volScalarField rAU(1.0/UEqn().A());
volScalarField rAtU(1.0/(1.0/rAU - UEqn().H1()));

volVectorField HbyA("HbyA", U);
HbyA = rAU*UEqn().H();

UEqn.clear();

bool closedVolume = false;

if (simple.transonic())
{
    surfaceScalarField phid
    (
        "phid",
        fvc::interpolate(psi)
       *(fvc::interpolate(HbyA) & mesh.Sf())
    );

    fvOptions.makeRelative(fvc::interpolate(psi), phid);

    surfaceScalarField phic
    (
        "phic",
        fvc::interpolate(rho*(rAtU - rAU))*fvc::snGrad(p)*mesh.magSf()
    );

    HbyA -= (rAU - rAtU)*fvc::grad(p);

    volScalarField rhorAtU("rhorAtU", rho*rAtU);

    while (simple.correctNonOrthogonal())
    {
        fvScalarMatrix pEqn
        (
            fvm::div(phid, p)
          + fvc::div(phic)
          - fvm::laplacian(rhorAtU, p)
         ==
            fvOptions(psi, p, rho.name())
        );

        // Relax the pressure equation to maintain diagonal dominance
        pEqn.relax();

        pEqn.setReference(pRefCell, pRefValue);

        pEqn.solve();

        if (simple.finalNonOrthogonalIter())
        {
            phi == phic + pEqn.flux();
        }
    }
}
else
{
    surfaceScalarField phiHbyA
    (
        "phiHbyA",
        fvc::interpolate(rho*HbyA) & mesh.Sf()
    );

    fvOptions.makeRelative(fvc::interpolate(rho), phiHbyA);

    closedVolume = adjustPhi(phiHbyA, U, p);

    phiHbyA += fvc::interpolate(rho*(rAtU - rAU))*fvc::snGrad(p)*mesh.magSf();
    HbyA -= (rAU - rAtU)*fvc::grad(p);

    volScalarField rhorAtU("rhorAtU", rho*rAtU);

    while (simple.correctNonOrthogonal())
    {
        fvScalarMatrix pEqn
        (
            fvc::div(phiHbyA)
          - fvm::laplacian(rhorAtU, p)
          ==
            fvOptions(psi, p, rho.name())
        );

        pEqn.setReference(pRefCell, pRefValue);

        pEqn.solve();

        if (simple.finalNonOrthogonalIter())
        {
            phi = phiHbyA + pEqn.flux();
        }
    }
}

// The incompressibe form of the continuity error check is appropriate for
// steady-state compressible also.
#include "incompressible/continuityErrs.H"

// Explicitly relax pressure for momentum corrector
p.relax();

U = HbyA - rAtU*fvc::grad(p);
U.correctBoundaryConditions();
fvOptions.correct(U);

// For closed-volume cases adjust the pressure and density levels
// to obey overall mass continuity
if (closedVolume)
{
    p += (initialMass - fvc::domainIntegrate(psi*p))
        /fvc::domainIntegrate(psi);
}

// Recalculate density from the relaxed pressure
rho = thermo.rho();
rho = max(rho, rhoMin);
rho = min(rho, rhoMax);

if (!simple.transonic())
{
    rho.relax();
}

Info<< "rho max/min : " << max(rho).value() << " " << min(rho).value() << endl;
