Writting an integral of a transmission/interface problem

General Discussion
1

Hi everyone,

I have a advection-diffusion problem with an interface, let’s say \Omega = \Omega_1 \cup \Omega_2, \Gamma = \partial \Omega_1 \cap \partial \Omega_2, where [T] = 0, [k\frac{\partial T}{\partial n}] = 0 on \Gamma.
I need to write the integral of something like this
\int_\Gamma \frac{\partial T_1}{\partial n} -\frac{\partial T_2}{\partial n} = \int_\Gamma (\frac{1}{k_1} - \frac{1}{k_2}) k_1 \frac{\partial T_1}{\partial n} = \int_\Gamma (\frac{1}{k_1} - \frac{1}{k_2}) k_2 \frac{\partial T_2}{\partial n}

How can i write the expression \frac{\partial T_1}{\partial n}, \frac{\partial T_2}{\partial n} or in general f(T_1, T_2) on \Gamma for a continuos problem?
I have done T_1 = T*(region==1) and T_2 = T*(region==2) , and after that compute the normal derivative, but i’m not getting what i want to get, and i think if i do that T_1 is different to T_2 in \Gamma.

Any idea?

Best regards,
Rodrigo

2

First you must clearly define the Gamma edge and number it for example by gam. Then you do:
real K1=1./k1;
real K2=1./k2;
real K=K1-K2;
int1d(Th2,gam)(K*(N.x*(dx(T2))+N.y*(dy(T2)));