Evaluation of Smagorinsky variants in large-eddy simulations of wall-resolved plane channel flows

Abstract

In recent years, variational multiscale (VMS) Smagorinsky models have emerged as new models for large-eddy simulations (LES). A common version is the small-small variant, which uses a small-scale extraction of the LES solution, obtained by high-pass filtering the resolved velocity field, to express a Smagorinsky term. The subsequent small-scale extraction of this term is used as a model. In the current work, three formulations of the small-small VMS model are investigated in large-eddy simulations of the plane channel flow. The basic small-small formulation (Model A) is modified to explicitly incorporate effects of the LES filter and the high-pass filter (Model B). A third modification (Model C) is further inertial-range consistent, allowing the use of constant model coefficients for filters widths which are situated in a finite Reynolds-number inertial subrange. We aim to evaluate the performance of these models in the presence of walls. Therefore, channel-flow simulations are performed for Reτ=110, 300, 400, and 650. Further, the effect of changes in the shape of the high-pass filter used for the three models is investigated. A sharp cutoff filter and a Gaussian high-pass filter are considered. In addition, a range of high-pass-filter widths is included in the analysis. Evaluations of the skin-friction, mean-velocity profiles, Reynolds stresses, and spanwise velocity spectra are presented. We show that Model C is most insensitive to changes in Reynolds number and filter shape, closely followed by Model B. Model A is the most sensitive to the considered variations, and simulation quality depends in particular on variations in the filter shape.