Localized dynamic kinetic-energy-based models for stochastic coherent adaptive large eddy simulation

Abstract

Stochastic coherent adaptive large eddy simulation (SCALES) is an extension of the large eddy simulation approach in which a wavelet filter-based dynamic grid adaptation strategy is employed to solve for the most “energetic” coherent structures in a turbulent field while modeling the effect of the less energetic background flow. In order to take full advantage of the ability of the method in simulating complex flows, the use of localized subgrid-scale models is required. In this paper, new local dynamic one-equation subgrid-scale models based on both eddy-viscosity and non-eddy-viscosity assumptions are proposed for SCALES. The models involve the definition of an additional field variable that represents the kinetic energy associated with the unresolved motions. This way, the energy transfer between resolved and residual flow structures is explicitly taken into account by the modeling procedure without an equilibrium assumption, as in the classical Smagorinsky approach. The wavelet-filtered incompressible Navier–Stokes equations for the velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy variable, are numerically solved by means of the dynamically adaptive wavelet collocation solver. The proposed models are tested for freely decaying homogeneous turbulence at Reλ=72. It is shown that the SCALES results, obtained with less than 0.5% of the total nonadaptive computational nodes, closely match reference data from direct numerical simulation. In contrast to classical large eddy simulation, where the energetic small scales are poorly simulated, the agreement holds not only in terms of global statistical quantities but also in terms of spectral distribution of energy and, more importantly, enstrophy all the way down to the dissipative scales.