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 Ivan October 25, 2012 08:30

Subgrid scale velocity

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?

 FMDenaro October 25, 2012 11:27

Quote:
 Originally Posted by Ivan (Post 388472) 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...

 Ivan October 25, 2012 14:16

Quote:
 Originally Posted by FMDenaro (Post 388509) 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 ?

 FMDenaro October 25, 2012 14:26

Quote:
 Originally Posted by Ivan (Post 388553) 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

 Ivan October 26, 2012 10:20

Quote:
 Originally Posted by FMDenaro (Post 388558) 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!

 FMDenaro October 26, 2012 10:48

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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