A posteriori analysis of low-pass spatial filters for approximate deconvolution large eddy simulations of homogeneous incompressible flows

摘要

The goal of this paper is twofold: first, it investigates the effect oflow-pass spatial filters for approximate deconvolution large eddy simulation(AD-LES) of turbulent incompressible flows. Second, it proposes thehyper-differential filter as a means of increasing the accuracy of the AD-LESmodel without increasing the computational cost. Box filters, Pad\'{e} filters,and differential filters with a wide range of parameters are studied in theAD-LES framework. The AD-LES model, in conjunction with these spatial filters,is tested in the numerical simulation of the three-dimensional Taylor-Greenvortex problem. The numerical results are benchmarked against direct numericalsimulation (DNS) data. An under-resolved numerical simulation is also used forcomparison purposes. Four criteria are used to investigate the AD-LES modelequipped with these spatial filters: (i) the time series of the volume-averagedenstrophy; (ii) the volume-averaged third-order structure function; (iii) the$L^2$-norm of the velocity and vorticity errors; and (iv) the volume-averagedvelocity and vorticity correlation coefficients. According to these criteria,the numerical results yield the following two conclusions: first, the AD-LESmodel equipped with any of these spatial filters yields accurate results at afraction of the computational cost of DNS. Second, the most accurate resultsare obtained with the hyper-differential filter, followed by the differentialfilter. We demonstrate that the results highly depend on the selection of thefiltering procedure. Although a careful parameter choice makes each class offilters used in this study competitive, it seems that filters whose transferfunction resembles that of the Fourier cut-off filter (such as thehyper-differential filters) tend to perform best.