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Source terms with gradient and curl

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Old   July 31, 2018, 19:06
Unhappy Source terms with gradient and curl
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Martin
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Hi, I am trying to solve an equation of the form:


\nabla^2A = - b \cdot (\nabla A-\nabla A^T)

being A and b vector fields; so, \nabla A is the Jacobian and \nabla A-\nabla A^T is a skew symmetric tensor. The equation can also be written as:

\nabla^2A = -b \times (\nabla \times A)

I am wondering wich is the best way to treat the RHS. I have been thinking of using simply

Code:
fvm::laplacian(A) == b ^ fvc::curl(A)
or
Code:
fvm::laplacian(A) == b & ( fvc::grad(A)-fvc::grad(A).T)
I know that positive sources should be treated implicitly, but the RHS is no actually a source. Also, the curl does not have an implicit implementation in OpenFOAM.

At last... I'm lost. Any suggestions to implement this equation would be welcome!

Thanks

Last edited by msaravia; July 31, 2018 at 20:34.
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Old   February 28, 2020, 17:00
Default any progress
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Thomas Flint
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Hi,


I'm implementing a similar equation. I thought I had some success converting one of my curls using identities but cant get rid of another.



Have you made any progress with this in openfoam?


Thanks,


Tom
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