Source terms with gradient and curl

msaravia · July 31, 2018, 19:06

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

tom_flint2012 · February 28, 2020, 17:00

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

July 31, 2018, 19:06	Source terms with gradient and curl	#1
msaravia Member Martin Join Date: Dec 2011 Posts: 40 Rep Power: 14	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.

February 28, 2020, 17:00	any progress	#2
tom_flint2012 Member Thomas Flint Join Date: Jan 2016 Posts: 60 Rep Power: 10	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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