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LES Filtering: how are the small and large scales equations solved? 

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September 5, 2012, 04:54 

#21  
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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 PortèAgel, Menevau and Parlange; the other ones are by TejadaMartinez and Jansen: PortéAgel F, Meneveau C, Parlange MB. 2000a. A scaledependent dynamic model for largeeddy simulation: application to a neutral atmospheric boundary layer. J Fluid Mech 415: 261284 “A parameterfree dynamic subgridscale model for largeeddy simulation”, A.E. Tejada Martinez and K.E. Jansen, Computer Methods in Applied Mechanics and Engineering,195 (2006), pp 29192938 “A Dynamic Smagorinsky Model with a Dynamic Filter Width Ratio”, A.E. TejadaMartinez and K.E. Jansen, Physics of Fluids, 16 (2004) 25142528 The work of TejadaMartinez 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. Last edited by sbaffini; September 5, 2012 at 05:07. Reason: corrected the incomplete references 

September 5, 2012, 05:45 

#22 
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Francesco Capuano
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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. 594597), 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. 

September 5, 2012, 06:44 

#23 
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Filippo Maria Denaro
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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 

December 5, 2012, 06:04 

#24 
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Albrecht vBoetticher
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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)


December 5, 2012, 09:02 

#25  
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Filippo Maria Denaro
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December 10, 2012, 06:44 

#26 
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Albrecht vBoetticher
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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.unirostock.de/en/cfdsoftware/
Found it due to a link by Hannes Kröger, thanks Hannes! 

December 10, 2012, 08:28 

#27  
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Filippo Maria Denaro
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April 17, 2013, 11:44 
Gaussing Filters and LES codes

#28  
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sankarv
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I have a general question about the use of filters other than tophat 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 nondynamic models, then I do not see where the filter shape will be used in the CFD code. Can you please clarify ? Thanks Vaidya 

April 17, 2013, 12:09 

#29  
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Filippo Maria Denaro
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[/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 nondynamic 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 scalesimilar 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 

April 17, 2013, 13:39 

#30 
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sankarv
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Thanks a lot for the quick reply. Your paper is certainly interesting. I will look into it carefully.


September 10, 2013, 23:46 

#31 
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Mahfuz Sarwar
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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? 

September 11, 2013, 03:58 

#32  
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Filippo Maria Denaro
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September 19, 2013, 22:56 

#33  
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Mahfuz Sarwar
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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? 

September 20, 2013, 11:02 

#34  
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Filippo Maria Denaro
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The smooth filter is characterized by a smoothing behaviour of the resolved frequencies. For example the tophat filter acts as sin (k*h) / (k*h). The first zero corresponds to the same cutoff frequency Kc=pi/h, but before it the components are now smoothed 

January 3, 2016, 10:44 

#35  
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Wen Xu
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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. Quote:
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 

January 3, 2016, 12:15 

#36 
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Filippo Maria Denaro
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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 

January 3, 2016, 20:49 

#37 
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Wen Xu
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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 Last edited by wenxu; January 3, 2016 at 22:06. 

January 4, 2016, 04:29 

#38 
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Filippo Maria Denaro
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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 

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filter, les, navier stokes equation 
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