CFD Online Discussion Forums - tangential laplacian, BC

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tangential laplacian, BC

Dear all,

I am new with openFOAM and I am trying to implement the following boundary condition at the conducting wall:

$\frac{\partial\varphi}{\partial n}$ = a $\cdot$ $\nabla^{2}_{t}$ $\varphi$
where $\varphi$ is electric potential, a is constant, $\nabla^{2}_{t}$ $\varphi$ is tangential Laplacian at the wall.

I wonder if anybody has an idea about the following question:
Is it possible to find tangential Laplacian at the wall in openFOAM and if so - how? I guess that it is only possible to find normal Laplacian, but I will be happy if I am wrong. Thanks in advance.

Best regards,
Tar

tangential laplacian

Hi,

I know it is an old post but, I am currently working on the same topic.
The boundary condition can be created inheriting from fixedGradient.
My idea to obtain the tangential components is applying the laplacian to the field, get its value at the boundary and then substract the second derivative of the normal component.

One way to obtain the second derivative is:

Code:

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 const volScalarField& PotE = this->db().objectRegistry::lookupObject<volScalarField> ("PotE");

volVectorField gradPotE = fvc::grad(PotE); 

const vectorField& Sf = patch().Sf(); // surface face vector area

const scalarField& magSf = patch().magSf(); // surface area magnitute

vectorField normFace = Sf/(magSf+SMALL);

// second derivative of normal component



scalarField normGradPotE = gradPotE.boundaryField()[patchi].snGrad() & normFace





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// update of gradient (lapPotEw is the laplacian at the boundary

gradient()= cWall_*(lapPotEw - normGradPotE);

I am unfortunately running into divergence problem in my code.
By the way, the tangential components of a vector can be extracted as:

Code:

n ^ (n ^ v)

where n is the normal vector direction. But you should apply the divergence to this vector that happens to be a vector field. So, don't know

Hope that this can help!

Hopefully somebody else has a better idea