Assessment of some models for LES without/with explicit filtering

The practical approach in LES is concerned with modelling the effective “subgrid-scale” stress due to the projection from the complete u i field to the incomplete ũ i field: a non-regular operation, the effect of which must be modelled. On the other hand, the mathematical approach usually assumes a regular explicit filter: a regular convolution acting on u i to produce ū i , leading to an effective “filtered-scale” stress. On can also consider practical LES with regular filtering added to the projection, thus solving for \({\bar \tilde u_i}\) instead of ũ i . The effective stress is then the sum of a filtered-scale stress (that can be reconstructed) and a subgrid-scale stress (that must be modelled). A view that reconciles both practical approaches is reviewed, together with some models. Of particular interest are models that behave as viscosity at low k and higher order viscosity at high k. The spectral behavior of the models is investigated numerically, in 483 LES of decaying isotropic turbulence (started from 2563 DNS). Two diagnostics are used: model dissipation spectrum and obtained energy spectrum.