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Implementating the Wilcox 2006 turbulence model

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Old   October 1, 2013, 13:53
Default Implementating the Wilcox 2006 turbulence model
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Ben Graves
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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
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File Type: png Equations for Wilcox 2006.png (19.3 KB, 9 views)
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Old   October 2, 2013, 11:13
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Matt Laurita
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If you take a look at the Tensor class (actually TensorI.H) there are global functions for calculating symmetric and skew-symmetric 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
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Old   October 2, 2013, 13:58
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Ben Graves
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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
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Old   October 3, 2013, 03:59
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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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Originally Posted by bgraves View Post
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
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