Help setting up a two-component coupled system

[bknight1]

Hi team,

I'm trying to set up a two-component system as follows:

$$ \frac{\partial C_{\text{A}}}{\partial t} = \nabla \cdot \left( D_{\text{AA}} \nabla C_{\text{A}} + D_{\text{AB}} \nabla C_{\text{B}} \right) $$

$$ \frac{\partial C_{\text{B}}}{\partial t} = \nabla \cdot \left( D_{\text{BB}} \nabla C_{\text{B}} + D_{\text{BA}} \nabla C_{\text{A}} \right) $$

Similar to what is outlined in eq 2 here.

I have a sympy matrix for the flux (F1) and dC/dt (F0) terms, which are (2,2) and (2, 1) in shape, respectively.

@julesghub suggested using the Vector_Projection solver, but I can't modify the F1 term to reflect my flux term due to how F1 is constructed.

Are there any other solvers I can use? I can't use the Poisson solver as it expects scalar F0 and F1 terms.

Cheers