Testing of a new mixed model for LES: the Leonard model supplemented by dynamic Smagorinsky term

A new mixed model which uses the Leonard expansion (truncated to one term) supplemented by a purely dissipative term (dynamic Smagorinsky) has been devel- oped and tested in actual Large Eddy Simulations (LES) of decaying homogeneous turbulence and of channel flow. This model assumes that the LES lter is smooth in wave space, which is the case of most lters dened in physical space (e.g. ,t op hat, Gaussian, discrete lters). The dynamic procedure has been extended for the mixed model. It is used to determine the model coecient, C, for the added Smagorinsky term. The one-term Leonard model provides signicant local backscatter while re- maining globally dissipative. In ap rioritesting, its correlation with DNS is greater than 0:9. However, when used on its own in actual LES, this model is found to provide too little dissipation. Hence the need for added dissipation, here provided by the dynamic Smagorinsky term. In 643 LES of decaying homogeneous turbu- lence started from Gaussian ltered 2563 DNS at Re' 90, the new mixed dynamic model performs signicantly better than the dynamic Smagorinsky model with same Gaussian ltering; it also outperforms the dynamic Smagorinsky model with sharp cuto ltering: much better energy spectra, much better energy and enstrophy de- cay. For the preliminary 483 LES runs on the channel flow at Re = 395 done with smooth LES ltering (Gaussian in the homogeneous directions, top hat in the non- homogeneous direction), the mixed dynamic model is also superior to the dynamic Smagorinsky model. However, the dynamic Smagorinsky model with sharp cuto test ltering in the homogeneous directions still produces a better mean velocity prole. This result calls for further investigations.