Smagorinsky constant

The Smagorinsky constant Cs 0.17 holds at high Reynolds number if the cut-off wavenumber kc falls in the inertial sub-range (Pope 2000). However, the same value is often used for LES at relatively low Reynolds number where no clear inertial sub-range can exist. 

However, apparently the value of Cs is not universal in LES either. In practice, Cs is adjusted to optimize the model results. Deardorff [28] [29] quoted several values of Cg based on Lilly s estimates. The exact value chosen depends on various factors like the filter used, the numerical method used, resolution, and so forth, but they are generally of the order of Cg = 0.2. However, from comparison with experimental results, Deardorff concluded that the constant in the Smagorinsky effective viscosity model should be smaller than this, and a value of about Cg = 0.10 was used. In addition, for the case of an anisotropic resolution (i.e., having different grid width Ax, Ay and Az in the different co-ordinate directions), the geometry of the resolution has to be accounted for. 

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