LES of Wall-Bounded Flows Using a New Subgrid Scale Model Based on Energy Spectrum Dissipation

A new one-equation subgrid scale (SGS) model that makes use of the transport equation for the SGS kinetic energy $(kSGS)$ to calculate a representative velocity scale for the SGS fluid motion is proposed. In the $kSGS$ transport equation used, a novel approach is developed for the calculation of the rate of dissipation of the SGS kinetic energy $(ε)$⁠. This new approach leads to an analytical computation of $ε$ via the assumption of a form for the energy spectrum. This introduces a more accurate representation of the dissipation term, which is then also used for the calculation of a representative length scale for the SGS based on their energy content. Therefore, the SG length scale is not associated simply with the grid resolution or the largest of the SGS but with a length scale representative of the overall SGS energy content. The formulation of the model is presented in detail, and the new approach is tested on a series of channel flow test cases with Reynolds number based on friction velocity varying from 180 to 1800. The model is compared with the Smagorinsky model (1963, “General Circulation Experiments With the Primitive Equations: 1. The Basic Experiment,” Mon. Weather Rev., 91, pp. 90–164) and the one-equation model of Yoshizawa and Horiuti (1985, “A Statistically-Derived Subgrid Scale Kinetic Energy Model for the Large Eddy Simulation of Turbulent Flows,” J. Phys. Soc. Jpn., 54(8), pp. 2834–2839). The results indicate that the proposed model can provide, on a given mesh, a more accurate representation of the SG scale effects.