Files
OpenFOAM-12/applications/solvers/multiphase/multiphaseEulerFoam/phaseSystems/phaseSystem/phaseSystem.C
Henry Weller da3f4cc92e fvModels, fvConstraints: Rational separation of fvOptions between physical modelling and numerical constraints
The new fvModels is a general interface to optional physical models in the
finite volume framework, providing sources to the governing conservation
equations, thus ensuring consistency and conservation.  This structure is used
not only for simple sources and forces but also provides a general run-time
selection interface for more complex models such as radiation and film, in the
future this will be extended to Lagrangian, reaction, combustion etc.  For such
complex models the 'correct()' function is provided to update the state of these
models at the beginning of the PIMPLE loop.

fvModels are specified in the optional constant/fvModels dictionary and
backward-compatibility with fvOption is provided by reading the
constant/fvOptions or system/fvOptions dictionary if present.

The new fvConstraints is a general interface to optional numerical constraints
applied to the matrices of the governing equations after construction and/or to
the resulting field after solution.  This system allows arbitrary changes to
either the matrix or solution to ensure numerical or other constraints and hence
violates consistency with the governing equations and conservation but it often
useful to ensure numerical stability, particularly during the initial start-up
period of a run.  Complex manipulations can be achieved with fvConstraints, for
example 'meanVelocityForce' used to maintain a specified mean velocity in a
cyclic channel by manipulating the momentum matrix and the velocity solution.

fvConstraints are specified in the optional system/fvConstraints dictionary and
backward-compatibility with fvOption is provided by reading the
constant/fvOptions or system/fvOptions dictionary if present.

The separation of fvOptions into fvModels and fvConstraints provides a rational
and consistent separation between physical and numerical models which is easier
to understand and reason about, avoids the confusing issue of location of the
controlling dictionary file, improves maintainability and easier to extend to
handle current and future requirements for optional complex physical models and
numerical constraints.
2021-03-07 22:45:01 +00:00

1012 lines
24 KiB
C++

/*---------------------------------------------------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Copyright (C) 2015-2021 OpenFOAM Foundation
\\/ M anipulation |
-------------------------------------------------------------------------------
License
This file is part of OpenFOAM.
OpenFOAM is free software: you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
\*---------------------------------------------------------------------------*/
#include "phaseSystem.H"
#include "surfaceTensionModel.H"
#include "aspectRatioModel.H"
#include "surfaceInterpolate.H"
#include "fvcDdt.H"
#include "localEulerDdtScheme.H"
#include "fvcDiv.H"
#include "fvcGrad.H"
#include "fvcSnGrad.H"
#include "CorrectPhi.H"
#include "fvcMeshPhi.H"
#include "alphaContactAngleFvPatchScalarField.H"
#include "unitConversion.H"
#include "dragModel.H"
#include "BlendedInterfacialModel.H"
#include "movingWallVelocityFvPatchVectorField.H"
#include "pimpleControl.H"
// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
namespace Foam
{
defineTypeNameAndDebug(phaseSystem, 0);
defineRunTimeSelectionTable(phaseSystem, dictionary);
}
const Foam::word Foam::phaseSystem::propertiesName("phaseProperties");
// * * * * * * * * * * * * Protected Member Functions * * * * * * * * * * * //
Foam::tmp<Foam::surfaceScalarField> Foam::phaseSystem::calcPhi
(
const phaseModelList& phaseModels
) const
{
tmp<surfaceScalarField> tmpPhi
(
surfaceScalarField::New
(
"phi",
fvc::interpolate(phaseModels[0])*phaseModels[0].phi()
)
);
for (label phasei=1; phasei<phaseModels.size(); phasei++)
{
tmpPhi.ref() +=
fvc::interpolate(phaseModels[phasei])*phaseModels[phasei].phi();
}
return tmpPhi;
}
void Foam::phaseSystem::generatePairs
(
const dictTable& modelDicts
)
{
forAllConstIter(dictTable, modelDicts, iter)
{
const phasePairKey& key = iter.key();
// pair already exists
if (phasePairs_.found(key))
{}
// new ordered pair
else if (key.ordered())
{
phasePairs_.insert
(
key,
autoPtr<phasePair>
(
new orderedPhasePair
(
phaseModels_[key.first()],
phaseModels_[key.second()]
)
)
);
}
// new unordered pair
else
{
phasePairs_.insert
(
key,
autoPtr<phasePair>
(
new phasePair
(
phaseModels_[key.first()],
phaseModels_[key.second()]
)
)
);
}
}
}
Foam::tmp<Foam::volScalarField> Foam::phaseSystem::sumAlphaMoving() const
{
tmp<volScalarField> sumAlphaMoving
(
volScalarField::New
(
"sumAlphaMoving",
movingPhaseModels_[0],
calculatedFvPatchScalarField::typeName
)
);
for
(
label movingPhasei=1;
movingPhasei<movingPhaseModels_.size();
movingPhasei++
)
{
sumAlphaMoving.ref() += movingPhaseModels_[movingPhasei];
}
return sumAlphaMoving;
}
void Foam::phaseSystem::setMixtureU(const volVectorField& Um0)
{
// Calculate the mean velocity difference with respect to Um0
// from the current velocity of the moving phases
volVectorField dUm(Um0);
forAll(movingPhaseModels_, movingPhasei)
{
dUm -=
movingPhaseModels_[movingPhasei]
*movingPhaseModels_[movingPhasei].U();
}
forAll(movingPhaseModels_, movingPhasei)
{
movingPhaseModels_[movingPhasei].URef() += dUm;
}
}
void Foam::phaseSystem::setMixturePhi
(
const PtrList<surfaceScalarField>& alphafs,
const surfaceScalarField& phim0
)
{
// Calculate the mean flux difference with respect to phim0
// from the current flux of the moving phases
surfaceScalarField dphim(phim0);
forAll(movingPhaseModels_, movingPhasei)
{
dphim -=
alphafs[movingPhaseModels_[movingPhasei].index()]
*movingPhaseModels_[movingPhasei].phi();
}
forAll(movingPhaseModels_, movingPhasei)
{
movingPhaseModels_[movingPhasei].phiRef() += dphim;
}
}
Foam::tmp<Foam::surfaceVectorField> Foam::phaseSystem::nHatfv
(
const volScalarField& alpha1,
const volScalarField& alpha2
) const
{
/*
// Cell gradient of alpha
volVectorField gradAlpha =
alpha2*fvc::grad(alpha1) - alpha1*fvc::grad(alpha2);
// Interpolated face-gradient of alpha
surfaceVectorField gradAlphaf = fvc::interpolate(gradAlpha);
*/
surfaceVectorField gradAlphaf
(
fvc::interpolate(alpha2)*fvc::interpolate(fvc::grad(alpha1))
- fvc::interpolate(alpha1)*fvc::interpolate(fvc::grad(alpha2))
);
// Face unit interface normal
return gradAlphaf/(mag(gradAlphaf) + deltaN_);
}
Foam::tmp<Foam::surfaceScalarField> Foam::phaseSystem::nHatf
(
const volScalarField& alpha1,
const volScalarField& alpha2
) const
{
// Face unit interface normal flux
return nHatfv(alpha1, alpha2) & mesh_.Sf();
}
void Foam::phaseSystem::correctContactAngle
(
const phaseModel& phase1,
const phaseModel& phase2,
surfaceVectorField::Boundary& nHatb
) const
{
const volScalarField::Boundary& gbf
= phase1.boundaryField();
const fvBoundaryMesh& boundary = mesh_.boundary();
forAll(boundary, patchi)
{
if (isA<alphaContactAngleFvPatchScalarField>(gbf[patchi]))
{
const alphaContactAngleFvPatchScalarField& acap =
refCast<const alphaContactAngleFvPatchScalarField>(gbf[patchi]);
vectorField& nHatPatch = nHatb[patchi];
vectorField AfHatPatch
(
mesh_.Sf().boundaryField()[patchi]
/mesh_.magSf().boundaryField()[patchi]
);
alphaContactAngleFvPatchScalarField::thetaPropsTable::
const_iterator tp =
acap.thetaProps()
.find(phasePairKey(phase1.name(), phase2.name()));
if (tp == acap.thetaProps().end())
{
FatalErrorInFunction
<< "Cannot find interface "
<< phasePairKey(phase1.name(), phase2.name())
<< "\n in table of theta properties for patch "
<< acap.patch().name()
<< exit(FatalError);
}
bool matched = (tp.key().first() == phase1.name());
scalar theta0 = degToRad(tp().theta0(matched));
scalarField theta(boundary[patchi].size(), theta0);
scalar uTheta = tp().uTheta();
// Calculate the dynamic contact angle if required
if (uTheta > small)
{
scalar thetaA = degToRad(tp().thetaA(matched));
scalar thetaR = degToRad(tp().thetaR(matched));
// Calculated the component of the velocity parallel to the wall
vectorField Uwall
(
phase1.U()().boundaryField()[patchi].patchInternalField()
- phase1.U()().boundaryField()[patchi]
);
Uwall -= (AfHatPatch & Uwall)*AfHatPatch;
// Find the direction of the interface parallel to the wall
vectorField nWall
(
nHatPatch - (AfHatPatch & nHatPatch)*AfHatPatch
);
// Normalise nWall
nWall /= (mag(nWall) + small);
// Calculate Uwall resolved normal to the interface parallel to
// the interface
scalarField uwall(nWall & Uwall);
theta += (thetaA - thetaR)*tanh(uwall/uTheta);
}
// Reset nHatPatch to correspond to the contact angle
scalarField a12(nHatPatch & AfHatPatch);
scalarField b1(cos(theta));
scalarField b2(nHatPatch.size());
forAll(b2, facei)
{
b2[facei] = cos(acos(a12[facei]) - theta[facei]);
}
scalarField det(1 - a12*a12);
scalarField a((b1 - a12*b2)/det);
scalarField b((b2 - a12*b1)/det);
nHatPatch = a*AfHatPatch + b*nHatPatch;
nHatPatch /= (mag(nHatPatch) + deltaN_.value());
}
}
}
Foam::tmp<Foam::volScalarField> Foam::phaseSystem::K
(
const phaseModel& phase1,
const phaseModel& phase2
) const
{
tmp<surfaceVectorField> tnHatfv = nHatfv(phase1, phase2);
correctContactAngle(phase1, phase2, tnHatfv.ref().boundaryFieldRef());
// Simple expression for curvature
return -fvc::div(tnHatfv & mesh_.Sf());
}
// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
Foam::phaseSystem::phaseSystem
(
const fvMesh& mesh
)
:
IOdictionary
(
IOobject
(
"phaseProperties",
mesh.time().constant(),
mesh,
IOobject::MUST_READ_IF_MODIFIED,
IOobject::NO_WRITE
)
),
mesh_(mesh),
referencePhaseName_(lookupOrDefault("referencePhase", word::null)),
phaseModels_
(
lookup("phases"),
phaseModel::iNew(*this, referencePhaseName_)
),
phi_(calcPhi(phaseModels_)),
dpdt_
(
IOobject
(
"dpdt",
mesh.time().timeName(),
mesh
),
mesh,
dimensionedScalar(dimPressure/dimTime, 0)
),
MRF_(mesh_),
cAlphas_(lookupOrDefault("interfaceCompression", cAlphaTable())),
deltaN_
(
"deltaN",
1e-8/pow(average(mesh_.V()), 1.0/3.0)
)
{
// Groupings
label movingPhasei = 0;
label stationaryPhasei = 0;
label anisothermalPhasei = 0;
label multiComponentPhasei = 0;
forAll(phaseModels_, phasei)
{
phaseModel& phase = phaseModels_[phasei];
movingPhasei += !phase.stationary();
stationaryPhasei += phase.stationary();
anisothermalPhasei += !phase.isothermal();
multiComponentPhasei += !phase.pure();
}
movingPhaseModels_.resize(movingPhasei);
stationaryPhaseModels_.resize(stationaryPhasei);
anisothermalPhaseModels_.resize(anisothermalPhasei);
multiComponentPhaseModels_.resize(multiComponentPhasei);
movingPhasei = 0;
stationaryPhasei = 0;
anisothermalPhasei = 0;
multiComponentPhasei = 0;
forAll(phaseModels_, phasei)
{
phaseModel& phase = phaseModels_[phasei];
if (!phase.stationary())
{
movingPhaseModels_.set(movingPhasei++, &phase);
}
if (phase.stationary())
{
stationaryPhaseModels_.set(stationaryPhasei++, &phase);
}
if (!phase.isothermal())
{
anisothermalPhaseModels_.set(anisothermalPhasei++, &phase);
}
if (!phase.pure())
{
multiComponentPhaseModels_.set(multiComponentPhasei++, &phase);
}
}
// Write phi
phi_.writeOpt() = IOobject::AUTO_WRITE;
// Blending methods
forAllConstIter(dictionary, subDict("blending"), iter)
{
blendingMethods_.insert
(
iter().keyword(),
blendingMethod::New
(
iter().keyword(),
iter().dict(),
phaseModels_.toc()
)
);
}
// Sub-models
generatePairsAndSubModels("surfaceTension", surfaceTensionModels_);
generatePairsAndSubModels("aspectRatio", aspectRatioModels_);
// Update motion fields
correctKinematics();
// Set the optional reference phase fraction from the other phases
if (referencePhaseName_ != word::null)
{
phaseModel* referencePhasePtr = &phases()[referencePhaseName_];
volScalarField& referenceAlpha = *referencePhasePtr;
referenceAlpha = 1;
forAll(phaseModels_, phasei)
{
if (&phaseModels_[phasei] != referencePhasePtr)
{
referenceAlpha -= phaseModels_[phasei];
}
}
}
forAll(phases(), phasei)
{
const volScalarField& alphai = phases()[phasei];
mesh_.setFluxRequired(alphai.name());
}
}
// * * * * * * * * * * * * * * * * Destructor * * * * * * * * * * * * * * * //
Foam::phaseSystem::~phaseSystem()
{}
// * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * * //
Foam::tmp<Foam::volScalarField> Foam::phaseSystem::rho() const
{
tmp<volScalarField> rho(movingPhaseModels_[0]*movingPhaseModels_[0].rho());
for
(
label movingPhasei=1;
movingPhasei<movingPhaseModels_.size();
movingPhasei++
)
{
rho.ref() +=
movingPhaseModels_[movingPhasei]
*movingPhaseModels_[movingPhasei].rho();
}
if (stationaryPhaseModels_.empty())
{
return rho;
}
else
{
return rho/sumAlphaMoving();
}
}
Foam::tmp<Foam::volVectorField> Foam::phaseSystem::U() const
{
tmp<volVectorField> U(movingPhaseModels_[0]*movingPhaseModels_[0].U());
for
(
label movingPhasei=1;
movingPhasei<movingPhaseModels_.size();
movingPhasei++
)
{
U.ref() +=
movingPhaseModels_[movingPhasei]
*movingPhaseModels_[movingPhasei].U();
}
if (stationaryPhaseModels_.empty())
{
return U;
}
else
{
return U/sumAlphaMoving();
}
}
Foam::tmp<Foam::volScalarField>
Foam::phaseSystem::E(const phasePairKey& key) const
{
if (aspectRatioModels_.found(key))
{
return aspectRatioModels_[key]->E();
}
else
{
return volScalarField::New
(
aspectRatioModel::typeName + ":E",
mesh_,
dimensionedScalar(dimless, 1)
);
}
}
Foam::tmp<Foam::volScalarField>
Foam::phaseSystem::sigma(const phasePairKey& key) const
{
if (surfaceTensionModels_.found(key))
{
return surfaceTensionModels_[key]->sigma();
}
else
{
return volScalarField::New
(
surfaceTensionModel::typeName + ":sigma",
mesh_,
dimensionedScalar(surfaceTensionModel::dimSigma, 0)
);
}
}
Foam::tmp<Foam::scalarField>
Foam::phaseSystem::sigma(const phasePairKey& key, label patchi) const
{
if (surfaceTensionModels_.found(key))
{
return surfaceTensionModels_[key]->sigma(patchi);
}
else
{
return tmp<scalarField>
(
new scalarField(mesh_.boundary()[patchi].size(), 0)
);
}
}
Foam::tmp<Foam::volScalarField>
Foam::phaseSystem::nearInterface() const
{
tmp<volScalarField> tnearInt
(
volScalarField::New
(
"nearInterface",
mesh_,
dimensionedScalar(dimless, 0)
)
);
forAll(phases(), phasei)
{
tnearInt.ref() = max
(
tnearInt(),
pos0(phases()[phasei] - 0.01)*pos0(0.99 - phases()[phasei])
);
}
return tnearInt;
}
Foam::tmp<Foam::volScalarField> Foam::phaseSystem::dmdtf
(
const phasePairKey& key
) const
{
const phasePair pair
(
phaseModels_[key.first()],
phaseModels_[key.second()]
);
return volScalarField::New
(
IOobject::groupName("dmdtf", pair.name()),
mesh(),
dimensionedScalar(dimDensity/dimTime, 0)
);
}
Foam::PtrList<Foam::volScalarField> Foam::phaseSystem::dmdts() const
{
return PtrList<volScalarField>(phaseModels_.size());
}
bool Foam::phaseSystem::incompressible() const
{
forAll(phaseModels_, phasei)
{
if (!phaseModels_[phasei].incompressible())
{
return false;
}
}
return true;
}
bool Foam::phaseSystem::implicitPhasePressure(const phaseModel& phase) const
{
return false;
}
bool Foam::phaseSystem::implicitPhasePressure() const
{
return false;
}
Foam::tmp<Foam::surfaceScalarField> Foam::phaseSystem::surfaceTension
(
const phaseModel& phase1
) const
{
tmp<surfaceScalarField> tSurfaceTension
(
surfaceScalarField::New
(
"surfaceTension",
mesh_,
dimensionedScalar(dimensionSet(1, -2, -2, 0, 0), 0)
)
);
forAll(phases(), phasej)
{
const phaseModel& phase2 = phases()[phasej];
if (&phase2 != &phase1)
{
phasePairKey key12(phase1.name(), phase2.name());
cAlphaTable::const_iterator cAlpha(cAlphas_.find(key12));
if (cAlpha != cAlphas_.end())
{
tSurfaceTension.ref() +=
fvc::interpolate(sigma(key12)*K(phase1, phase2))
*(
fvc::interpolate(phase2)*fvc::snGrad(phase1)
- fvc::interpolate(phase1)*fvc::snGrad(phase2)
);
}
}
}
return tSurfaceTension;
}
void Foam::phaseSystem::correct()
{
forAll(phaseModels_, phasei)
{
phaseModels_[phasei].correct();
}
}
void Foam::phaseSystem::correctContinuityError()
{
const PtrList<volScalarField> dmdts = this->dmdts();
forAll(movingPhaseModels_, movingPhasei)
{
phaseModel& phase = movingPhaseModels_[movingPhasei];
const volScalarField& alpha = phase;
volScalarField& rho = phase.thermoRef().rho();
volScalarField source
(
volScalarField::New
(
IOobject::groupName("source", phase.name()),
mesh_,
dimensionedScalar(dimDensity/dimTime, 0)
)
);
if (fvModels().addsSupToField(rho.name()))
{
source += fvModels().source(alpha, rho)&rho;
}
if (dmdts.set(phase.index()))
{
source += dmdts[phase.index()];
}
phase.correctContinuityError(source);
}
}
void Foam::phaseSystem::correctKinematics()
{
bool updateDpdt = false;
forAll(phaseModels_, phasei)
{
phaseModels_[phasei].correctKinematics();
updateDpdt = updateDpdt || phaseModels_[phasei].thermo().dpdt();
}
// Update the pressure time-derivative if required
if (updateDpdt)
{
dpdt_ = fvc::ddt(phaseModels_.begin()().thermo().p());
}
}
void Foam::phaseSystem::correctThermo()
{
forAll(phaseModels_, phasei)
{
phaseModels_[phasei].correctThermo();
}
}
void Foam::phaseSystem::correctReactions()
{
forAll(phaseModels_, phasei)
{
phaseModels_[phasei].correctReactions();
}
}
void Foam::phaseSystem::correctSpecies()
{
forAll(phaseModels_, phasei)
{
phaseModels_[phasei].correctSpecies();
}
}
void Foam::phaseSystem::correctTurbulence()
{
forAll(phaseModels_, phasei)
{
phaseModels_[phasei].correctTurbulence();
}
}
void Foam::phaseSystem::correctEnergyTransport()
{
forAll(phaseModels_, phasei)
{
phaseModels_[phasei].correctEnergyTransport();
}
}
void Foam::phaseSystem::meshUpdate()
{
if (mesh_.changing())
{
MRF_.update();
// forAll(phaseModels_, phasei)
// {
// phaseModels_[phasei].meshUpdate();
// }
}
}
void Foam::phaseSystem::correctBoundaryFlux()
{
forAll(movingPhases(), movingPhasei)
{
phaseModel& phase = movingPhases()[movingPhasei];
const volVectorField::Boundary& UBf = phase.U()().boundaryField();
FieldField<fvsPatchField, scalar> phiRelBf
(
MRF_.relative(mesh_.Sf().boundaryField() & UBf)
);
surfaceScalarField::Boundary& phiBf = phase.phiRef().boundaryFieldRef();
forAll(mesh_.boundary(), patchi)
{
if
(
isA<fixedValueFvsPatchScalarField>(phiBf[patchi])
&& !isA<movingWallVelocityFvPatchVectorField>(UBf[patchi])
)
{
phiBf[patchi] == phiRelBf[patchi];
}
}
}
}
void Foam::phaseSystem::correctPhi
(
const volScalarField& p_rgh,
const tmp<volScalarField>& divU,
nonOrthogonalSolutionControl& pimple
)
{
forAll(movingPhases(), movingPhasei)
{
phaseModel& phase = movingPhases()[movingPhasei];
volVectorField::Boundary& Ubf = phase.URef().boundaryFieldRef();
surfaceVectorField::Boundary& UfBf = phase.UfRef().boundaryFieldRef();
forAll(Ubf, patchi)
{
if (Ubf[patchi].fixesValue())
{
Ubf[patchi].initEvaluate();
}
}
forAll(Ubf, patchi)
{
if (Ubf[patchi].fixesValue())
{
Ubf[patchi].evaluate();
UfBf[patchi] = Ubf[patchi];
}
}
}
// Correct fixed-flux BCs to be consistent with the velocity BCs
correctBoundaryFlux();
{
phi_ = Zero;
PtrList<surfaceScalarField> alphafs(phaseModels_.size());
forAll(movingPhases(), movingPhasei)
{
phaseModel& phase = movingPhases()[movingPhasei];
const label phasei = phase.index();
const volScalarField& alpha = phase;
alphafs.set(phasei, fvc::interpolate(alpha).ptr());
// Calculate absolute flux
// from the mapped surface velocity
phi_ += alphafs[phasei]*(mesh_.Sf() & phase.Uf());
}
CorrectPhi
(
phi_,
movingPhases()[0].U(),
p_rgh,
// surfaceScalarField("rAUf", fvc::interpolate(rAU())),
dimensionedScalar(dimTime/dimDensity, 1),
divU(),
pimple
);
// Make the flux relative to the mesh motion
fvc::makeRelative(phi_, movingPhases()[0].U());
setMixturePhi(alphafs, phi_);
}
}
bool Foam::phaseSystem::read()
{
if (regIOobject::read())
{
bool readOK = true;
forAll(phaseModels_, phasei)
{
readOK &= phaseModels_[phasei].read();
}
// models ...
return readOK;
}
else
{
return false;
}
}
Foam::tmp<Foam::volScalarField> Foam::byDt(const volScalarField& vf)
{
if (fv::localEulerDdt::enabled(vf.mesh()))
{
return fv::localEulerDdt::localRDeltaT(vf.mesh())*vf;
}
else
{
return vf/vf.mesh().time().deltaT();
}
}
Foam::tmp<Foam::surfaceScalarField> Foam::byDt(const surfaceScalarField& sf)
{
if (fv::localEulerDdt::enabled(sf.mesh()))
{
return fv::localEulerDdt::localRDeltaTf(sf.mesh())*sf;
}
else
{
return sf/sf.mesh().time().deltaT();
}
}
// ************************************************************************* //