The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence

Abstract

The variational multiscale method is applied to the large eddy simulation ͑LES͒ of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation ͑DNS͒ data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic Smagorinsky model. The results are somewhat remarkable when one realizes that the multiscale method is almost identical to the Smagorinsky model ͑the least accurate model!͒ except for removal of the eddy viscosity from a very small percentage of the lowest modes.

Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: Comparison of dynamic Smagorinsky and multiscale models over a range of discretizations

“…The relative simplicity of the problem and the availability of well-resolved DNS results make it an attractive test bed. The variational multiscale method for the LES simulation of homogeneous isotropic turbulence was presented in Hughes et al 9 The velocity field was partitioned into coarse-scale (low wave number) and fine-scale (high wave number) components. The subgrid scale stress was then made a function of the fine-scale velocity field, and applied only to the fine-scale motions.…”

“…Effectively, the LES model extracted energy only from high wave number modes. The method has a variational basis, as it relies on "projecting" the subgrid model onto the fine-scale motions, 10 and it was shown to outperform conventional LES models in Hughes et al 9 It appeared that extracting energy only from high wave number modes led to better results than formulations which extract energy from all modes. Subsequent studies have also confirmed the good behavior of the variational multiscale method on a variety of problems: see Hughes, Oberai, and Mazzei, 11 Winckelmans and Jeanmart, 12 Oberai and Hughes, 13 Farhat and Koobus, 14 Jeanmart and Winckelmans, 15 Holmen et al, 16 Koobus and Farhat,17 Ramakrishnan and Collis.…”

Final Report on the “New Directions in the Variational Multiscale Formulation of Large Eddy Simulation of Turbulence”

“…We have also observed that the performance of the dynamic multiscale model is better than both the dynamic single scale model [18] and the static multiscale model [17]. In fact this model appears to combine the advantages of both these approaches.…”

“…As a result, this method retains the spectral accuracy of the coarse or the large scale modes while guaranteeing convergence to the entropy solution. It is interesting to note that in the context of the large eddy simulation (LES) of incompressible turbulent flows, the multiscale method of Hughes et al [16,17], also involves applying a numerical viscosity only to the fine scale equations.…”

The Effect of Subfilter-Scale Physics on Regularization Models

“…Because of the k +1 spectrum associated with rigid bodies, however, LANS-α may not considered useful as a SFS model. Therefore, there is no need for further tests of LANS-α against newer models such as the Variational Multiscale Method [26]. Note, however, that suitable spectra can be obtained with a modified viscous length scale [29].…”