pEqn.H

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rho = thermo.rho();
rho.relax();

// Thermodynamic density needs to be updated by psi*d(p) after the
// pressure solution
const volScalarField psip0(psi*p);

const volScalarField rAU("rAU", 1.0/UEqn.A());
const surfaceScalarField rhorAUf("rhorAUf", fvc::interpolate(rho*rAU));

tmp<volScalarField> rAtU
(
    pimple.consistent()
  ? volScalarField::New("rAtU", 1.0/(1.0/rAU - UEqn.H1()))
  : tmp<volScalarField>(nullptr)
);
tmp<surfaceScalarField> rhorAtUf
(
    pimple.consistent()
  ? surfaceScalarField::New("rhoRAtUf", fvc::interpolate(rho*rAtU()))
  : tmp<surfaceScalarField>(nullptr)
);

const volScalarField& rAAtU = pimple.consistent() ? rAtU() : rAU;
const surfaceScalarField& rhorAAtUf =
    pimple.consistent() ? rhorAtUf() : rhorAUf;

volVectorField HbyA(constrainHbyA(rAU*UEqn.H(), U, p));

if (pimple.nCorrPiso() <= 1)
{
    tUEqn.clear();
}

surfaceScalarField phiHbyA
(
    "phiHbyA",
    fvc::interpolate(rho)*fvc::flux(HbyA)
  + MRF.zeroFilter(rhorAUf*fvc::ddtCorr(rho, U, phi, rhoUf))
);

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

// Update the pressure BCs to ensure flux consistency
constrainPressure(p, rho, U, phiHbyA, rhorAAtUf, MRF);

fvc::makeRelative(phiHbyA, rho, U);

bool adjustMass = false;

if (pimple.transonic())
{
    const surfaceScalarField phid
    (
        "phid",
        (fvc::interpolate(psi)/fvc::interpolate(rho))*phiHbyA
    );

    // Subtract the compressible part
    // The resulting flux will be zero for a perfect gas
    phiHbyA -= fvc::interpolate(psi*p)*phiHbyA/fvc::interpolate(rho);

    if (pimple.consistent())
    {
        phiHbyA += (rhorAAtUf - rhorAUf)*fvc::snGrad(p)*mesh.magSf();
        HbyA += (rAAtU - rAU)*fvc::grad(p);
    }

    fvScalarMatrix pDDtEqn
    (
        fvc::ddt(rho) + psi*correction(fvm::ddt(p))
      + fvc::div(phiHbyA) + fvm::div(phid, p)
     ==
        fvModels.source(psi, p, rho.name())
    );

    while (pimple.correctNonOrthogonal())
    {
        fvScalarMatrix pEqn(pDDtEqn - fvm::laplacian(rhorAAtUf, p));

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

        pEqn.setReference
        (
            pressureReference.refCell(),
            pressureReference.refValue()
        );

        pEqn.solve();

        if (pimple.finalNonOrthogonalIter())
        {
            phi = phiHbyA + pEqn.flux();
        }
    }
}
else
{
    if (mesh.schemes().steady())
    {
        adjustMass = adjustPhi(phiHbyA, U, p);
    }

    if (pimple.consistent())
    {
        phiHbyA += (rhorAAtUf - rhorAUf)*fvc::snGrad(p)*mesh.magSf();
        HbyA += (rAAtU - rAU)*fvc::grad(p);
    }

    fvScalarMatrix pDDtEqn
    (
        fvc::ddt(rho) + psi*correction(fvm::ddt(p))
      + fvc::div(phiHbyA)
     ==
        fvModels.source(psi, p, rho.name())
    );

    while (pimple.correctNonOrthogonal())
    {
        fvScalarMatrix pEqn(pDDtEqn - fvm::laplacian(rhorAAtUf, p));

        pEqn.setReference
        (
            pressureReference.refCell(),
            pressureReference.refValue()
        );

        pEqn.solve();

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

if (mesh.schemes().steady())
{
    #include "incompressible/continuityErrs.H"
}
else
{
    const bool constrained = fvConstraints.constrain(p);

    // Thermodynamic density update
    thermo.correctRho(psi*p - psip0);

    if (constrained)
    {
        rho = thermo.rho();
    }

    #include "rhoEqn.H"
    #include "compressibleContinuityErrs.H"
}

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

U = HbyA - rAAtU*fvc::grad(p);
U.correctBoundaryConditions();
fvConstraints.constrain(U);
K = 0.5*magSqr(U);

if (mesh.schemes().steady())
{
    fvConstraints.constrain(p);
}

// For steady compressible closed-volume cases adjust the pressure level
// to obey overall mass continuity
if (adjustMass && !thermo.incompressible())
{
    p += (initialMass - fvc::domainIntegrate(thermo.rho()))
        /fvc::domainIntegrate(psi);
    p.correctBoundaryConditions();
}

if (mesh.schemes().steady() || pimple.simpleRho() || adjustMass)
{
    rho = thermo.rho();
}

// Correct rhoUf if the mesh is moving
fvc::correctRhoUf(rhoUf, rho, U, phi, MRF);

if (mesh.schemes().steady() || pimple.simpleRho())
{
    rho.relax();
}

if (thermo.dpdt())
{
    dpdt = fvc::ddt(p);

    if (mesh.moving())
    {
        dpdt -= fvc::div(fvc::meshPhi(rho, U), p);
    }
}