models. The original SF model is due to Métais and Lesieur.