Investigation of eddy-viscosity models modified using discrete filters : A simplified regularized variational multiscale model and an enhanced field model

Subgrid-scale (SGS) models for large-eddy simulation (LES) having the formalism of an effective eddy-viscosity model, but that operates on a modified velocity field, are further evaluated and new ones are proposed. The modified field is obtained using regular filtering of the LES field carried out in physical space. This is actually done by using a discrete and compact operator (only using nearest neighbors values), eventually iterated; this ensures that the proper filtering behavior is preserved, even for near wall points. The first model investigated here is inspired by the variational multiscale approach originally proposed by T. J. Hughes [Phys. Fluids 13, 505 (2001)]. Here, the modelling is simplified, leading to a SGS viscosity effect operating on the "small-scale LES field" that is obtained by subtracting the LES field from its filtered counterpart. Such a model (here called RVMM for short) was already proposed and partially evaluated {e.g., see G. S. Winckelmans and H. Jeanmart [Direct and Large-Scale Eddy Simulation IV (Kluwer, Dordrecht, 2001)] and H. Jeanmart and G. S. Winckelmans (CTR Proceedings of the Summer Program, 2002), the "model M2" of A. W. Vreman [Phys. Fluids 15, L61 (2003)], the "high-pass filtered Smagorinsky model" of S. Stolz [Direct and Large-Eddy Simulation V (Kluwer, Dordrecht, 2004) and Phys. Fluids 17, 065103 (2005)]}. The other model investigated here is an "enhanced field model" (EFM). The SGS viscosity model then operates on a LES field that is artificially enhanced at the small scales; that obtained by adding to the LES field the small-scale field. The two model families are presented in a unified way; they have a behavior that combines viscous and hyperviscous effects, while remaining simple and practical. They however do not naturally have the proper y(3) near wall behavior for the SGS dissipation; hence, they need some near wall damping. To ensure the proper near-wall behavior, we use here the dynamic procedure (self-consistent for each model). The performance of both models is compared to that of other models (also dynamic): the Smagorinsky model, hyperviscosity models, and a hybrid model combining explicitly a Smagorinsky term and a hyperviscosity term. The cases here investigated are LES of decaying isotropic turbulence starting at Re-lambda=90 and LES of turbulent channel flow at Re-tau=395. A good behavior of the RVMM and EFM, as compared to the others, is observed in all cases. They constitute an easily implemented and better alternative than the dynamic Smagorinsky model. (C) 2007 American Institute of Physics.