[sbaffini]

Originally Posted by francesco_capuano

I would like to go deeper into the highlighted sentence together with Prof Denaro. Besides vanishing for laminar flows, a good SGS model should also vanish (or at least diminish) automatically if the local filter width (i.e. a measure of the grid size, for implicit filtering), is comparable to the Kolmogorov scale: if we apply an LES model to a DNS grid, the subgrid stress should be ideally zero. But also, if an LES grid has regions with very fine resolution (down to the Kolmogorov scale), then the SGS stress should vanish in those regions but not in the rest of the grid.

Now, my doubt is: which part of a (let's say dynamic) SGS model is responsible for this? Is it the dynamic calculation of the constant? I guess the standard Smagorinsky is not capable of doing that, as the constant is fixed and is calculated assuming, a priori, a certain position of the filter width along the spectrum, is that right?

I'm not completely sure 100% but i'm pretty confident that no part of the classical dynamic procedure has the capability to make the constant null in the case of a fully resolved DNS.

Actually, it can be shown that assuming the constant to be equal at the two filter levels imply that the computed dynamic constant is that at the test filter level and not at the basic filter level (either explicit or implicit).

Of course, for a very well resolved DNS this is not a real issue, also because the delta^2 factor will still be at work. Nonetheless, it is a well known inconsistency of the classical dynamic procedure.

There are two known modifications of the dynamic procedure to overcome this issue. The first one is proposed by Portè-Agel, Menevau and Parlange; the other ones are by Tejada-Martinez and Jansen:

Porté-Agel F, Meneveau C, Parlange MB. 2000a. A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J Fluid Mech 415: 261-284
“A parameter-free dynamic subgrid-scale model for large-eddy simulation”, A.E. Tejada Martinez and K.E. Jansen, Computer Methods in Applied Mechanics and Engineering,195 (2006), pp 2919-2938
“A Dynamic Smagorinsky Model with a Dynamic Filter Width Ratio”, A.E. Tejada-Martinez and K.E. Jansen, Physics of Fluids, 16 (2004) 2514-2528

The work of Tejada-Martinez also adresses the issue of determining the delta ratio when the basic filter is implicit and you can't simply fix a value based on the computational cell. However, i'm not pretty confident on this work as in some cases (i.e., the finite volume based dynamic procedure of Prof. Denaro) i found some inconsistencies in applying such procedure.

[francesco_capuano]

Dear Paolo, thank you very much! That is exactly what I was looking for, and I'll go through the references you suggested. I think the underlying problem for classical SGS models is that they imply a certain filter, rather then adapting to the actual filter.

However, one more reference I suggest is a part from the book by Pope (p. 594-597), when he talks about the limiting behaviors of the Smagorinsky model (filter in the dissipative range, filter being large compared to the integral scale and laminar flow).

In any case, as you also said, this is just a theoretical issue: from a practical point of view there is no concrete inconsistency.

[FMDenaro]

Remember that the Germano identity is exact, it is the SGS model you introduce in it that generates the approximations (and the inconsistences).
You can think about several improvements ... different functions model at different grid levels, or some modification in the eddy viscosity assumption...
I hope you can work on it

[vonboett]

Adressing the filtering, there is aswll the point of averaging the SGS model constant when using dynamic SGS models. Averaging along homogenious flow directions is a theoretical case when simulating natural flows, the dynamic localization approach has its own drawbacks, so I wonder what you would think about a lagrangian dynamic mixed smagorinsky / scale similarity SGS model? (not implemented in OpenFOAM yet)

[FMDenaro]

Originally Posted by vonboett

Adressing the filtering, there is aswll the point of averaging the SGS model constant when using dynamic SGS models. Averaging along homogenious flow directions is a theoretical case when simulating natural flows, the dynamic localization approach has its own drawbacks, so I wonder what you would think about a lagrangian dynamic mixed smagorinsky / scale similarity SGS model? (not implemented in OpenFOAM yet)

recently, this problem was superseeded by the integral-based dynamic procedure, no averaging of the model function is required as the extraction from filter is automatic

[vonboett]

I see. So I wonder what you 'd think about the dynamic mixed version of Meneveau's lagrangian SGS model in comparison to the dynamic mixed model, both provided for OpenFOAM by Prof. Kornev: http://www.lemos.uni-rostock.de/en/cfd-software/

Found it due to a link by Hannes Kröger, thanks Hannes!

[FMDenaro]

Originally Posted by vonboett

I see. So I wonder what you 'd think about the dynamic mixed version of Meneveau's lagrangian SGS model in comparison to the dynamic mixed model, both provided for OpenFOAM by Prof. Kornev: http://www.lemos.uni-rostock.de/en/cfd-software/

Found it due to a link by Hannes Kröger, thanks Hannes!

In general, taking into account the literature, I see an improvemnt in the Lagrangian version, some comparative testing were presented since 1999 (Sarghini et. al, PoF). Unfortunately, I have no knowledge of the perfomances when tested using OF.

[sankarv]

Originally Posted by FMDenaro

Just to add a comment, at best of my knowledge explicit filtering is only an acadamic issue, no commercial LES code (FLuent, TransAT, etc) or open-source (OpenFOAM, Code_Saturne) use that, the filter is always implicitly defined by the discretization.
That makes very often confusing to distinguish in the manuals the LES from URAN equations, they are written formally in the same way..

Dear Fillipo

I have a general question about the use of filters other than top-hat filter in CFD codes.

Let us consider implicitly filtered LES approach, Smagorinsky model without dynamic coefficient estimation and finite volume CFD code.

If I want to use Gaussian filter, where will the Gaussian filter kernel appear in the cfd code ? The filtered LES equation only needs filter length scale for the subgrid model. If I want to use Gaussian filter how will the CFD code see the filter kernel shape ?

Will the filter length scale be different from cube root of cell volume if I want to use Gaussian filter ?

If I use dynamic smagorinsky or mixed models for subgrid stresses, there will be a step to explicit filter where the filter shape information is used by the code. If I use non-dynamic models, then I do not see where the filter shape will be used in the CFD code.

Can you please clarify ?

Thanks
Vaidya

[FMDenaro]

Originally Posted by sankarv

Dear Fillipo

I have a general question about the use of filters other than top-hat filter in CFD codes.

Let us consider implicitly filtered LES approach, Smagorinsky model without dynamic coefficient estimation and finite volume CFD code.

If I want to use Gaussian filter, where will the Gaussian filter kernel appear in the cfd code ? The filtered LES equation only needs filter length scale for the subgrid model. If I want to use Gaussian filter how will the CFD code see the filter kernel shape ?

In no way an implicit filtering-based CFD code contains some filter you can choose to use... in your example, the filter is defined by the type of FV discretization. If you want to use a Gaussian filter then you must introduce it in an explicit filtering formulation. But in any case you must be aware that the FV formulation always imply that a smooth filter is acted on, thus adding a Gaussian filter in an explicit formulation can result is a strong smoothing (the two filter kernel are not idempotent)


[/QUOTE] Will the filter length scale be different from cube root of cell volume if I want to use Gaussian filter ?

If I use dynamic smagorinsky or mixed models for subgrid stresses, there will be a step to explicit filter where the filter shape information is used by the code. If I use non-dynamic models, then I do not see where the filter shape will be used in the CFD code.

Can you please clarify ?

Thanks
Vaidya[/QUOTE]

actually, both in scale-similar and mixed (static) model, the shape of the second filter must be prescribed as it is really applied on the variable to formulate the SGS model.
To complete the answers, the lenght of the filter should be deduced by the transfer function that is really in action in the code. The cube root of the cell measure is a rude approximation.

Further details can be found here: http://www.sciencedirect.com/science...21999111000933

[sankarv]

Thanks a lot for the quick reply. Your paper is certainly interesting. I will look into it carefully.

[mahfuzsarwar]

In most of the cases we are talking about the filter size is larger than the grid size in the case of explicit filtering or almost equals to grid size if implicitly filtered.


What will happen if the filter width is less than the grid cell? Whether it will create any unphysical condition? What will be the effect on the SGS modelling?

[FMDenaro]

Originally Posted by mahfuzsarwar

In most of the cases we are talking about the filter size is larger than the grid size in the case of explicit filtering or almost equals to grid size if implicitly filtered.


What will happen if the filter width is less than the grid cell? Whether it will create any unphysical condition? What will be the effect on the SGS modelling?

When the computational size h is chosen, you fixed also the Nyquist frequency Kc=pi/h. In no way you can have a filter width lesser than the computational size, simply because there is nothing to filter ...

[mahfuzsarwar]

Originally Posted by FMDenaro

When the computational size h is chosen, you fixed also the Nyquist frequency Kc=pi/h. In no way you can have a filter width lesser than the computational size, simply because there is nothing to filter ...

Thanks Filippo, for the reply.
It would be a great help if you just clear me up in this regards, what is the difference between sharp cutoff filter and smooth filter in LES?

[FMDenaro]

Originally Posted by mahfuzsarwar

Thanks Filippo, for the reply.
It would be a great help if you just clear me up in this regards, what is the difference between sharp cutoff filter and smooth filter in LES?

In the Fourier space, the sharp cut-off retains components (unmodified) at all frequencies up to Kc=pi/h.
The smooth filter is characterized by a smoothing behaviour of the resolved frequencies. For example the top-hat filter acts as sin (k*h) / (k*h). The first zero corresponds to the same cut-off frequency Kc=pi/h, but before it the components are now smoothed

[wenxu]

Dear Prof. Denar,

Happy New Year!

You really clarified many points of the explicit filter in this thread. Thank you very much!

But I still have a question about the explicit filter that coded in OF. Could you give us some explanation of the following description in the laplaceFilter.H file.

Kernel as filter as Test filter with ratio 2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~
Box filter: g = delta2/24 -> g = delta2/6
Spherical box filter: g = delta2/64 -> g = delta2/16
Gaussian filter: g = delta2/24 -> g = delta2/6

1) What's the meaning of "g" and "delta2"? Is it the LES cell size? Why there is a "2" there? (I guess the "g" is the filter function, and the delta2/24 is the filter size. Why is it not the delta, but that value in the equation as in the description?)

2) What's the meaning of the number in the denominator? such as 24, 64, 24

3) How to choose the filter kernel? It seems there is no need to set the filter kernel? Then which one is the default kernel? How can I choose another one?

4) How to set the widthCoeff for a specific kernel?

5) I found that if the test filter with ratio 2, then the "g" value is reduced by a factor of 4. If I use the filter with ratio 4, then the "g" value will be reduced by a factor of 14?

Could you give me a help?

Thank you in advance!

Best regards,
Wen

[FMDenaro]

First, I strongly suggest a reading of well known books about this topic, you can find sections detailing many issues.

However:
- delta2 should actually be delta^2, delta being the filter size. That is not the grid size.
- g is the filter kernel
- the coefficient 24 comes from the "differential filter", that is a Taylor expansion integrated over the box width.
- I do not believe OF has an explicit filter in the main program, the choice of the type of filtering should be related to the "test filtering" used in the dynamic procedure.

Heppy new year

[wenxu]

Thank you very much for your very kind reply.

Yes, I think it is very necessary to read a book to know the details about this topic. Do you have any recommendation of the reference book or the related materials?

I want to use the test filter to "thicken" the flame. So the explicit filter should be used.

Best regards,
Wen

[FMDenaro]

for example, general topic on LES and its SGS modelling can be found in
http://www.springer.com/cn/book/9783540263449

while more specific mathematical properties are detailed in
http://www.springer.com/la/book/9783540263166

[juliom]

Dear Mr. ATM. Could you please cite one of the paper where you came across of that explicit definition for filtering? Thanks!