[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?

[FMDenaro]

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...

[Ivan]

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 ?

[FMDenaro]

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

[Ivan]

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!

[FMDenaro]

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 ....