AIP Digital Archive
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 Δeq=(Δ1Δ2Δ3)1/3 is given a rigorous basis. For more general grid anisotropies, the Smagorinsky eddy viscosity is recast as νT=[csΔeqf(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 asymptotic behavior of νT 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.
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