[Getdp] ... coordinates in integrals ...

[Matt Koch]

Hi All,

thanks to Bernard Kubicek's groundwork (FaceConduct2D in GetDP Wiki 
Examples), I have finally made some small progress in solving my thermal 
interface problem. I am NOT using his exact implementation, and I was 
able to make the two regions NOT be connected, but his line of thinking 
helped me break a long existing deadlock.

To go farther, I have to learn about coordinates in integrals. 
Basically, my interface is a small gap between two parallel disks, and 
the integral involves radial coordinates from both sides of the gap, 
i.e. radial coordinates of both disk surfaces facing the gap. The 
function to be integrated on either surface is something as follows, 
although the exact form really does not matter.

f(r1,r2,h) =(r1^2+r2^2+h^2)^2/[(r1^2+r2^2+h^2)^2 - 4*r1^2*r2^2]^1.5

Hereby, r1 is a radius on one surface, r2 is a radius on the other 
surface and h is the separation of the two surfaces, i.e. the gap. The 
actual integrals are as follows:

1) F1(r1,h) = Int{f(r1,r2,h)}dA2 with dA2 = 2*pi*r2*dr2
2) F2(r2,h) = Int{f(r1,r2,h)}dA1 with dA1 = 2*pi*r1*dr1

The important part is that the dependencies of F1 and F2 on r1 and r2, 
respectively, must be retained, while those on r2 and r1, respectively, 
are eliminated. So, one question is, how do I access r1 on one surface 
and r2 on the other surface. I have read about $X (or X[]) and $XS (or 
XS[]) in section 2.5 of the manual, but I do not know if the concept of 
source and destination applies here, and if so, which would be source 
and which would be destination.

Any clues as to how to attack these integrals would be much appreciated. 
Once I have this answer, I will still need to extend it to where the 
integral actually contains an unknown field variable in addition to the 
above function f, but I'll try to cross that bridge when I get there.

Thanks and Regards,

Matt Koch