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April 22, 2022, 08:00 |
C5 term in SSG Reynolds Stress Model
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#1 |
Senior Member
Agustín Villa
Join Date: Apr 2013
Location: Alcorcón
Posts: 314
Rep Power: 15 |
Hi everyone,
I am checking the SSG implementation, concretely the C5 term. In the reference, the skwe of the velocity gradient is defined as: When checking how this is implemented in OpenFOAM: Code:
Omega(skew(gradU)) which is just the transpose of the expected skew tensor in the model. Am I missing something? Is therefore properly implemented this term or am I right and it should be modified? |
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April 22, 2022, 10:39 |
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#2 |
Senior Member
Join Date: Apr 2020
Location: UK
Posts: 736
Rep Power: 14 |
Can you be more explicit please - I assume you are talking about the SSG Reynolds stress closure? If so, which term are you talking about and which reference?
Edit: ok, I see now. You are talking about the SSG model, and the term from the Speziale paper which is coded in SSG.C (https://cpp.openfoam.org/v8/SSG_8C_source.html) as: Code:
volTensorField Omega(skew(gradU)); ... + C5_*twoSymm(b&Omega) |
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April 22, 2022, 11:15 |
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#3 |
Senior Member
Join Date: Apr 2020
Location: UK
Posts: 736
Rep Power: 14 |
I think it comes down to semantics and the definition of the gradient in tensor notation (see an earlier thread, for example: discrepancy in fvc::grad(U)). In their JFM paper, eqn 23, Speziale etc write the term of the velocity gradient as:
which is the inverse of the way that the OpenFOAM tensors are defined (again refer to the above thread ... if you have the patience!). To be clear, in OF, the term of the velocity gradient is: . This means that the definition of in the Speziale paper has inverted indices as well ... and so I think that the implemented model is probably correct. Hope that helps. |
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April 22, 2022, 15:29 |
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#4 |
Senior Member
Agustín Villa
Join Date: Apr 2013
Location: Alcorcón
Posts: 314
Rep Power: 15 |
Thanks Tobermory! It was impossible that after more than 9 OF versions nobody noticed it before.
As all of you discuss in that thread, it seems that OF knows already how we expect to operate with gradU. However, the programmer's guide equation (2.3) is confusing (that guide is quite old). Mathematically it is ok, but there is no link with the actual implementation of the gradient of a vector. I used the OF programmer's guide to define some terms in custom turbulence models, whose results are ok. I have to review what the heck want on there. After a test using Omega(skew(gradU)) and Omega(skew(gradU.T)) the original implmentation was the good one. As you say, maybe the transposed of Speciale et al and the transposed of OF cancel this effect. |
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