# Smagorinsky model and Sij terms

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 December 6, 2004, 12:30 Smagorinsky model and Sij terms #1 James Guest   Posts: n/a 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

 December 6, 2004, 15:32 Re: Smagorinsky model and Sij terms #2 agg Guest   Posts: n/a I think the above implementation is correct. Sij**2 = Sij:Sij = Sij*Sji

 December 6, 2004, 20:24 Re: Smagorinsky model and Sij terms #3 Adrin Gharakhani Guest   Posts: n/a 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 Adrin Gharakhani

 December 7, 2004, 11:20 Re: Smagorinsky model and Sij terms #4 James Guest   Posts: n/a The current code in indeed correct. I should try to remember how tensor notation works!

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