[Phigo90]

Hi everyone,

I am trying to understand the equation system, which is solved by the InterCondensatingEvaporatingFoam.

First I want to understand the alphaEqn. The implemented header File ("alphaEqn.h) ist from the "interPhaseChangeFoam" (Path:$(FOAM_SOLVERS)/multiphase/interPhaseChangeFoam)).

However, first of all I try to understand the following part

  if (MULESCorr)
    {
        fvScalarMatrix alpha1Eqn
        (
            fv::EulerDdtScheme<scalar>(mesh).fvmDdt(alpha1)
          + fv::gaussConvectionScheme<scalar>
            (
                mesh,
                phi,
                upwind<scalar>(mesh, phi)
            ).fvmDiv(phi, alpha1)
          - fvm::Sp(divU, alpha1)
         ==
            fvm::Sp(vDotvmcAlphal, alpha1)
          + vDotcAlphal
        );

        alpha1Eqn.solve();

        Info<< "Phase-1 volume fraction = "
            << alpha1.weightedAverage(mesh.Vsc()).value()
            << "  Min(" << alpha1.name() << ") = " << min(alpha1).value()
            << "  Max(" << alpha1.name() << ") = " << max(alpha1).value()
            << endl;

        talphaPhi = alpha1Eqn.flux();
    }

Does anyone of you know a literature reference within which this part is explained or still better, the whole "alphaEqn.H" file?

If not, can anyone answer the following questions?:

1) Is there a difference between "fvmDdt" and "fvm::ddt". Ddt could be the material derivative (because of the capital "D"), but it does not make sense in this context.

2)The second and third part of the LHS of the alpha equation are:

+ fv::gaussConvectionScheme<scalar>
            (
                mesh,
                phi,
                upwind<scalar>(mesh, phi)
            ).fvmDiv(phi, alpha1)
          - fvm::Sp(divU, alpha1)

In my view, this lines corresponds to: div(v*alpha)-div(v)*alpha, whereby v is the velocity vector and alpha the phase fraction. With the product rule this term can be rewritten as v*grad(alpha). Is this correct? Can anyone explain this parts? In my view it should be div(v*alpha) without the third term on the RHS.

3) With the above-mentioned comments, the alphaEqn can be written in my view as:

d/dt(alpha)+v*grad(alpha)=V_cond(1-alpha)+V_vap*alpha (Note that d/dt is the partial derivation)

Do I understand this in the right manner?

Kind regards from Germany and thanks for your help!

[Phigo90]

I am still interested in solving this problem =)