Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term

Large-eddy simulation (LES) with regular explicit filtering is investigated. The filtered-scale stress due to the explicit filtering is here partially reconstructed using the tensor-diffusivity model: It provides for backscatter along the stretching direction(s), and for global dissipation, both also attributes of the exact filtered-scale stress. The necessary LES truncations (grid and numerical method) are responsible for an additional subgrid-scale stress. A natural mixed model is then the tensor-diffusivity model supplemented by a dynamic Smagorinsky term. This model is reviewed, together with useful connections to other models, and is tested against direct numerical simulation (DNS) of turbulent isotropic decay starting with $Reλ=90$ (thus moderate Reynolds number): LES started from a $2563$ DNS truncated to $643$ and Gaussian filtered. The tensor-diffusivity part is first tested alone; the mixed model is tested next. Diagnostics include energy decay, enstrophy decay, and energy spectra. After an initial transient of the dynamic procedure (observed with all models), the mixed model is found to produce good results. However, despite expectations based on favorable a priori tests, the results are similar to those obtained when using the dynamic Smagorinsky model alone in LES without explicit filtering. Nevertheless, the dynamic mixed model appears as a good compromise between partial reconstruction of the filtered-scale stress and modeling of the truncations effects (incomplete reconstruction and subgrid-scale effects). More challenging $483$ LES are also done: Again, the results of both approaches are found to be similar. The dynamic mixed model is also tested on the turbulent channel flow at $Reτ=395.$ The tensor-diffusivity part must be damped close to the wall in order to avoid instabilities. Diagnostics are mean profiles of velocity, stress, dissipation, and reconstructed Reynolds stresses. The velocity profile obtained using the damped dynamic mixed model is slightly better than that obtained using the dynamic Smagorinsky model without explicit filtering. The damping used so far is however crude, and this calls for further work.