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Divergence of third order tensor

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Old   April 28, 2006, 12:46
Default I'm trying to calculate a tens
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Maka Mohu
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I'm trying to calculate a tensor (d/dx_k)(s_ik * u_j). s_ik is a second order strain rate tensor (symm(fvc::grad(Uprime))). I read the programmer manual, but I have a question:

can I use divergence operator on third order tensor (div(s*u)) and how it is defined (on which index the summation convention works? is it the first?).

There is another way to do it but less compact:

(d/dx_k)(s_ik * u_j) = ((d/dx_k) s_ik) * u_j + s_ik * ((d/dx_k) u_j);

in the programmers guide: div(s) = (d/dx_i) s_ij

This transform the relation to (s_ij is symmetric):

(d/dx_k)(s_ik * u_j) = div(s) * u + s * fvc::grad(u); Am I right? Thanks.

Best regards,
Maaka
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