John Wanderer

Variational formulation of the Germano identity for the Navier–Stokes equations

The variational counterpart of the Germano identity for the large eddy simulation (LES) of turbulent flows is derived. The differences between the variational and the filter-based identities are explained on the basis of the role of an LES model in these two formulations. The variational Germano identity is then used to determine parameters in LES models. The performance of this identity in predicting the Smagorinsky eddy viscosity during the decay of homogeneous isotropic turbulence is evaluated. It is found that it yields results that are as accurate as its filter-based counterpart and that it is less sensitive to the exact approach used in evaluating the unknown parameters.

A two-parameter variational multiscale method for large eddy simulation

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...