[babakflame]

Dear Fellows

I am trying to understand the idea behind the blockCoupledScalarTransportFoam.C available in Foam-extend 3.1 (and more recent versions).

This code is supposed to solve these two equations in a coupled manner:

 fvScalarMatrix TEqn
            (
                fvm::div(phi, T)
              - fvm::laplacian(DT, T)
             ==
                 alpha*Ts
              - fvm::Sp(alpha, T)
            );

            TEqn.relax();

            fvScalarMatrix TsEqn
            (
              - fvm::laplacian(DTs, Ts)
             ==
                 alpha*T
              - fvm::Sp(alpha, Ts)
            );

            TsEqn.relax();

i am able to follow the code up to here:

   //- Add off-diagonal terms and remove from block source
            forAll(d, i)
            {
                d[i](0, 1) = -alpha.value()*mesh.V()[i];
                d[i](1, 0) = -alpha.value()*mesh.V()[i];

                blockB[i][0] -= alpha.value()*blockX[i][1]*mesh.V()[i];
                blockB[i][1] -= alpha.value()*blockX[i][0]*mesh.V()[i];
            }

As far as I understand, d is the diagonal components of the matrix M from this line:

 Field<tensor2>& d = blockM.diag().asSquare();

what does

d[i] (0,1)

mean ?
I suppose that each element of d has four components and (0,1) and (1,0) are the off-diagonal of each element???? Since here, i goes from 0 to 1.

This part is some how, clear for me:

   blockB[i][0] -= alpha.value()*blockX[i][1]*mesh.V()[i];
   blockB[i][1] -= alpha.value()*blockX[i][0]*mesh.V()[i];

In "blockB" which is the matrix of knowns, "[i][0]" refers to first equation (T variable) which Ts from second equation (blockX[i][1]) is present on right hand side as a known parameter so above snippet describes .

But, would some body describe this part for me?

d[i](0, 1) = -alpha.value()*mesh.V()[i];
d[i](1, 0) = -alpha.value()*mesh.V()[i];

Is the way that I described these lines correct? Any suggestion is appreciated.