Reformulation and improvement of a universal subgrid eddy viscosity model based on the multiscale framework

Abstract

A universal multiscale Smagorinsky model (UMSM) is established for the large eddy simulation (LES) of wall-bounded turbulent flows by reformulating a universal subgrid eddy viscosity model presented by Gu et al. (Europhysics Letter 94(3):34003,2011). The UMSM is adapted to the LES of wall-bounded turbulent flows by integrating the “small-all” form of the multiscale Smagorinsky model with the dynamic subgrid characteristic length, controlled by subgrid-scale (SGS) motions. The dynamic subgrid characteristic length is determined by the characteristic wave number, which is calculated from a new energy-weighted-mean method when the SGS turbulent kinetic energy and the dissipation wave number are known. The dissipation wave number is derived from the SGS turbulent kinetic energy spectrum equation and the total dissipation rate spectrum equation. The UMSM is used to simulate the fully developed channel flow and the turbulent flow past a square cylinder. The dynamic subgrid characteristic length, as a counterpart of Germano’s procedure, evaluates the rapidly fluctuating small-scale behavior and spatial variations of turbulent characteristics. The results for fully developed channel flow show that the errors in the streamwise velocity and the velocity fluctuations change slowly. The flat nature of the UMSM error across different multiscale Smagorinsky coefficients (Cs’) indicates that the model is relatively insensitive to the value of Cs′. Additionally, the UMSM is less sensitive to grid resolution since more details of turbulence fluctuations are captured on the same grid-points compared to the RVBMM (Journal of Computational Physics, 234:79-107,2013) and DSM (Journal of Fluid Mechanics 319:353-385,1996). Overall, the proposed model and the DSM exhibit similar behavior, and both LES formulations provide good agreement with reference data from direct numerical simulations. However, the UMSM is more computationally efficient, being 17% faster than the dynamic Smagorinsky model.