Integration issue
 

My problem is that I know what I need to do, I'm just no sure how to code it. :mad:

Here's the integral I'm working with:

I=-ρ b∫ ∂V/∂n dl

rho and b are known constants. ∂V/∂n is the partial of Voltage normal to the plane and dl is obviously my differential length. With this integral I'm finding the corona current around a wire with fairly high current.

I'm basically having issues with two parts. The first is figuring out how to find the partial of voltage normal to my plane (wire). I have solved for the voltage field throughout my mesh but don't know how to single out the values around the wire. I know that the values at the wire itself all are normal to the plane so all I need to find are the magnitudes of each mesh cells voltage at the wire.

Secondly I'm having problems finding the differential length of my cells. I'm 99.9% sure that my mesh is uniform around the wire, so I'd probably only need the length of one cell.

I've been searching the source code info for any functions to solve for what I'm looking for but, so far I'm coming up dry. Any help that could be provided is much appreciated.

I've been working on a modified electrostaticFoam solver. So far I've only added the following:

volVectorField E("E",-fvc::grad(phi)); //Solve For E-Field

Now I'm still trying to figure out how to solve for my integral. I've been looking and think that maybe I need to use nCells at the wire and then divide that by the circumference of my wire. If the mesh is uniform this will give me the dl I need. Having said that, I'm not sure how to actually go about doing it.

This is driving me a little crazy. It's so frustrating when you know what you need to do but not how to do it! :mad::mad:

Any help you could give would be greatly appreciated!