Temporal large-eddy simulation based on direct deconvolution

Abstract

In this work, we propose an approach for Temporal Large-Eddy Simulation (TLES) with direct deconvolution. In contrast to previous approaches such as the Temporal Approximate Deconvolution Model (TADM) by Pruett et al. ["A temporal approximate deconvolution model for large-eddy simulation,"Phys. Fluids 18, 028104 (2006)], the non-filtered velocity field is recovered using the differential form of the filter operation rather than from a truncated series expansion of the inverse filter operator. This direct deconvolution is used to obtain formal closure of an analytic evolution equation of the temporal residual-stress tensor. Thus, the Temporal Direct Deconvolution Model (TDDM) has advantages relative to the TADM in being both more accurate and requiring less computational effort. As for the TADM, a secondary regularization term based on selective frequency damping is employed. The TDDM was implemented in the spectral element code Nek5000 (Argonne National Laboratory, NEK5000 Version 17.0, 2019, https://nek5000.mcs.anl.gov) to simulate two canonical incompressible flows as three test cases: an a priori test case of Homogeneous Isotropic Turbulence (HIT) at Reλ = 50, a greatly coarsened a posteriori HIT case at Reλ = 190, and an a posteriori highly anisotropic turbulent channel flow at Reτ = 180. Analyses of the energy spectrum, the mean flow, the root-mean-square of the velocity fluctuations, and the Reynolds stresses are presented. The results demonstrate a significant improvement compared to no-model solutions regarding the mean flow in the turbulent channel and the energy spectrum in the HIT case, while the computational cost is reduced dramatically compared to the direct numerical simulation.