alphaEqn.H

1. Scheme Selection and Off-Centering

word alphaScheme("div(phi,alpha)");
word alpharScheme("div(phirb,alpha)");
 
tmp<fv::ddtScheme<scalar>> ddtAlpha
(
    fv::ddtScheme<scalar>::New
    (
        mesh,
        mesh.ddtScheme("ddt(alpha)")
    )
);

This section selects the numerical schemes for the convection terms and time derivative. It also sets up off-centering for the Crank-Nicolson scheme if used.

2. Interface Compression

surfaceScalarField phic(mixture.cAlpha()*mag(phi/mesh.magSf()));
 
if (icAlpha > 0)
{
    phic *= (1.0 - icAlpha);
    phic += (mixture.cAlpha()*icAlpha)*fvc::interpolate(mag(U));
}

This part calculates the interface compression term phic, which helps maintain a sharp interface between phases.

3. MULES (Multidimensional Universal Limiter with Explicit Solution) Correction

if (MULESCorr)
{
    fvScalarMatrix alpha1Eqn
    (
        // ... equation setup ...
    );
 
    alpha1Eqn.solve();
 
    // ... MULES correction ...
}

This section applies the MULES algorithm to ensure boundedness of the volume fraction.

4. Main Solution Loop

for (int aCorr=0; aCorr<nAlphaCorr; aCorr++)
{
    // ... calculate fluxes ...
 
    // ... solve alpha equation ...
 
    // ... update alpha2 and mixture properties ...
}

This loop iteratively solves the volume fraction equation, applying corrections and updating related properties.

5. Final Updates

if
(
    word(mesh.ddtScheme("ddt(rho,U)"))
 == fv::EulerDdtScheme<vector>::typeName
)
{
    rhoPhi = alphaPhi*(rho1 - rho2) + phiCN*rho2;
}
else
{
    // ... calculate end-of-time-step fluxes ...
}

This section finalizes the solution by updating mass fluxes based on the solved volume fraction.

The alphaEqn.H file is crucial for accurately tracking the interface between phases in multiphase simulations, ensuring mass conservation and maintaining a sharp interface.