Testing of a new mixed model for LES : the Leonard model supplemented by a 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 developed and tested in actual Large Eddy Simulations (LES) of decaying homogeneous turbulence and of channel flow. This model assumes that the LES filter is smooth in wave space, which is the case of most filters defined in physical space (e.g., top hat, Gaussian, discrete filters). The dynamic procedure has been extended for the mixed model. It is used to determine the model coefficient, C, for the added Smagorinsky term. The one-term Leonard model provides significant local backscatter while remaining globally dissipative. In a priori testing, 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 64 LES of decaying homogeneous turbulence started from Gaussian filtered 256 DNS at Reλ ' 90, the new mixed dynamic model performs significantly better than the dynamic Smagorinsky model with same Gaussian filtering; it also outperforms the dynamic Smagorinsky model with sharp cutoff filtering: much better energy spectra, much better energy and enstrophy decay. For the preliminary 48 LES runs on the channel flow at Reτ = 395 done with smooth LES filtering (Gaussian in the homogeneous directions, top hat in the nonhomogeneous direction), the mixed dynamic model is also superior to the dynamic Smagorinsky model. However, the dynamic Smagorinsky model with sharp cutoff test filtering in the homogeneous directions still produces a better mean velocity profile. This result calls for further investigations.