Second-oder Crank-Nicolson implicit ddt using the current and previous time-step fields as well as the previous time-step ddt. More...

Inheritance diagram for CrankNicolsonDdtScheme< Type >:

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Collaboration diagram for CrankNicolsonDdtScheme< Type >:

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Data Structures
class	DDt0Field
	Class to store the ddt0 fields on the objectRegistry for use in the. More...

Public Types
typedef ddtScheme< Type >::fluxFieldType	fluxFieldType

Public Types inherited from ddtScheme< Type >
typedef GeometricField< typename flux< Type >::type, fvsPatchField, surfaceMesh >	fluxFieldType

Public Member Functions
	TypeName ("CrankNicolson")
	Runtime type information. More...

	CrankNicolsonDdtScheme (const fvMesh &mesh)
	Construct from mesh. More...

	CrankNicolsonDdtScheme (const fvMesh &mesh, Istream &is)
	Construct from mesh and Istream. More...

const fvMesh &	mesh () const
	Return mesh reference. More...

scalar	ocCoeff () const
	Return the off-centreing coefficient. More...

tmp< GeometricField< Type, fvPatchField, volMesh > >	fvcDdt (const dimensioned< Type > &)

tmp< GeometricField< Type, fvPatchField, volMesh > >	fvcDdt (const GeometricField< Type, fvPatchField, volMesh > &)

tmp< GeometricField< Type, fvPatchField, volMesh > >	fvcDdt (const dimensionedScalar &, const GeometricField< Type, fvPatchField, volMesh > &)

tmp< GeometricField< Type, fvPatchField, volMesh > >	fvcDdt (const volScalarField &, const GeometricField< Type, fvPatchField, volMesh > &)

tmp< GeometricField< Type, fvPatchField, volMesh > >	fvcDdt (const volScalarField &alpha, const volScalarField &rho, const GeometricField< Type, fvPatchField, volMesh > &psi)

tmp< fvMatrix< Type > >	fvmDdt (const GeometricField< Type, fvPatchField, volMesh > &)

tmp< fvMatrix< Type > >	fvmDdt (const dimensionedScalar &, const GeometricField< Type, fvPatchField, volMesh > &)

tmp< fvMatrix< Type > >	fvmDdt (const volScalarField &, const GeometricField< Type, fvPatchField, volMesh > &)

tmp< fvMatrix< Type > >	fvmDdt (const volScalarField &alpha, const volScalarField &rho, const GeometricField< Type, fvPatchField, volMesh > &psi)

tmp< fluxFieldType >	fvcDdtUfCorr (const GeometricField< Type, fvPatchField, volMesh > &U, const GeometricField< Type, fvsPatchField, surfaceMesh > &Uf)

tmp< fluxFieldType >	fvcDdtPhiCorr (const GeometricField< Type, fvPatchField, volMesh > &U, const fluxFieldType &phi)

tmp< fluxFieldType >	fvcDdtUfCorr (const volScalarField &rho, const GeometricField< Type, fvPatchField, volMesh > &U, const GeometricField< Type, fvsPatchField, surfaceMesh > &Uf)

tmp< fluxFieldType >	fvcDdtPhiCorr (const volScalarField &rho, const GeometricField< Type, fvPatchField, volMesh > &U, const fluxFieldType &phi)

tmp< surfaceScalarField >	meshPhi (const GeometricField< Type, fvPatchField, volMesh > &)

tmp< surfaceScalarField >	fvcDdtUfCorr (const GeometricField< scalar, fvPatchField, volMesh > &U, const GeometricField< scalar, fvsPatchField, surfaceMesh > &Uf)

tmp< surfaceScalarField >	fvcDdtPhiCorr (const volScalarField &U, const surfaceScalarField &phi)

tmp< surfaceScalarField >	fvcDdtUfCorr (const volScalarField &rho, const volScalarField &U, const surfaceScalarField &Uf)

tmp< surfaceScalarField >	fvcDdtPhiCorr (const volScalarField &rho, const volScalarField &U, const surfaceScalarField &phi)

Public Member Functions inherited from ddtScheme< Type >
virtual const word &	type () const =0
	Runtime type information. More...

	declareRunTimeSelectionTable (tmp, ddtScheme, Istream,(const fvMesh &mesh, Istream &schemeData),(mesh, schemeData))

	ddtScheme (const fvMesh &mesh)
	Construct from mesh. More...

	ddtScheme (const fvMesh &mesh, Istream &)
	Construct from mesh and Istream. More...

virtual	~ddtScheme ()
	Destructor. More...

const fvMesh &	mesh () const
	Return mesh reference. More...

tmp< surfaceScalarField >	fvcDdtPhiCoeff (const GeometricField< Type, fvPatchField, volMesh > &U, const fluxFieldType &phi, const fluxFieldType &phiCorr)

tmp< surfaceScalarField >	fvcDdtPhiCoeff (const GeometricField< Type, fvPatchField, volMesh > &U, const fluxFieldType &phi)

Public Member Functions inherited from refCount
	refCount ()
	Construct null with zero count. More...

int	count () const
	Return the reference count. More...

bool	okToDelete () const
	Return true if the reference count is zero. More...

void	resetRefCount ()
	Reset the reference count to zero. More...

void	operator++ ()
	Increment the reference count. More...

void	operator++ (int)
	Increment the reference count. More...

void	operator-- ()
	Decrement the reference count. More...

void	operator-- (int)
	Decrement the reference count. More...

Private Member Functions
	CrankNicolsonDdtScheme (const CrankNicolsonDdtScheme &)
	Disallow default bitwise copy construct. More...

void	operator= (const CrankNicolsonDdtScheme &)
	Disallow default bitwise assignment. More...

template<class GeoField >
DDt0Field< GeoField > &	ddt0_ (const word &name, const dimensionSet &dims)

template<class GeoField >
bool	evaluate (const DDt0Field< GeoField > &ddt0) const
	Check if the ddt0 needs to be evaluated for this time-step. More...

template<class GeoField >
scalar	coef_ (const DDt0Field< GeoField > &) const
	Return the coefficient for Euler scheme for the first time-step. More...

template<class GeoField >
scalar	coef0_ (const DDt0Field< GeoField > &) const
	Return the old time-step coefficient for Euler scheme for the. More...

template<class GeoField >
dimensionedScalar	rDtCoef_ (const DDt0Field< GeoField > &) const
	Return the reciprocal time-step coefficient for Euler for the. More...

template<class GeoField >
dimensionedScalar	rDtCoef0_ (const DDt0Field< GeoField > &) const
	Return the reciprocal old time-step coefficient for Euler for the. More...

template<class GeoField >
tmp< GeoField >	offCentre_ (const GeoField &ddt0) const
	Return ddt0 multiplied by the off-centreing coefficient. More...

Private Attributes
scalar	ocCoeff_
	Off-centering coefficient, 1 -> CN, less than one blends with EI. More...

Additional Inherited Members
Static Public Member Functions inherited from ddtScheme< Type >
static tmp< ddtScheme< Type > >	New (const fvMesh &mesh, Istream &schemeData)
	Return a pointer to a new ddtScheme created on freestore. More...

Protected Member Functions inherited from ddtScheme< Type >
	ddtScheme (const ddtScheme &)
	Disallow copy construct. More...

void	operator= (const ddtScheme &)
	Disallow default bitwise assignment. More...

Protected Attributes inherited from ddtScheme< Type >
const fvMesh &	mesh_

Detailed Description

template<class Type>
class Foam::fv::CrankNicolsonDdtScheme< Type >

Second-oder Crank-Nicolson implicit ddt using the current and previous time-step fields as well as the previous time-step ddt.

The Crank-Nicolson scheme is often unstable for complex flows in complex geometries and it is necessary to "off-centre" the scheme to stabilize it while retaining greater temporal accuracy than the first-order Euler-implicit scheme. Off-centering is specified via the mandatory coefficient in the range [0,1] following the scheme name e.g.

ddtSchemes
{
    default         CrankNicolson 0.9;
}

With a coefficient of 1 the scheme is fully centred and second-order, with a coefficient of 0 the scheme is equivalent to Euler-implicit. A coefficient of 0.9 has been found to be suitable for a range of cases for which higher-order accuracy in time is needed and provides similar accuracy and stability to the backward scheme. However, the backward scheme has been found to be more robust and provides formal second-order accuracy in time.

The advantage of the Crank-Nicolson scheme over backward is that only the new and old-time values are needed, the additional terms relating to the fluxes and sources are evaluated at the mid-point of the time-step which provides the opportunity to limit the fluxes in such a way as to ensure boundedness while maintaining greater accuracy in time compared to the Euler-implicit scheme. This approach is now used with MULES in the interFoam family of solvers. Boundedness cannot be guaranteed with the backward scheme.

Note

The Crank-Nicolson coefficient for the implicit part of the RHS is related to the off-centering coefficient by

    cnCoeff = 1.0/(1.0 + ocCoeff);

See also: Foam::Euler Foam::backward

Source files

Definition at line 94 of file CrankNicolsonDdtScheme.H.

Member Typedef Documentation

◆ fluxFieldType

typedef ddtScheme<Type>::fluxFieldType fluxFieldType

Definition at line 287 of file CrankNicolsonDdtScheme.H.

Constructor & Destructor Documentation

◆ CrankNicolsonDdtScheme() [1/3]

CrankNicolsonDdtScheme ( const CrankNicolsonDdtScheme< Type > & )

private

Disallow default bitwise copy construct.

◆ CrankNicolsonDdtScheme() [2/3]

CrankNicolsonDdtScheme ( const fvMesh & mesh )

inline

Construct from mesh.

Definition at line 196 of file CrankNicolsonDdtScheme.H.

◆ CrankNicolsonDdtScheme() [3/3]

CrankNicolsonDdtScheme	(	const fvMesh &	mesh,
		Istream &	is
	)

inline

Construct from mesh and Istream.

Definition at line 203 of file CrankNicolsonDdtScheme.H.

References Foam::exit(), Foam::FatalIOError, FatalIOErrorInFunction, and CrankNicolsonDdtScheme< Type >::ocCoeff_.

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Member Function Documentation

◆ operator=()

void operator= ( const CrankNicolsonDdtScheme< Type > & )

private

Disallow default bitwise assignment.

◆ ddt0_()

CrankNicolsonDdtScheme< Type >::DDt0Field< GeoField > & ddt0_	(	const word &	name,
		const dimensionSet &	dims
	)

private

Definition at line 106 of file CrankNicolsonDdtScheme.C.

References IOobject::AUTO_WRITE, Foam::dimTime, mesh, IOobject::MUST_READ, Foam::name(), IOobject::NO_READ, Time::startTime(), Time::startTimeIndex(), regIOobject::store(), TimeState::timeIndex(), timeName, Time::timeName(), and dimensioned::value().

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◆ evaluate()

bool evaluate ( const DDt0Field< GeoField > & ddt0 ) const

private

Check if the ddt0 needs to be evaluated for this time-step.

Definition at line 187 of file CrankNicolsonDdtScheme.C.

References mesh.

◆ coef_()

scalar coef_ ( const DDt0Field< GeoField > & ddt0 ) const

private

Return the coefficient for Euler scheme for the first time-step.

for and CN thereafter

Definition at line 197 of file CrankNicolsonDdtScheme.C.

References mesh, CrankNicolsonDdtScheme< Type >::DDt0Field< GeoField >::startTimeIndex(), and timeIndex.

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◆ coef0_()

scalar coef0_ ( const DDt0Field< GeoField > & ddt0 ) const

private

Return the old time-step coefficient for Euler scheme for the.

second time-step and for CN thereafter

Definition at line 215 of file CrankNicolsonDdtScheme.C.

References mesh, CrankNicolsonDdtScheme< Type >::DDt0Field< GeoField >::startTimeIndex(), and timeIndex.

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◆ rDtCoef_()

dimensionedScalar rDtCoef_ ( const DDt0Field< GeoField > & ddt0 ) const

private

Return the reciprocal time-step coefficient for Euler for the.

first time-step and CN thereafter

Definition at line 233 of file CrankNicolsonDdtScheme.C.

References mesh.

◆ rDtCoef0_()

dimensionedScalar rDtCoef0_ ( const DDt0Field< GeoField > & ddt0 ) const

private

Return the reciprocal old time-step coefficient for Euler for the.

second time-step and CN thereafter

Definition at line 244 of file CrankNicolsonDdtScheme.C.

References mesh.

◆ offCentre_()

tmp< GeoField > offCentre_ ( const GeoField & ddt0 ) const

private

Return ddt0 multiplied by the off-centreing coefficient.

Definition at line 255 of file CrankNicolsonDdtScheme.C.

◆ TypeName()

TypeName ( "CrankNicolson" )

Runtime type information.

◆ mesh()

const fvMesh& mesh ( ) const

inline

Return mesh reference.

Definition at line 223 of file CrankNicolsonDdtScheme.H.

References ddtScheme< Type >::mesh().

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◆ ocCoeff()

scalar ocCoeff ( ) const

inline

Return the off-centreing coefficient.

Definition at line 229 of file CrankNicolsonDdtScheme.H.

References CrankNicolsonDdtScheme< Type >::ocCoeff_.

◆ fvcDdt() [1/5]

tmp< GeometricField< Type, fvPatchField, volMesh > > fvcDdt ( const dimensioned< Type > & dt )

virtual

Implements ddtScheme< Type >.

Definition at line 285 of file CrankNicolsonDdtScheme.C.

References dimensioned::dimensions(), Foam::dimTime, mesh, dimensioned::name(), and timeName.

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◆ fvcDdt() [2/5]

tmp< GeometricField< Type, fvPatchField, volMesh > > fvcDdt ( const GeometricField< Type, fvPatchField, volMesh > & vf )

virtual

Implements ddtScheme< Type >.

Definition at line 347 of file CrankNicolsonDdtScheme.C.

References GeometricField::boundaryField(), dimensioned::dimensions(), Foam::fv::ff(), GeometricField::internalField(), mesh, GeometricField::oldTime(), timeName, and dimensioned::value().

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◆ fvcDdt() [3/5]

tmp< GeometricField< Type, fvPatchField, volMesh > > fvcDdt	(	const dimensionedScalar &	rho,
		const GeometricField< Type, fvPatchField, volMesh > &	vf
	)

virtual

Implements ddtScheme< Type >.

Definition at line 436 of file CrankNicolsonDdtScheme.C.

References GeometricField::boundaryField(), dimensioned::dimensions(), Foam::fv::ff(), GeometricField::internalField(), mesh, GeometricField::oldTime(), rho, timeName, and dimensioned::value().

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◆ fvcDdt() [4/5]

tmp< GeometricField< Type, fvPatchField, volMesh > > fvcDdt	(	const volScalarField &	rho,
		const GeometricField< Type, fvPatchField, volMesh > &	vf
	)

virtual

Implements ddtScheme< Type >.

Definition at line 526 of file CrankNicolsonDdtScheme.C.

References GeometricField::boundaryField(), dimensioned::dimensions(), Foam::fv::ff(), GeometricField::internalField(), mesh, GeometricField::oldTime(), rho, timeName, and dimensioned::value().

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◆ fvcDdt() [5/5]

tmp< GeometricField< Type, fvPatchField, volMesh > > fvcDdt	(	const volScalarField &	alpha,
		const volScalarField &	rho,
		const GeometricField< Type, fvPatchField, volMesh > &	psi
	)

virtual

Implements ddtScheme< Type >.

Definition at line 626 of file CrankNicolsonDdtScheme.C.

References Foam::constant::atomic::alpha, GeometricField::boundaryField(), dimensioned::dimensions(), Foam::fv::ff(), GeometricField::internalField(), mesh, dimensioned::name(), GeometricField::oldTime(), rho, timeName, and dimensioned::value().

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◆ fvmDdt() [1/4]

tmp< fvMatrix< Type > > fvmDdt ( const GeometricField< Type, fvPatchField, volMesh > & vf )

virtual

Implements ddtScheme< Type >.

Definition at line 756 of file CrankNicolsonDdtScheme.C.

References Foam::dimTime, Foam::dimVol, Foam::fv::ff(), mesh, GeometricField::oldTime(), and fvMatrix::source().

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◆ fvmDdt() [2/4]

tmp< fvMatrix< Type > > fvmDdt	(	const dimensionedScalar &	rho,
		const GeometricField< Type, fvPatchField, volMesh > &	vf
	)

virtual

Implements ddtScheme< Type >.

Definition at line 838 of file CrankNicolsonDdtScheme.C.

References Foam::dimTime, Foam::dimVol, Foam::fv::ff(), mesh, GeometricField::oldTime(), rho, and fvMatrix::source().

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◆ fvmDdt() [3/4]

tmp< fvMatrix< Type > > fvmDdt	(	const volScalarField &	rho,
		const GeometricField< Type, fvPatchField, volMesh > &	vf
	)

virtual

Implements ddtScheme< Type >.

Definition at line 920 of file CrankNicolsonDdtScheme.C.

References Foam::dimTime, Foam::dimVol, Foam::fv::ff(), mesh, GeometricField::oldTime(), rho, and fvMatrix::source().

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◆ fvmDdt() [4/4]

tmp< fvMatrix< Type > > fvmDdt	(	const volScalarField &	alpha,
		const volScalarField &	rho,
		const GeometricField< Type, fvPatchField, volMesh > &	psi
	)

virtual

Implements ddtScheme< Type >.

Definition at line 1010 of file CrankNicolsonDdtScheme.C.

References Foam::constant::atomic::alpha, dimensioned::dimensions(), Foam::dimTime, Foam::dimVol, Foam::fv::ff(), mesh, dimensioned::name(), GeometricField::oldTime(), rho, and fvMatrix::source().

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◆ fvcDdtUfCorr() [1/4]

tmp< typename CrankNicolsonDdtScheme< Type >::fluxFieldType > fvcDdtUfCorr	(	const GeometricField< Type, fvPatchField, volMesh > &	U,
		const GeometricField< Type, fvsPatchField, surfaceMesh > &	Uf
	)

virtual

Implements ddtScheme< Type >.

Definition at line 1121 of file CrankNicolsonDdtScheme.C.

References Foam::fvc::interpolate(), mesh, timeName, U, and Uf.

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◆ fvcDdtPhiCorr() [1/4]

tmp< typename CrankNicolsonDdtScheme< Type >::fluxFieldType > fvcDdtPhiCorr	(	const GeometricField< Type, fvPatchField, volMesh > &	U,
		const fluxFieldType &	phi
	)

virtual

Implements ddtScheme< Type >.

Definition at line 1182 of file CrankNicolsonDdtScheme.C.

References Foam::fvc::interpolate(), mesh, phi, timeName, and U.

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◆ fvcDdtUfCorr() [2/4]

tmp< typename CrankNicolsonDdtScheme< Type >::fluxFieldType > fvcDdtUfCorr	(	const volScalarField &	rho,
		const GeometricField< Type, fvPatchField, volMesh > &	U,
		const GeometricField< Type, fvsPatchField, surfaceMesh > &	Uf
	)

virtual

Implements ddtScheme< Type >.

Definition at line 1243 of file CrankNicolsonDdtScheme.C.

References Foam::abort(), Foam::fvc::ddtCorr(), Foam::dimVelocity, Foam::FatalError, FatalErrorInFunction, Foam::fvc::interpolate(), mesh, rho, timeName, U, and Uf.

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◆ fvcDdtPhiCorr() [2/4]

tmp< typename CrankNicolsonDdtScheme< Type >::fluxFieldType > fvcDdtPhiCorr	(	const volScalarField &	rho,
		const GeometricField< Type, fvPatchField, volMesh > &	U,
		const fluxFieldType &	phi
	)

virtual

Implements ddtScheme< Type >.

Definition at line 1338 of file CrankNicolsonDdtScheme.C.

References Foam::abort(), Foam::fvc::ddtCorr(), Foam::dimArea, Foam::dimVelocity, Foam::FatalError, FatalErrorInFunction, Foam::fvc::interpolate(), mesh, phi, rho, timeName, and U.

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◆ meshPhi()

tmp< surfaceScalarField > meshPhi ( const GeometricField< Type, fvPatchField, volMesh > & vf )

virtual

Implements ddtScheme< Type >.

Definition at line 1432 of file CrankNicolsonDdtScheme.C.

References Foam::dimVolume, mesh, Foam::name(), IOobject::NO_READ, IOobject::NO_WRITE, phi, and timeName.

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◆ fvcDdtUfCorr() [3/4]

tmp< surfaceScalarField > fvcDdtUfCorr	(	const GeometricField< scalar, fvPatchField, volMesh > &	U,
		const GeometricField< scalar, fvsPatchField, surfaceMesh > &	Uf
	)

◆ fvcDdtPhiCorr() [3/4]

tmp< surfaceScalarField > fvcDdtPhiCorr	(	const volScalarField &	U,
		const surfaceScalarField &	phi
	)

◆ fvcDdtUfCorr() [4/4]

tmp< surfaceScalarField > fvcDdtUfCorr	(	const volScalarField &	rho,
		const volScalarField &	U,
		const surfaceScalarField &	Uf
	)

◆ fvcDdtPhiCorr() [4/4]

tmp< surfaceScalarField > fvcDdtPhiCorr	(	const volScalarField &	rho,
		const volScalarField &	U,
		const surfaceScalarField &	phi
	)

Field Documentation

◆ ocCoeff_

scalar ocCoeff_

private

Off-centering coefficient, 1 -> CN, less than one blends with EI.

Definition at line 140 of file CrankNicolsonDdtScheme.H.

Referenced by CrankNicolsonDdtScheme< Type >::CrankNicolsonDdtScheme(), and CrankNicolsonDdtScheme< Type >::ocCoeff().

The documentation for this class was generated from the following files:

src/finiteVolume/finiteVolume/ddtSchemes/CrankNicolsonDdtScheme/CrankNicolsonDdtScheme.H
src/finiteVolume/finiteVolume/ddtSchemes/CrankNicolsonDdtScheme/CrankNicolsonDdtScheme.C

Data Structures

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class Type> class Foam::fv::CrankNicolsonDdtScheme< Type >

Member Typedef Documentation

◆ fluxFieldType

Constructor & Destructor Documentation

◆ CrankNicolsonDdtScheme() [1/3]

◆ CrankNicolsonDdtScheme() [2/3]

◆ CrankNicolsonDdtScheme() [3/3]

Member Function Documentation

◆ operator=()

◆ ddt0_()

◆ evaluate()

◆ coef_()

◆ coef0_()

◆ rDtCoef_()

◆ rDtCoef0_()

◆ offCentre_()

◆ TypeName()

◆ mesh()

◆ ocCoeff()

◆ fvcDdt() [1/5]

◆ fvcDdt() [2/5]

◆ fvcDdt() [3/5]

◆ fvcDdt() [4/5]

◆ fvcDdt() [5/5]

◆ fvmDdt() [1/4]

◆ fvmDdt() [2/4]

◆ fvmDdt() [3/4]

◆ fvmDdt() [4/4]

◆ fvcDdtUfCorr() [1/4]

◆ fvcDdtPhiCorr() [1/4]

◆ fvcDdtUfCorr() [2/4]

◆ fvcDdtPhiCorr() [2/4]

◆ meshPhi()

◆ fvcDdtUfCorr() [3/4]

◆ fvcDdtPhiCorr() [3/4]

◆ fvcDdtUfCorr() [4/4]

◆ fvcDdtPhiCorr() [4/4]

Field Documentation

◆ ocCoeff_

template<class Type>
class Foam::fv::CrankNicolsonDdtScheme< Type >