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July 12, 2011, 12:31 
How about dynamic Smagorinsky?

#21 
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Bernhard
Join Date: Sep 2009
Location: Delft
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Hi all,
I have some questions about this same issue with respect to the dynamic Smagorinsky model. I think I am making a mistake somewhere, but please correct me if I am wrong. I've tried to look at other locations for the same issue, but couldn't find it. I compare the dynamic model in OpenFOAM (not caring about the domain averages coefficient) with the dynamic model (described in Lilly and Pope). I think we agree on the following (D defined in OpenFOAM, S common definition) Now, looking at the code (dynSmagorinsky 1.7, homogeneousDynSmagorinsky 2.0), in the .C file at line 57, 62 respectively: as compared to the original of Lilly (in Pope this expression If D_ij=S_ij, but S=sqrt(2) D, then the second term in the OF implementation is off by a factor sqrt(2). (Where the factor 4 is from the double width of the test filter, and the minus sine is also present in L) Somewhere I must have skipped a step, I hope one of you can point it out for me. Thanks in advance! 

July 15, 2011, 03:35 

#22 
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Bernhard
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Anybody that can give a comment on this?


July 18, 2011, 04:47 

#23 
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Bernhard
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August 26, 2011, 07:39 

#24  
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Gregor Olenik
Join Date: Jun 2009
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Quote:
let symm(gradU) be S, then dev(S) = S  1/3 trace(S)I however in a incompressible case 1/3 trace(S)I = 0, since trace(S) is the continuity eq. . Therefore in an incrompessible case it doesnt matter whether you take dev(S) or not , but consider a compressible case then 1/3 trace(S) doesn't vanish. In a compressible or variable density case the solver calls divDevRhoBeff to compute the source term due to SGS stress B = 2/3k I  2 nu_t S_D. (See Fureby http://pof.aip.org/resource/1/phfle6/v9/i5/p1416_s1 Eq. 3) There you have the deviatoric part of D. But i guess openFoam uses nu_t = c Delta^2 S_D and B = 2/3k I  2 nu_t S. So it takes S_D for the turbulent viscosity and S for the SGS stress tensor B. 

January 24, 2013, 11:40 

#25  
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Join Date: Nov 2012
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Quote:
For the compressible Smagorinsky model, the parameters for ck=0.02, ce=1.048 Following the following line: Cs=sqrt(ck*sqrt(ck/ce)) => Cs=0.0525... Does anybody know the references for these specification of the ck and ce for compressible Smagorinsky model? 

March 11, 2013, 23:25 

#26 
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sqing
Join Date: Sep 2012
Location: Dalian
Posts: 77
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Hi Yingkun,
As you mentioned, in the incompressible solvers Cs=sqrt(Ck*sqrt(Ck/Ce)). So if I want to set Cs=1, Do I just need to modify Ck and Ce in the LESProperties？Or are there other rules I must obey? Code:
SmagorinskyCoeffs { ce 1.05; ck 0.0472; } 

February 28, 2014, 04:03 

#27 
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Florian Ries
Join Date: Feb 2014
Posts: 76
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Hi Bernhard and everybody,
I compare the dynamic model in OpenFOAM (homoDynSmag OF 2.2.2) with the dynamic model (described in Lilly and Pope) and I have the same Problem. To reanimate the discussion: In Pope (F(.) means filtered): [1] nu_SGS = cS * delta^2 * sqrt(2 * S_ij S_ij) [2] cs = (M_ij L_ij)/(M_kl M_kl) where [3] S_ij = 0.5 (ui,j + uj,i) [4] M_ij = 2 * delta^2 * (F(sqrt(2 * S_ij S_ij) S_ij)  F(sqrt(2 * S_ij S_ij)) F(S_ij)) [5] L_ij = F(ui uj)  F(ui) F(uj) In OF 2.2.2 (homogeneousDySmagorinsky, <.> means averaged): [6] nu_SGS = cD * delta^2 * sqrt(S_ij S_ij) [7] cD = 0.5 (<L_ij M_ij>)/(<M_kl M_kl>) [8] S_ij = D_ij = S_ij Pope [9] M_ij = delta^2 * (F(sqrt(S_kl S_kl) Sij)  4 * sqrt(<S_kl> <S_kl>) <S_ij>) [10] L_ij = F(ui uj)  F(ui) F(uj) I marked the differences of these models.  First difference is the factor 0.5 in Eq[7] in comparison to Eq[2]. This comes from the factor 2 in Eq[4]. If we put this in Eq[2] we get 0.5 (ok)  Second difference is the different filtering in M_ij. What effect does this have???? (x)  Third difference is the factor 4 in Eq[9] in comparison to Eq[4]. Bernhard: here the factor 4 is from the double width of the test filter can you please explain that?? Why we don`t get a fector in the other filtered terms??? (x)  Fourth difference is the factor 2 in mag(S_ij). (x) In my opinion these models are different or I`m not able to bring the OFmodel in the form of popemodel. If it is possible, anyone can please give some advice? kind regards Florian 

October 28, 2014, 03:39 

#28 
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wenxu
Join Date: May 2014
Location: HangZhou,China
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Quote:
the third one shoub be sqrt(2*Sij*Sij) 

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