foam-extend4.1-coherent-io/applications/solvers/combustion/PDRFoam/XiEqns

    // Calculate Xi according to the selected flame wrinkling model
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    // Calculate coefficients for Gulder's flame speed correlation
    // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    volScalarField up = uPrimeCoef*sqrt((2.0/3.0)*k);
    volScalarField epsilonPlus = pow(uPrimeCoef, 3)*epsilon;

    volScalarField tauEta = sqrt(mag(thermo->muu()/(rhou*epsilonPlus)));
    volScalarField Reta = up/
    (
        sqrt(epsilonPlus*tauEta)
      + dimensionedScalar("1e-8", up.dimensions(), 1e-8)
    );

    else if (XiModel == "algebraic")
    {
        // Simple algebraic model for Xi based on Gulders correlation
        // with a linear correction function to give a plausible profile for Xi
        // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        volScalarField GEta = GEtaCoef/tauEta;
        volScalarField XiEqEta = 1.0 + XiCoef*sqrt(up/(Su + SuMin))*Reta;

        volScalarField R =
            GEta*XiEqEta/(XiEqEta - 0.999) + GIn*XiIn/(XiIn - 0.999);

        volScalarField XiEqStar = R/(R - GEta - GIn);

        //- Calculate the unweighted b
        //volScalarField Rrho = thermo->rhou()/thermo->rhob();
        //volScalarField bbar = b/(b + (Rrho*(1.0 - b)));

        Xi == 1.0 + (1.0 + (2*XiShapeCoef)*(0.5 - b))*(XiEqStar - 1.0);
    }
    else if (XiModel == "transport")
    {
        // Calculate Xi transport coefficients based on Gulders correlation
        // and DNS data for the rate of generation
        // with a linear correction function to give a plausible profile for Xi
        // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        volScalarField GEta = GEtaCoef/tauEta;
        volScalarField XiEqEta = 1.0 + XiCoef*sqrt(up/(Su + SuMin))*Reta;

        volScalarField R =
            GEta*XiEqEta/(XiEqEta - 0.999) + GIn*XiIn/(XiIn - 0.999);

        volScalarField XiEqStar = R/(R - GEta - GIn);

        volScalarField XiEq =
            1.0 + (1.0 + (2*XiShapeCoef)*(0.5 - b))*(XiEqStar - 1.0);

        volScalarField G = R*(XiEq - 1.0)/XiEq;

    // Calculate Xi flux
    // ~~~~~~~~~~~~~~~~~
    surfaceScalarField phiXi =
        phiSt
      + (
          - fvc::interpolate(fvc::laplacian(Dbf, b)/mgb)*nf
          + fvc::interpolate(rho)*fvc::interpolate(Su*(1.0/Xi - Xi))*nf
        );


        // Solve for the flame wrinkling
        // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
        solve
        (
            betav*fvm::ddt(rho, Xi)
          + mvConvection->fvmDiv(phi, Xi)
          + fvm::div(phiXi, Xi, "div(phiXi,Xi)")
          - fvm::Sp(fvc::div(phiXi), Xi)
         ==
            betav*rho*R
          - fvm::Sp(betav*rho*(R - G), Xi)
        );


        // Correct boundedness of Xi
        // ~~~~~~~~~~~~~~~~~~~~~~~~~
        Xi.max(1.0);
        Xi = min(Xi, 2.0*XiEq);
        Info<< "max(Xi) = " << max(Xi).value() << endl;
        Info<< "max(XiEq) = " << max(XiEq).value() << endl;
    }
    else
    {
        FatalError
            << args.executable() << " : Unknown Xi model " << XiModel
            << abort(FatalError);
    }