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-   -   Smagorinsky model and Sij terms (https://www.cfd-online.com/Forums/main/8420-smagorinsky-model-sij-terms.html)

 James December 6, 2004 12:30

Smagorinsky model and Sij terms

I'm currently updating a code that uses the Smagorinsky model as its sgs model. At present the code calculates Sij in the form:

Sij**2 = S11**2 + S22**2 + S33**2 + 2S12**2 + 2S13**2 + 2S23**2

in order to calculate the eddiy viscostiy.

Now, as the |S| term is SQRT(2SijSij), is is clear that the Sij**2 shown above and SijSij calculated normally do not commute, so which one should I use? Is the above implmentation wrong?

Thanks,

James

 agg December 6, 2004 15:32

Re: Smagorinsky model and Sij terms

I think the above implementation is correct. Sij**2 = Sij:Sij = Sij*Sji

 Adrin Gharakhani December 6, 2004 20:24

Re: Smagorinsky model and Sij terms

It all depends on the definitions of S11, S22, S12, etc. in the code. The equation you have written is neither wrong nor right; you have simply not provided sufficient information.

This is a two minute exercise in algebra. You know Sij = {ui,j + uj,i}/2 and Sij*Sij simply uses the repeated index notation. You can then verify by yourself whether your code is right or wrong