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how to solve for a vovector field that appears in an equation with an inner product?

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Old   November 13, 2024, 07:55
Default how to solve for a vovector field that appears in an equation with an inner product?
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Mahdi
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Hi all,

Can anyone suggest how to solve for a volvectorfield \OMEGA which appears as a dot product in an equation such as the one below:

Dei/Dt=\OMEGA.ei

lets says we have ei as a volvectorfield input, and we want to calculate \OMEGA. note fvm:: does not support inner dot product.


To give some context:
I am trying to obtain a non-objective \omega=curl of velocity (for those of you who are familiar with fluid mechanics you might know Omega is non-objective so one should replace this with objective version \bar{\omega} which ca be calculated as :

\bar{\omega}=\omega- \OMEGA

where \OMEGA satisfies:
De_i/Dt=\OMEGA.ei

with ei being eigenvectores of deformation rate.


Does anyone know a solver of a library which has doen this? I am sure someone has doen this before so maybe best would be to see what they did instead of calculating eigenvector etc etc

Thanks for any help
Mahdi
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