# Subgrid scale velocity

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 October 25, 2012, 08:30 Subgrid scale velocity #1 New Member   Ivan Join Date: Aug 2012 Posts: 22 Rep Power: 7 Dear all, I would like to recover the subgrid-scale 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 Kolmogorv-like 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?

October 25, 2012, 11:27
#2
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,684
Rep Power: 41
Quote:
 Originally Posted by Ivan Dear all, I would like to recover the subgrid-scale 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 Kolmogorv-like 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?

No matter what you do, you cannot recover the subgrid velocity components in the part of the spectrum behind the Nyquist cut-off...

You can only recover the resolved wavenumbers component close to the cut-off, but only if you use a smooth filter, by using a deconvolution procedure.
If you use a spectral filter, the deconvolution is useless...

October 25, 2012, 14:16
#3
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Ivan
Join Date: Aug 2012
Posts: 22
Rep Power: 7
Quote:
 Originally Posted by FMDenaro No matter what you do, you cannot recover the subgrid velocity components in the part of the spectrum behind the Nyquist cut-off... You can only recover the resolved wavenumbers component close to the cut-off, but only if you use a smooth filter, by using a deconvolution procedure. If you use a spectral filter, the deconvolution is useless...
The filter I use should be a Gaussian one. So are you saying I cannot recover it from the Smagorinsky model itself? If i got it, I should use something like

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 ?

October 25, 2012, 14:26
#4
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,684
Rep Power: 41
Quote:
 Originally Posted by Ivan The filter I use should be a Gaussian one. So are you saying I cannot recover it from the Smagorinsky model itself? If i got it, I should use something like 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 ?
how do you say your filter is Gaussian? What kind of transfer function you have from your discretization?

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

October 26, 2012, 10:20
#5
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Ivan
Join Date: Aug 2012
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Quote:
 Originally Posted by FMDenaro how do you say your filter is Gaussian? What kind of transfer function you have from your discretization? 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
The kind of filtered should be implicitely imposed by the model you are using right? Following Pope, (turbulent flows, pp.588) this should be very close to a Gaussian one for a Smagorinsky model, at least for the analytical, filtered equations...I do not know how it is modified by the discretization then.

I will use the approach you suggested to estimate the velocity!

Thank you!

 October 26, 2012, 10:48 #6 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,684 Rep Power: 41 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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