Generalized Smagorinsky model for anisotropic grids

Alberto Scotti and Charles Meneveau
Department of Mechanical Engineering
The Johns Hopkins University, Baltimore MD 21218
Douglas K. Lilly
Center for the Analysis and Prediction of Storms
University of Oklahoma, Norman OK 73019-0628

ABSTRACT: The Smagorinsky subgrid model is revised to properly account for grid-anisotropy, using energy equilibrium considerations in isotropic turbulence. For moderate resolution anisotropies, Deardorff's estimate involving an equivalent grid-scale Deq = (D1D2D3)^(1/3) is given a rigorous basis. For more general grid anisotropies, the Smagorinsky eddy viscosity is recast as n = [Cseq f(a1,a2)]^2 |S|, where f(a1,a2)is a function of the grid aspect-ratios a1 and a2, and |S| is the resolved strain rate magnitude. The asympotic behaviour of n at several limits of the aspect ratios are examined. Approximation formulae are developed so that f(a1,a2) can easily be evaluated in practice, for arbitrary values of a1 and a2. It is argued that these results should be used in conjuction with the dynamic model of Germano et al. whenever the anisotropy of the test-filter differs significantly from that of the basic grid.

Phys. Fluids A 5 (1993), p. 2306