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October 1, 2013, 13:53 
Implementating the Wilcox 2006 turbulence model

#1 
New Member
Ben Graves
Join Date: Dec 2012
Posts: 18
Rep Power: 5 
Hi everyone,
I am trying to implement the Wilcox 2006 turbulence model into openFOAM, and have gotten a little stuck. I have been able to code up everything except the closure coefficient chi_omega. The equation determines the coefficient Beta. The equation for chi_omega can be seen in the attached image. I know that the Omega_ij term is the skew symmetric matrix, what I am not sure of is how to code in Omega_jk and S_ki. I would really appreciate any insight that can be provided. Thanks for your help in advance Ben Graves 

October 2, 2013, 11:13 

#2 
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Matt Laurita
Join Date: Jan 2012
Location: New York
Posts: 8
Rep Power: 6 
If you take a look at the Tensor class (actually TensorI.H) there are global functions for calculating symmetric and skewsymmetric parts of a matrix. In this case, if you start with the gradient of the velocity, grad(U), then symm(grad(U)) gives you S and skew(grad(U)) gives you Omega. You'll probably also have to make use of the inner product and mag() functions here as well to get to Chi_omega.
MJL 

October 2, 2013, 13:58 

#3 
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Ben Graves
Join Date: Dec 2012
Posts: 18
Rep Power: 5 
Hi Matt,
Thanks for the reply! I know how to get Omega_ij and S_ij, what I wanted to know was how to get Omega_jk and S_ki. Basically my question is how do I specify the different index. Thanks, Ben 

October 3, 2013, 03:59 

#4 
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Join Date: Nov 2012
Posts: 13
Rep Power: 5 
Hi Ben,
S_ij is the same as S_ki, both are a component of the tensor S. When calculating chi_omega, you should use i,j,k = 1, 2, 3 to construct each term and then add them up (in total there will be 27 terms, due to Einstein convention of repeated indices). You should have some basic knowledge of tensor. 

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