Subgrid scale velocity
Dear all,
I would like to recover the subgridscale velocity in a LES in someway. I use a dynamic smagorinsky model, so an idea would be to recover it from the model itself. The model says nu_r = cs*delta^2 * S, with S = sqrt(2*Sij*Sij) (filtered quantities). If my calculations are correct, using a Kolmogorvlike approximation, I get u'_delta = (nu_r/delta) * cs^(2/3). Hope it is correct. Nevertheless, the model is based on the modelling of the S_ij (strain tensor). My question is: if my field is NOT isotropic, may I still use this approach? Are there different ways? 
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No matter what you do, you cannot recover the subgrid velocity components in the part of the spectrum behind the Nyquist cutoff... You can only recover the resolved wavenumbers component close to the cutoff, but only if you use a smooth filter, by using a deconvolution procedure. If you use a spectral filter, the deconvolution is useless... 
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u'_delta = c*abs( U_f1  U_f2) where U_f1 and U_f2 are the quantities fitered with 2 different filters (So U_f1 may be the one coming from the equations and U_f2 an explicit filtering of the first). But how can I know the constant c ? 
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The SGS model is for the unresolved tensor, V_bar V_bar  (VV)_bar, if you want an estimation of the filtered fluctuations you must compute: V = V_bar + V' > V'_bar = V_bar  (V_bar)_bar 
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I will use the approach you suggested to estimate the velocity! Thank you! 
No ... the type of filter is implicitly defined by the numerical discretization. In no way the SGS model defines the filter, it is rather the opposite ....

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