[FMDenaro]

Originally Posted by juliom

Thank you very much professor; I am still struggling with this but I expect to fully understand with the material you gave me.
Professor, I read the other paper (Direct and Large-Eddy Simulation VIII Volume 15 of the series ERCOFTAC Series pp 27-32).
There, you used two different test width: 3*deltaX*3*deltaZ and 5*deltaX*3deltaZ. Also, in the section 5.1 from: A new development of the dynamic procedure
in large-eddy simulation based on a Finite Volume integral approach. Application to
stratified turbulence you specified a stencil of 3x3 for alpha = 2 and 5x5 for alpha = 4.
Having said that: the width of the test filter what basically means is the amount of volumes I use to do the filtering or (volume average) rather than antoher mesh with different delta that overlap the main mesh?.
On the other hand, the velocity field is the one I apply the test filter on. Hence, I have to interpolate the velocity from the cell (staggered grid) to the center of the node to have these velocity ready for the filtering procedure?
Finally, professor do you have the expression (as you presented for 2*deltaX*2deltaY in On the relevance of the type of contraction of the Germano identity in the new integralbased dynamic Smagorinsky model) for the other test width you presented on the other two works I referred above?

Thanks in advances
Very Respectfully
Julio Mendez

While using the top-hat as test filtering the filter width is not strictly the size of the volume. This aspect is illustrated in the LES literature and you can find some details in my JCP paper you read. The best way is define the filter width from the transfer function.

Furthermore, since you filter separately the velocity components u,v,w you can apply the test filtering on each component without interpolation on centred node

[juliom]

Thank you very much professor. I will read thoroughly the paper. I need to really understand the implementation.

Thank you very much for you time.

Respectfully
Julio Mendez

[juliom]

Dear Professor;
I read the papers and I think that now the physics and the numerical representation is clear. Thank you very much for your kindness answering my questions and sharing your papers; very illustrative your papers. Nonetheless; I have a couple of questions regarding the notation you used and other questions related to the numerical implementation.
The paper from JCP in the section 4.1 (equations 59), you introduced the variable m. that basically defines the width of the test filter. Am I right?
Then I read equations (60 and 61) for m = 2 and m = 4 respectively. In other words the width of the test filter is twice the computational grid for equation (60) and 4 times the computational grid for equation (61). Is it right?
Since deltaX and delta Y are constant in these two equations, you applied a wider stencil for equation (61) compared to equation (60). Is this also right?
However, in point 4.3 you introduce the different cases and and you mentioned that case 1 (equation 60 for m = 2) you ued alpha = 2, 3 and 4. Alpha = (delta_exe)/(delta_eff). I am confused with this, because once you define equation (60 for m=2) the value for alpha is directly constrained; is it not? If no, what is the difference between alpha and m?
Professor; I am using the staggered velocity (MAC). Without any deep analysis I think that I can apply equations (60) and (61) over the velocity cell on the staggered configuration.is it always true?
Also, I would like to know your recommendation to treat the nodes near the boundaries.
Finally; Professor you claimed that the best results were obtained for m = 4 which is the opposite to what Lund and Germano concluded. Is your conclusion based on the integral formulation only?

Thanks in advance for your time.
Very respectfully
Julio Mendez

[FMDenaro]

Originally Posted by juliom

Dear Professor;
I read the papers and I think that now the physics and the numerical representation is clear. Thank you very much for your kindness answering my questions and sharing your papers; very illustrative your papers. Nonetheless; I have a couple of questions regarding the notation you used and other questions related to the numerical implementation.
The paper from JCP in the section 4.1 (equations 59), you introduced the variable m. that basically defines the width of the test filter. Am I right?
Then I read equations (60 and 61) for m = 2 and m = 4 respectively. In other words the width of the test filter is twice the computational grid for equation (60) and 4 times the computational grid for equation (61). Is it right?
Since deltaX and delta Y are constant in these two equations, you applied a wider stencil for equation (61) compared to equation (60). Is this also right?
However, in point 4.3 you introduce the different cases and and you mentioned that case 1 (equation 60 for m = 2) you ued alpha = 2, 3 and 4. Alpha = (delta_exe)/(delta_eff). I am confused with this, because once you define equation (60 for m=2) the value for alpha is directly constrained; is it not? If no, what is the difference between alpha and m?
Professor; I am using the staggered velocity (MAC). Without any deep analysis I think that I can apply equations (60) and (61) over the velocity cell on the staggered configuration.is it always true?
Also, I would like to know your recommendation to treat the nodes near the boundaries.
Finally; Professor you claimed that the best results were obtained for m = 4 which is the opposite to what Lund and Germano concluded. Is your conclusion based on the integral formulation only?

Thanks in advance for your time.
Very respectfully
Julio Mendez

The Eq.(59) introduces m just as a multiplying factor for the size of the computational grid. But that does not define rigorously the filter width as 2 and 4 the mesh size. According to the transfer functions In fig.6, you can see some estimations giving greater values, for example see Eq(64).

As a consequence, if you read Sec.4.1, fixing the alpha value does not say what discrete test filtering is used. Alpha and m are really different things...

Eq.(60) and (61) can be used for the scalar component u,v,w separately even on staggered grids.

What do you need to treat near the boundary? the 2D test filtering has only the need of periodic links between the values.

Of course, all the conclusions in my paper are well suited for the integral-based formulation. Lund and Germano used always the differential formulation.

[juliom]

Thank you very much professor;
Professor; If I assumed that the discretization process does not introduce any deviation due to:truncation, round-off, numerical scheme and so forth. Hence, delta_eff is strictly function of h and delta_exx is strictly function of the width of the test filter. Can I assume that m represents the filter width? In several papers the authors use equation (59) with m = 2 to define the width of the test filter as twice the computational grid. That is why I am confused.
Finally, why are your conclusions different from Germano and Lund (besides that are based on different approaches), even though both are based on conservation laws. From your experience what are causing such deviation from the other authors ?

I am very thankful for your time and patience. This discussion has been very helpful for me

Very Respectfully
Julio Mendez

[FMDenaro]

of course, it is not possible to eliminate the truncation error, but if it were disregardeble then the filter width would be defined by the extension of the integrals in continuous form...

The differential and integral forms produce many differences...just as example, see the different Germano identities

[juliom]

Thanks professor;
Assuming that all those error are negligible. The width of the test filter is defined by m in the integrals?. Also, alpha and m are directly related by the value of the width of the test filter "m" ?
Thanks
Julio Mendez

[FMDenaro]

The answer is no ... consider the 1D case and the continuous integral between [-h,+h]. If you see the trasfer function, it has an infinite number of zeros along the wavenumber axis. That does not define a specific cut in the frequencies according to a value of m.
In literature, a way to define the filter width can be to evaluate the wavenumber for which the transfer function is equal to 0.5. But, while this is effective in 1D, when you have a multidimensional case also the transfer function is multidimensional and this estimation is more complex.

Only the discretization of the domain introduces a grid-filtering (projective cut-off)

[juliom]

Thank you professor. This is a very complex study domain. I hope to master this (or at least understand) details in the next years with more study and hands-on experience.
This discussion has been very rich for me. Now, I need to move to temporal filtering.
My advisor wants me to implement the temporal filtering rather than a spatial filtering...

Thank you very much professor.

Very Respectfully
Julio Mendez

[FMDenaro]

be careful, the time filtering does not exclude the co-existance of a spatial filtering in LES

[juliom]

I imagined it professor. Do you recommend something specific to read?

[FMDenaro]

Originally Posted by juliom

I imagined it professor. Do you recommend something specific to read?

there are several papers of Pruett on temporal filtering, but you can find also different authors working on that...
In addition, I suggest the state-of-the art books about LES (Sagaut, Layton et al., etc.)

[juliom]

Dear colleagues;
Is the dynamic procedure a model based on scale similarities? I am very confused because in Germano's papers he never defined it explicitly as a scale similarity model. Instead, he used the central moment to obtain obtain the value of the constant. My issue is also to visualize the role of the central moment because what I end up always seeing is that he introduced the Germano identity and this allowed him to obtain the Cs. So, where does the central moment come into play?? Because L_ij is based on the resolved scales and some how it uses the scale similarity framework.

Thanks in advance!!

[FMDenaro]

The Germano identity is exact, just it follows as a consequence of a filter hierarchy...
Then you decide the type of approximation by introducing the SGS model, it can be an eddy viscosity, a scale similar or a mixed one (1 or 2 coefficients).

[juliom]

Thank you very much dear professor; but where does the averaging come into play, because he claimed that this procedure is invariant to the particular averaging operation.
Finally professor; are you referring to the type of the approximation of the SGS model for the test level ? Because, what we are focus on is the value of the C_s.

Thanks

[FMDenaro]

Originally Posted by juliom

Thank you very much dear professor; but where does the averaging come into play, because he claimed that this procedure is invariant to the particular averaging operation.
Finally professor; are you referring to the type of the approximation of the SGS model for the test level ? Because, what we are focus on is the value of the C_s.

Thanks

Consider the filtered momentum equation without any model, where you have the exact unresolved term. Now, apply any other filter further to this filtered equation and you get the Germano identity without any approximation due to the model...

Then, you can introduce an SGS model both a test and primary level...

for example see;
http://ntrs.nasa.gov/archive/nasa/ca...0000039436.pdf

[juliom]

Thank you very much professor; very interesting your explanation and the paper you suggested.

[FMDenaro]

Originally Posted by juliom

Thank you very much professor; very interesting your explanation and the paper you suggested.

good, just remember that the width of the test filter must be greater than that of the primary

[syavash]

Originally Posted by FMDenaro

good, just remember that the width of the test filter must be greater than that of the primary

Dear prof. Denaro,

I have faced a problem and hope you can provide me some insight

I have tried to simulate channel395 in OpenFOAM through both dynamic Smagorinsky (local) and an explicit SGS stress tensor adding to momentum equations.

The first approach is a well-known eddy-viscosity method which calculates nuSgs and adds it to nu to constitute nuEff and finally calculates divDevReff from something like:

fvm::laplacian(nuEff, U)

The second approach does not calculate nuSgs directly, but instead calculates SGS stress tensor B from the following relation:

B = -2 * nu_t * S_ij

where nu_t is equal to nuSgs and S_ij is the resolved strain rate tensor. The only difference from the first approach is that divDevReff is now an explicit source term which is added to momentum equation as the following term:

fvc:: div(B) - fvm::laplacian(nu, U)

Well, I would expect to get the same results in term of viscous stress (u_tau) in the case of channel395 with default grid spacing, but it is not as thought. The first approach (currently used in OF) yields a reasonable Re_tau=370 but the second approach strongly over-predicts viscous stress, yielding a Re_tau=500!!

I would like to ask if such a big difference should be expected from the second approach.


Sincerely,
Syavash

[FMDenaro]

Originally Posted by syavash

Dear prof. Denaro,

I have faced a problem and hope you can provide me some insight

I have tried to simulate channel395 in OpenFOAM through both dynamic Smagorinsky (local) and an explicit SGS stress tensor adding to momentum equations.

The first approach is a well-known eddy-viscosity method which calculates nuSgs and adds it to nu to constitute nuEff and finally calculates divDevReff from something like:

fvm::laplacian(nuEff, U)

The second approach does not calculate nuSgs directly, but instead calculates SGS stress tensor B from the following relation:

B = -2 * nu_t * S_ij

where nu_t is equal to nuSgs and S_ij is the resolved strain rate tensor. The only difference from the first approach is that divDevReff is now an explicit source term which is added to momentum equation as the following term:

fvc:: div(B) - fvm::laplacian(nu, U)

Well, I would expect to get the same results in term of viscous stress (u_tau) in the case of channel395 with default grid spacing, but it is not as thought. The first approach (currently used in OF) yields a reasonable Re_tau=370 but the second approach strongly over-predicts viscous stress, yielding a Re_tau=500!!

I would like to ask if such a big difference should be expected from the second approach.


Sincerely,
Syavash

To tell my opinion, I would consider fvm::laplacian(nuEff, U) a wrong approach. The second one appers correct as it retains the SGS viscosity under the divergence operator. Remember that in the dynamic procedure it is a point-wise and time-dependent function.