Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence

Abstract

Inviscid regularization modeling of turbulent flow is investigated. Homogeneous, isotropic, decaying turbulence is simulated at a range of filter widths. A coarse-graining of turbulent flow arises from the direct regularization of the convective nonlinearity in the Navier-Stokes equations. The regularization is translated into its corresponding sub-filter model to close the equations for large-eddy simulation (LES). The accuracy with which primary turbulent flow features are captured by this modeling is investigated for the Leray regularization, the Navier-Stokes-α formulation (NS-α), the simplified Bardina model and a modified Leray approach. On a PDE level, each regularization principle is known to possess a unique, strong solution with known regularity properties. When used as turbulence closure for numerical simulations, significant differences between these models are observed. Through a comparison with direct numerical simulation (DNS) results, a detailed assessment of these regularization principles is made. The regularization models retain much of the small-scale variability in the solution. The smaller resolved scales are dominated by the specific sub-filter model adopted. We find that the Leray model is in general closest to the filtered DNS results, the modified Leray model is found least accurate and the simplified Bardina and NS-α models are in between, as far as accuracy is concerned. This rough ordering is based on the energy decay, the Taylor Reynolds number and the velocity skewness, and on detailed characteristics of the energy dynamics, including spectra of the energy, the energy transfer and the transfer power. At filter widths up to about 10% of the computational domain-size, the Leray and NS-α predictions were found to correlate well with the filtered DNS data. Each of the regularization models underestimates the energy decay rate and overestimates the tail of the energy spectrum. The correspondence with unfiltered DNS spectra was observed often to be closer than with filtered DNS for several of the regularization models.

Inertial Manifolds for Certain Subgrid-Scale $\alpha$-Models of Turbulence

“…An upper bound of the dimension of the global attractor and an analysis of the energy spectrum of the solutions of the 3D version of (2) were established in [10], which suggested that the Leray-α model has great potential to become a good sub-grid scale large-eddy simulation model of turbulence. See also a computational study of this model in [27,36,37].…”

Note on the Use of Camassa–holm Equations for Simulation of Incompressible Fluid Turbulence

“…in Geurts and Holm [14,15] or Ilyin et al [21]. The comparison with other LES (or DNS) model predictions are shown and discussed in Chen et al [6], Geurts and Holm [16], Geurts et al [17], Holm and Titi [18], Foias et al [11].…”

Regularization modeling for LES of separated boundary layer flow

“…These models are derived from an assumed dynamic principle that is aimed to coarsen the flow description while (Holm et al, 1998). To date, these models were applied to the simplest canonical flow-problems, i.e., homogeneous, isotropic turbulence (Chen et al, 1999;Geurts et al, 2008), and flow in a temporally developing mixing layer (Geurts and Holm, 2006). We reviewed regularized mixing and showed that the results are comparable to and often better than those obtained with the dynamic eddy-viscosity model.…”