[Rafael Jurado]

Hello everyone,

I would like to modify the IcoFoam solver to solve two MassTransport equation which are coupled like this:

1.- ∂C1/∂t + ∂Ui·C1/∂xj = D11 · ∂^2 C1/∂^2xj + D12 · ∂^2 C2/∂^2xj
2.- ∂C2/∂t + ∂Ui·C2/∂xj = D22 · ∂^2 C2/∂^2xj + D21 · ∂^2 C1/∂^2xj

I would like to do this time discretization:

(C1^(n+1) - C1^(n))/dt = 0.5*[DiffC1 + DiffC2]^(n+1)
+ 0.5*[DiffC1 + DiffC2]^(n)
+ 1.5*ConvC1^(n) - 0.5*ConvC1^(n-1)


(C2^(n+1) - C2^(n))/dt = 0.5*[DiffC2 + DiffC1]^(n+1)
+ 0.5*[DiffC2 + DiffC1]^(n)
+ 1.5*ConvC2^(n) - 0.5*ConvC2^(n-1)

So, I have tried this in OpenFOAM:

1.-
solve
(
fvm::ddt(C1)
+ 0.5*(fvm::div(phi, C1) + fvc::div(phi, C1))
- 0.5*(fvm::laplacian(D11, C1) + fvc::laplacian(D11, C1))
- 0.5*(fvm::laplacian(D12, C2) + fvc::laplacian(D12, C2))
);

2.-
solve
(
fvm::ddt(C2)
+ 0.5*(fvm::div(phi, C2) + fvc::div(phi, C2))
- 0.5*(fvm::laplacian(D22, C2) + fvc::laplacian(D22, C2))
- 0.5*(fvm::laplacian(D21, C1) + fvc::laplacian(D21, C1))
);

and I have putted this into a loop to iterate until C1 and C2 is converged.

The problem comes from the term [fvm::laplacian(D12, C2)] in the first equation and [fvm::laplacian(D21, C1)] in the second one. I think that this is because, you can not use an implicit term of a variable while solving the other one. Let say the term [fvm::laplacian(D12, C2)] (i.e. DiffC2^(n+1)) in the first equation.

So I have two question, the first one and the most important is:
1.- How can I managed to introduce the other Concentration explicitly in each equation in OpenFOAM?

And the second one is;

2.- How can I take the concentration variable of two previous timesteps for using an Adam-Bashforth time discretization in the convection terms, i.e. [-0.5*ConvCi^(n-1)]?

Thank you in advance...

Kind regards,

[Rafael Jurado]

Is there anyone who can help me??

Thank you in advance...