GENERALIZED SMAGORINSKY MODEL FOR ANISOTROPIC GRIDS

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 DELTA(eq) = (DELTA1DELTA2DELTA3)1/3 is given a rigorous basis. For more general grid anisotropies, the Smagorinsky eddy viscosity is recast as nu(T) = [c(s)DELTA(eq)f(a1, a2)]2 absolute value of S, where f (a1,a2) is a function of the grid aspect ratios a1 and a2, and absolute value of S is the resolved strain rate magnitude. The asymptotic behavior of nu(T) at several limits of the aspect ratios are examined. Approximation formulas 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 conjunction with the dynamic model of Germano et al. whenever the anisotropy of the test-filter differs significantly from that of the basic grid.