[celestial]

Hello everybody

I want to solve the Laplace equation in a vacuum

solve
(
fvm::laplacian(V)
);

subject to a 2D electrode charged to a constant voltage 1000V and with a spherical arc shape (but not a sphere as I don't want it to enclose a 3D domain) .
So let it lie inside a very large bounded box where we approximate the electric field to be 0 on all sides of this box.

Therefore, file casename/0/V
contains the following snippet:

boundaryField
{
farfield
{
type fixedGradient;
gradient uniform 0;
}

}

The question is how to code the 1000V voltage condition on this arc since it is not on a patch (it is not on the boundary of a 3D domain)

For those who prefer a fluid dynamics setting, you could have the analogous problem (in 2D though not 3D !!) with an incompressible irrotational fluid. Voltage V would be replaced by a streamline phi, phi would be constant on the circular arc and gradient uniform 0 becomes gradient uniform Velocity;


Have a nice weekend

[celestial]

I believe the answer is that the OPEN arc is a limiting case of a very thin CLOSED surface and is treated in many analytic fluid dynamics books. Afterall, in real life, we deal with a 3D body surrounded by air. In openFoam, this closed surface does indeed become a boundary of the outer air domain.

So unless somebody has anything to add, this thread is closed.

Thanks for watching