The effect of sub-filter scale dynamics in large eddy simulation of turbulence

Abstract

We study the effect of sub-filter scale (SFS) dynamics on the accuracy of direct deconvolution models (DDM) in large eddy simulation of isotropic turbulence at different filter-to-grid ratios (FGR), by using several types of invertible filters including the Gaussian, Helmholtz I and II, Butterworth, Chebyshev I and II, Cauchy, Pao, and rapidly decaying filters. We show that the FGR is crucial in controlling errors to ensure an accurate prediction of SFS stresses. In the case of FGR of 1, the DDM models cannot accurately reconstruct SFS stress, since the effect of SFS dynamics on SFS stress is not properly resolved by the coarse grid. The prediction abilities of most DDM models are significantly improved at FGR of 2, giving rise to quite an accurate reconstruction of SFS stresses, except for the situation of Helmholtz I and II filters. All the DDM models give very accurate results at FGR of 4. Moreover, the DDM models are comprehensively compared against various traditional SFS models, including the velocity gradient model, dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and the approximate deconvolution model. In the a priori study, the correlation coefficients of SFS stress for the DDM are much larger than those of the traditional models. In the a posteriori study, DDM outperforms DSM and DMM models in the prediction of various velocity statistics and instantaneous flow structures. These results indicate that the DDM framework with an appropriate FGR has much potential in developing high-fidelity SFS models in the LES of turbulence.