Generalized Smagorinsky model for anisotropic grids

Abstract

The paper revises the Smagorinsky subgrid model to properly account for grid anisotropy on the basis of energy equilibrium considerations in isotropic turbulence. For moderate resolution anisotropies, Deardorff's (1970) estimate involving an equivalent grid scale Delta(eq) = (Delta1 Delta2 Delta3) exp 1/3 is given a rigorous basis. It is argued that the results obtained should be used in conjunction with the dynamic model of Germano et al. (1991) whenever the anisotropy of the test filter differs significantly from that of the basic grid.