A two-parameter variational multiscale method for large eddy simulation

Abstract

A two-parameter version of the variational multiscale (VMS) formulation with two Smagorinsky-type terms is proposed for the large eddy simulation of incompressible turbulent flows. One of the terms is the standard Smagorinsky eddy viscosity model that is applied to all resolved scales. The other is a fine scale addition that is constructed from the fine scale velocity field and is applied only to the fine scale equations. The new model is a generalization of the original variational multiscale model, which employs an eddy viscosity that acts only in the fine scales. The ability of the new two-parameter model to accurately predict sustained homogeneous isotropic turbulence is assessed by implementing it in a spectral code. Its performance is compared to the Smagorinsky model and the single-parameter VMS model. It is found that the single-parameter VMS model performs well at low to moderate Reynolds numbers, that the Smagorinsky model is more accurate at high Reynolds numbers, and that the new two-parameter VMS model performs well over the entire range. This performance is explained on the basis of the effective wavenumber dependent eddy viscosity for each model.