Eddy viscosity enhanced temporal direct deconvolution models for temporal large-eddy simulation of turbulence

A dynamic eddy viscosity (DEV) model and a constant eddy viscosity (CEV) model are proposed for stabilizing the temporal direct deconvolution model (TDDM) in temporal large-eddy simulation of turbulence. Compared to the original unresolved subfilter-scale model used in TDDM, the new eddy viscosity models reduce the number of empirical coefficients and make TDDM more convenient to be applied in practice. The DEV model does not have any empirical coefficients, and the CEV model has only one constant model coefficient that is independent of the filter width and insensitive to the grid resolution. To solve the stability issue of TDDM, an algorithm called the variable filter-width method (VFM) is proposed. In VFM, the filter width is initialized by a small value or 0 and then grows linearly in a small number of time steps until it reaches the target filter width. The three dimensional homogeneous isotropic turbulence is applied to investigate the performance of the proposed models. In the a posteriori testing at different grid resolutions, eddy viscosity enhanced temporal direct deconvolution models show a good accuracy in predicting various statistics and instantaneous spatial structures of turbulence, and they perform better than the original model, especially in the prediction of subfilter-scale (SFS) stress and SFS energy flux. Moreover, the energy spectrum and other flow statistics predicted by the CEV model with a fixed model coefficient 0.03 are in a good agreement with the filtered DNS.