
[Sponsors] 
June 28, 2009, 08:55 
Smagorinsky model details

#1 
Senior Member
Daniel WEI (老魏)
Join Date: Mar 2009
Location: Beijing, China
Posts: 689
Blog Entries: 9
Rep Power: 13 
Sorry, I do not understand, I saw in "Smagorinsky.H",
Code:
tmp<volScalarField> k(const tmp<volTensorField>& gradU) const { return (2.0*ck_/ce_)*sqr(delta())*magSqr(dev(symm(gradU))); } Question 1: Why using magSqr(dev(symm(gradU))) instead of symm(gradU) && symm(gradU) to get ???? Question 2: If magSqr(dev(symm(gradU))) = symm(gradU) && symm(gradU) = , then But I saw in "Smagorinsky.C" Code:
nuSgs_ = ck_*delta()*sqrt(k(gradU)); Then, replace K with Compare with We'll get But I heard somone said So, I'm puzzled, I wonder if it was a mistake, that k should be written as Code:
tmp<volScalarField> k(const tmp<volTensorField>& gradU) const { return (ck_/ce_)*sqr(delta())*magSqr(dev(symm(gradU))); } Thank you
__________________
~ Daniel WEI  Boeing Research & Technology  China Beijing, China 

August 19, 2009, 12:42 

#2 
New Member
Gabriela Bracho
Join Date: Mar 2009
Location: Valencia, Valencia, Spain
Posts: 14
Rep Power: 9 
Hi Daniel,
Did you find any answer to this question?. in the paper: "A SUBGRIDSCALE MODEL FOR LARGEEDDY SIMULATION OF PLANETARY BOUNDARYLAYER FLOWS PETER E SULLIVAN, JAMES C. McWILLIAMS, and CHINHOH MOENG" 1994, they defined Cs as: Cs=(Ck*(Ck/Ce)^0.5)^0.5 So, I think you are right... Now, I'm confused, why it is defined in Smagorinsky.H like 2*Ck/Ce ?? Is it because of the symm(grad(U)) definition??? It would be great if you could share your opinion... Gaby 

August 20, 2009, 08:35 

#3 
Senior Member
Daniel WEI (老魏)
Join Date: Mar 2009
Location: Beijing, China
Posts: 689
Blog Entries: 9
Rep Power: 13 
Sorry, you see, no one come and help.
And you have noticed, I have done a detailed deduction in my top post, I still don't know why they use
__________________
~ Daniel WEI  Boeing Research & Technology  China Beijing, China 

August 20, 2009, 19:59 

#4  
Senior Member
Sandy Lee
Join Date: Mar 2009
Posts: 213
Rep Power: 10 
Quote:
Sandy sandy.lee37@gmail.com 

October 6, 2010, 05:00 
tensor norm definition

#5 
Member
Andrea Petronio
Join Date: Mar 2009
Location: Trieste, Italy
Posts: 38
Rep Power: 9 
Hallo,
I was also trying to understand the implementation of Smagorinsky model. As it is said here http://www.cfdonline.com/Forums/ope...rainrate.html the definition of the norm of a tensor differs from what is computed in OF, so in my opinion the 2 before ck_/ce_ is exaclty the missing sqr(2) in the definition. so, if S = sqrt(2 S:S) then 2 magSqr(S) = 2 sqrt(S:S)^2 = sqrt(2*S:S)^2 = S^2 Am I right? PS: default Smagorinsky constant should be Cs =0.1677 (in Pope's book is said to be around 0.17) given ck=0.094, ce= 1.048 

March 23, 2011, 16:31 

#6 
New Member
Join Date: Feb 2010
Posts: 8
Rep Power: 8 
Hello
I am also trying to understand how the Smagorinsky model is coded, for the incompressible version and also for the compressible version. And It seems that for the incompressible Smagorinsky model, the default constant Cs is equal to Cs=sqrt(ck*sqrt(2*ck/ce)) If I define Cs such that the eddy viscosity is equal to nuSgs=( Cs *delta)^2 * D if ck=0.094 and ce=1.048 then Cs=0.1995.. ~ 0.2 Same question as Andrea : am I right? 

April 22, 2011, 23:22 

#8 
Senior Member
Alberto Passalacqua
Join Date: Mar 2009
Location: Ames, Iowa, United States
Posts: 1,910
Rep Power: 27 
__________________
Alberto Passalacqua GeekoCFD  A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as in both physical and virtual formats. OpenQBMM  An opensource implementation of quadraturebased moment methods. To obtain more accurate answers, please specify the version of OpenFOAM you are using. 

May 1, 2011, 11:53 

#9 
Senior Member

Thanks Alberto for the useful reference.
As MaximeIST and lakeat told if we compare what is stated in your reference and openFoam smagorinsky with Pope's book we reach to Cs=0.2. As stated in Pope's book this constant can be 0.1~0.2 and using 0.2 can be cause of high diffusivity. Please tell me if this is true. My cyclone simulation with Smagorinsky has high diffusivity and i want use 0.1 for Cs, How can i do that? Which one of Ck or Ce should be changed? I mean are they be used elsewhere or not? Regards, Last edited by maysmech; May 1, 2011 at 14:03. 

May 1, 2011, 18:27 

#10 
Senior Member
Alberto Passalacqua
Join Date: Mar 2009
Location: Ames, Iowa, United States
Posts: 1,910
Rep Power: 27 
I'd just use the dynamic Smagorinsky model, so that you do not have to fiddle with the coefficient, and you do not need to play with dumping functions.
__________________
Alberto Passalacqua GeekoCFD  A free distribution based on openSUSE 64 bit with CFD tools, including OpenFOAM. Available as in both physical and virtual formats. OpenQBMM  An opensource implementation of quadraturebased moment methods. To obtain more accurate answers, please specify the version of OpenFOAM you are using. 

May 2, 2011, 21:59 

#11 
Member
桂莹
Join Date: Apr 2011
Posts: 36
Rep Power: 7 
Hi,Andrea:
I think what you have said is right,the reason is just the different expression of Vsgs 

May 12, 2011, 06:50 

#13 
Member
桂莹
Join Date: Apr 2011
Posts: 36
Rep Power: 7 
hi,Maysam:
since Cs=sqrt(ck*sqrt(*ck/ce), in smagorinsky.c Ck=0.094 , in GenEddyVisc.c Ce=1.048, then Cs=0.167 as we all know ,am I right? 

May 12, 2011, 08:33 

#15 
Member
Andrea Petronio
Join Date: Mar 2009
Location: Trieste, Italy
Posts: 38
Rep Power: 9 
It's Cs \approx 0.17. You need just to follow the way it's computed. The question is why the simple Smagorinsky model is implemented in a such confusing way? We rewrote our Smag. with just Cs required.


May 12, 2011, 09:12 

#16  
New Member
Join Date: Feb 2010
Posts: 8
Rep Power: 8 
Quote:
I may keep on confusing people, but the way it is coded, if I am not doing mistake is Cs=sqrt(ck*sqrt(2*ck/ce)) in the incompressible Smagorinsky.H line 114. There is a factor 2 added in the rootmean squared. And in the case where Ce=1.048 and Ck=0.094, and with this factor 2, we obtain Cs=0.1995. May be I miss something? Maxime 

May 13, 2011, 08:23 

#17  
Member
桂莹
Join Date: Apr 2011
Posts: 36
Rep Power: 7 
Quote:
In the incompressible Smagorinsky.H line 114,it's the expression of K,not Ck,it means k=2Ck/Ce*(delta^2)*(Sof^2),may be my blog can help you: http://blog.sina.com.cn/s/blog_6d9c27ab0100u9ez.html it's just what I think, I'm not sure. 

May 13, 2011, 11:10 

#18 
New Member
Join Date: Feb 2010
Posts: 8
Rep Power: 8 
Hello Yingkun
I agree with you that it is the expression of k which is in line 114 of the Smagorinsky.H. But the factor 2 is still there and as lakeat shown in the first message of this thread, we still get Cs=sqrt(ck*sqrt(2*ck/ce)) I have been in your blog, and I think you lost this factor 2 in the passage of equation (7) to the last equation of the page. Maxime 

May 14, 2011, 01:01 

#19  
Member
桂莹
Join Date: Apr 2011
Posts: 36
Rep Power: 7 
Quote:
I think you don't understand exactly what I mean,the difference is just caused by the different expressions of S between turbulent therory and Openfoam,there is a factor of sqrt(2) difference,lakeat just regards them the same 

May 16, 2011, 06:13 

#20  
New Member
Join Date: Feb 2010
Posts: 8
Rep Power: 8 
Quote:
It's true I don't understand what is written in your blog, chinese is not easy for me ! So you said that the sqrt(2) is a consequence of the definition of S in OpenFoam. In this case, the default constant in the incompressible Smagorinsky is 0.167. good to know! 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Multiphase flow. Dispersed and free surface model  Luis  CFX  8  May 29, 2007 18:13 
KatoLaunder model  sam  Main CFD Forum  13  September 21, 2006 10:15 
Kinetic air props model  conductivity HALF?  Chris Bailey  FLUENT  1  March 7, 2006 11:38 
Reply to Tim Re Dynamic Smagorinsky model  Ajay S. Parihar  Main CFD Forum  9  June 2, 2002 16:24 
Biharmonic Viscosity with Smagorinsky model  Wen Long  Main CFD Forum  4  May 15, 2002 05:54 