Implementation of a verification MMS case for the Soret Effect

[rekomodo]

Resolves #19 .

[rekomodo]

I modified the exact solution, and the error is uncomfortably large. You might want to see the graph for this one.

[RemDelaporteMathurin]

Indeed it seems like the computed and exact solutions don't agree very well. I noticed that the equation you have written isn't the same as in the code.

You wrote (note the + sign in front of the first term):

$$ S = D\nabla \cdot \left(\frac{Q^* c_\mathrm{exact}}{R_g T^2} \ \nabla{T} \right) -12 D $$

and in the FESTIM model:

https://github.com/festim-dev/V-V-report/blob/9de4d62d12ac16f14ecb9b3a11991e02a43403dd/report/verification/mms/soret.md?plain=1#L124-L128

[rekomodo]

Indeed it seems like the computed and exact solutions don't agree very well. I noticed that the equation you have written isn't the same as in the code.

You wrote (note the + sign in front of the first term):

S=D∇⋅(Q∗cexactRgT2 ∇T)−12D

and in the FESTIM model:

https://github.com/festim-dev/V-V-report/blob/9de4d62d12ac16f14ecb9b3a11991e02a43403dd/report/verification/mms/soret.md?plain=1#L124-L128

I didn't notice this but the model is correct sign-wise. I'll keep looking.