GENERALIZED SMAGORINSKY MODEL FOR ANISOTROPIC GRIDS

The Smagorinsky subgrid model is revised to properly account for grid anisotropy, using energy equilibrium considerations in isotropic turbu lence. For moderate resolution anisotropies, Deardorff's estimate invo lving an equivalent grid scale DELTA(eq) = (DELTA1DELTA2DELTA3)1/3 is given a rigorous basis. For more general grid anisotropies, the Smagor insky eddy viscosity is recast as nu(T) = [c(s)DELTA(eq)f(a1, a2)]2 ab solute value of S, where f (a1,a2) is a function of the grid aspect ra tios a1 and a2, and absolute value of S is the resolved strain rate ma gnitude. The asymptotic behavior of nu(T) at several limits of the asp ect 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 conjunct ion with the dynamic model of Germano et al. whenever the anisotropy o f the test-filter differs significantly from that of the basic grid.