Temporal Large-Eddy Simulation based on Direct Deconvolution

We propose an approach for Temporal Large-Eddy Simulation (TLES) with direct deconvolution. In this model the non-filtered fields are recovered using a direct deconvolution given by the differential form of the filter operator. Closure is obtained by an evolution equation of the temporal residual-stress tensor, which is analytically derived from the relation of the filtered and the non-filtered fields. A secondary regularization term based on selective frequency damping is employed. The Temporal Direct Deconvolution Model was implemented in the spectral element code Nek5000 to simulate different test cases such as homogeneous isotropic turbulence at Re_λ=190, turbulent channel flow at Re_τ=180, Taylor-Green vortex at Re=3000 and flow over a periodic hill at Re=10595. The following simulation data are discussed: Energy spectra of the homogeneous isotropic turbulence as well as mean flow, root-mean-square of the velocity fluctuations, and the Reynolds stresses of turbulent channel and periodic hill flows. The results demonstrate an improvement compared to no-model solutions, while the computational cost is reduced dramatically compared to direct numerical simulation. Furthermore, an analysis of the relation between temporal and spatial filtering is presented.