Advancing the temporal direct deconvolution method with spatial regularization

Abstract

This study continues the exploration of temporal large-eddy simulation, particularly the extension of the temporal direct deconvolution method (TDDM) with a regularization term based on spatial dissipation. Furthermore, we aim to put insight stemming from previous work to test. Specifically, the hypothesis is that the temporal residual-stress leads to a reduction of the required artificial dissipation in under-resolved simulations. Moreover, this work seeks corroborate earlier discoveries with a posteriori results. We perform a numerical examination of two different spatial regularization terms in conjunction with TDDM: a spatial variant of selective frequency damping, functioning as a relaxation term that gradually drifts the velocity toward the filtered velocity, and the dynamic Smagorinsky model incorporating a prefactor. We test various cases, including the Taylor–Green vortex flow with a Reynolds number of Re = 3000, forced homogeneous isotropic turbulence with Reλ=200, turbulent channel flow at Reτ=590, and the flow over a periodic hill with Re = 10 935. Additionally, we also analyze the various dissipation contributions in TDDM as well as their interrelations. We also discuss grid artifacts and energy budget errors using these to compare the different models. Our results confirm the hypothesis that residual-stress dissipation reduces the necessary artificial dissipation. Because of the numerical ill-conditioning of deconvolution, whether temporal or spatial, there are practical limitations in the size of the filter width. Due to these limitations, the impact remains relatively minor. The a posteriori results of the new spatial regularization term show it to be effective in eliminating energy from the high wavenumber range.