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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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 > &)

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

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

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

template<>
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
int	count () const
	Return the current reference count. More...

bool	unique () const
	Return true if the reference count is 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...

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 Member Functions inherited from refCount
	refCount ()
	Construct null initializing count to 0. 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

typedef ddtScheme<Type>::fluxFieldType fluxFieldType

Definition at line 287 of file CrankNicolsonDdtScheme.H.

Constructor & Destructor Documentation

CrankNicolsonDdtScheme ( const fvMesh & mesh )

inline

Construct from mesh.

Definition at line 196 of file CrankNicolsonDdtScheme.H.

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, and FatalIOErrorInFunction.

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Member Function Documentation

TypeName ( "CrankNicolson" )

Runtime type information.

const fvMesh& mesh ( ) const

inline

Return mesh reference.

Definition at line 223 of file CrankNicolsonDdtScheme.H.

References ddtScheme< Type >::mesh().

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scalar ocCoeff ( ) const

inline

Return the off-centreing coefficient.

Definition at line 229 of file CrankNicolsonDdtScheme.H.

References Foam::constant::atomic::alpha, CrankNicolsonDdtScheme< Type >::fvcDdt(), CrankNicolsonDdtScheme< Type >::fvmDdt(), psi, and rho.

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

virtual

Implements ddtScheme< Type >.

Definition at line 285 of file CrankNicolsonDdtScheme.C.

References dimensioned< Type >::dimensions(), Foam::dimTime, CoEulerDdtScheme< Type >::mesh(), dimensioned< Type >::name(), fvMesh::time(), Time::timeName(), fvMesh::V(), fvMesh::V0(), fvMesh::V00(), and Foam::Zero.

Referenced by Foam::fv::ff(), CrankNicolsonDdtScheme< Type >::fvcDdt(), and CrankNicolsonDdtScheme< Type >::ocCoeff().

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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< Type, PatchField, GeoMesh >::boundaryField(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::fv::ff(), CrankNicolsonDdtScheme< Type >::fvcDdt(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), fvMesh::time(), Time::timeName(), fvMesh::V(), fvMesh::V0(), and fvMesh::V00().

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

virtual

Implements ddtScheme< Type >.

Definition at line 434 of file CrankNicolsonDdtScheme.C.

References GeometricField< Type, PatchField, GeoMesh >::boundaryField(), dimensioned< Type >::dimensions(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::fv::ff(), CrankNicolsonDdtScheme< Type >::fvcDdt(), CoEulerDdtScheme< Type >::mesh(), dimensioned< Type >::name(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), GeometricField< Type, PatchField, GeoMesh >::primitiveField(), fvMesh::time(), Time::timeName(), fvMesh::V(), fvMesh::V0(), fvMesh::V00(), and dimensioned< Type >::value().

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

virtual

Implements ddtScheme< Type >.

Definition at line 524 of file CrankNicolsonDdtScheme.C.

References GeometricField< Type, PatchField, GeoMesh >::boundaryField(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::fv::ff(), CrankNicolsonDdtScheme< Type >::fvcDdt(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), GeometricField< Type, PatchField, GeoMesh >::primitiveField(), fvMesh::time(), Time::timeName(), fvMesh::V(), fvMesh::V0(), and fvMesh::V00().

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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 624 of file CrankNicolsonDdtScheme.C.

References GeometricField< Type, PatchField, GeoMesh >::boundaryField(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::fv::ff(), CrankNicolsonDdtScheme< Type >::fvmDdt(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), GeometricField< Type, PatchField, GeoMesh >::primitiveField(), fvMesh::time(), Time::timeName(), fvMesh::V(), fvMesh::V0(), and fvMesh::V00().

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

virtual

Implements ddtScheme< Type >.

Definition at line 754 of file CrankNicolsonDdtScheme.C.

References lduMatrix::diag(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::dimTime, Foam::dimVol, Foam::fv::ff(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), fvMatrix< Type >::source(), fvMesh::V(), fvMesh::V0(), and fvMesh::V00().

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

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

virtual

Implements ddtScheme< Type >.

Definition at line 836 of file CrankNicolsonDdtScheme.C.

References lduMatrix::diag(), dimensioned< Type >::dimensions(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::dimTime, Foam::dimVol, Foam::fv::ff(), CrankNicolsonDdtScheme< Type >::fvmDdt(), CoEulerDdtScheme< Type >::mesh(), dimensioned< Type >::name(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), fvMatrix< Type >::source(), fvMesh::V(), fvMesh::V0(), fvMesh::V00(), and dimensioned< Type >::value().

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

virtual

Implements ddtScheme< Type >.

Definition at line 918 of file CrankNicolsonDdtScheme.C.

References GeometricField< Type, PatchField, GeoMesh >::boundaryField(), lduMatrix::diag(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::dimTime, Foam::dimVol, Foam::fv::ff(), CrankNicolsonDdtScheme< Type >::fvmDdt(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), GeometricField< Type, PatchField, GeoMesh >::primitiveField(), fvMatrix< Type >::source(), fvMesh::V(), fvMesh::V0(), and fvMesh::V00().

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

virtual

Implements ddtScheme< Type >.

Definition at line 1008 of file CrankNicolsonDdtScheme.C.

References GeometricField< Type, PatchField, GeoMesh >::boundaryField(), lduMatrix::diag(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::dimTime, Foam::dimVol, Foam::fv::ff(), CrankNicolsonDdtScheme< Type >::fvcDdtUfCorr(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), GeometricField< Type, PatchField, GeoMesh >::primitiveField(), fvMatrix< Type >::source(), fvMesh::V(), fvMesh::V0(), and fvMesh::V00().

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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 1119 of file CrankNicolsonDdtScheme.C.

References DimensionedField< Type, GeoMesh >::dimensions(), ddtScheme< Type >::fvcDdtPhiCoeff(), CrankNicolsonDdtScheme< Type >::fvcDdtPhiCorr(), Foam::fvc::interpolate(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), fvMesh::Sf(), fvMesh::time(), and Time::timeName().

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

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

virtual

Implements ddtScheme< Type >.

Definition at line 1180 of file CrankNicolsonDdtScheme.C.

References DimensionedField< Type, GeoMesh >::dimensions(), Foam::fvc::dotInterpolate(), ddtScheme< Type >::fvcDdtPhiCoeff(), CrankNicolsonDdtScheme< Type >::fvcDdtUfCorr(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), fvMesh::Sf(), fvMesh::time(), and Time::timeName().

Referenced by CrankNicolsonDdtScheme< Type >::fvcDdtUfCorr().

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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 1242 of file CrankNicolsonDdtScheme.C.

References Foam::abort(), Foam::fvc::ddtCorr(), DimensionedField< Type, GeoMesh >::dimensions(), Foam::dimVelocity, Foam::FatalError, FatalErrorInFunction, ddtScheme< Type >::fvcDdtPhiCoeff(), CrankNicolsonDdtScheme< Type >::fvcDdtPhiCorr(), CoEulerDdtScheme< Type >::fvcDdtUfCorr(), Foam::fvc::interpolate(), CoEulerDdtScheme< Type >::mesh(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::null(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), fvMesh::Sf(), fvMesh::time(), and Time::timeName().

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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 1337 of file CrankNicolsonDdtScheme.C.

References Foam::abort(), Foam::fvc::ddtCorr(), Foam::dimArea, DimensionedField< Type, GeoMesh >::dimensions(), Foam::dimVelocity, Foam::fvc::dotInterpolate(), Foam::FatalError, FatalErrorInFunction, ddtScheme< Type >::fvcDdtPhiCoeff(), CoEulerDdtScheme< Type >::fvcDdtPhiCorr(), CoEulerDdtScheme< Type >::mesh(), CrankNicolsonDdtScheme< Type >::meshPhi(), IOobject::name(), GeometricField< Type, PatchField, GeoMesh >::null(), GeometricField< Type, PatchField, GeoMesh >::oldTime(), fvMesh::Sf(), fvMesh::time(), and Time::timeName().

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

virtual

Implements ddtScheme< Type >.

Definition at line 1432 of file CrankNicolsonDdtScheme.C.

References Foam::dimVolume, CoEulerDdtScheme< Type >::mesh(), Foam::name(), IOobject::NO_READ, IOobject::NO_WRITE, GeometricField< Type, PatchField, GeoMesh >::oldTime(), phi, fvMesh::phi(), and timeName.

Referenced by CrankNicolsonDdtScheme< Type >::fvcDdtPhiCorr().

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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
	)

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

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

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