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")

	CrankNicolsonDdtScheme (const fvMesh &mesh)

	CrankNicolsonDdtScheme (const fvMesh &mesh, Istream &is)

const fvMesh &	mesh () const

scalar	ocCoeff () const

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

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

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

	ddtScheme (const fvMesh &mesh)

	ddtScheme (const fvMesh &mesh, Istream &is)

virtual	~ddtScheme ()=default

const fvMesh &	mesh () const

virtual tmp< GeometricField< Type, fvsPatchField, surfaceMesh > >	fvcDdt (const GeometricField< Type, fvsPatchField, surfaceMesh > &)

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

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

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

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

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

Public Member Functions inherited from refCount
constexpr	refCount () noexcept

int	count () const noexcept

bool	unique () const noexcept

void	operator++ () noexcept

void	operator++ (int) noexcept

void	operator-- () noexcept

void	operator-- (int) noexcept

Public Member Functions inherited from ddtSchemeBase
	ddtSchemeBase ()

	ddtSchemeBase ()

Additional Inherited Members
Static Public Member Functions inherited from ddtScheme< Type >
static tmp< ddtScheme< Type > >	New (const fvMesh &mesh, Istream &schemeData)

Static Public Attributes inherited from ddtSchemeBase
static bool	experimentalDdtCorr

Protected Member Functions inherited from ddtScheme< Type >
	ddtScheme (const ddtScheme &)=delete

void	operator= (const ddtScheme &)=delete

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

scalar	ddtPhiCoeff_

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 ocCoeff in the range [0,1] following the scheme name e.g.

ddtSchemes
{
    default         CrankNicolson 0.9;
}

or with an optional "ramp" function to transition from the Euler scheme to Crank-Nicolson over a initial period to avoid start-up problems, e.g.

ddtSchemes
{
    default         CrankNicolson
    ocCoeff
    {
        type scale;
        scale linearRamp;
        duration 0.01;
        value 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 112 of file CrankNicolsonDdtScheme.H.

Member Typedef Documentation

◆ fluxFieldType

typedef ddtScheme<Type>::fluxFieldType fluxFieldType

Definition at line 288 of file CrankNicolsonDdtScheme.H.

Constructor & Destructor Documentation

◆ CrankNicolsonDdtScheme() [1/2]

CrankNicolsonDdtScheme ( const fvMesh & mesh )

Definition at line 279 of file CrankNicolsonDdtScheme.C.

References CrankNicolsonDdtScheme< Type >::mesh(), polyMesh::moving(), and fvMesh::V00().

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◆ CrankNicolsonDdtScheme() [2/2]

CrankNicolsonDdtScheme	(	const fvMesh &	mesh,
		Istream &	is
	)

Definition at line 295 of file CrankNicolsonDdtScheme.C.

References dict, Foam::exit(), Foam::FatalIOError, FatalIOErrorInFunction, token::isNumber(), mesh, token::number(), ocCoeff, and Istream::putBack().

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Member Function Documentation

◆ TypeName()

TypeName ( "CrankNicolson" )

◆ mesh()

const fvMesh& mesh ( ) const

inline

Definition at line 224 of file CrankNicolsonDdtScheme.H.

References ddtScheme< Type >::mesh().

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

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◆ ocCoeff()

scalar ocCoeff ( ) const

inline

Definition at line 230 of file CrankNicolsonDdtScheme.H.

References CrankNicolsonDdtScheme< Type >::mesh().

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◆ fvcDdt() [1/5]

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

virtual

Implements ddtScheme< Type >.

Definition at line 341 of file CrankNicolsonDdtScheme.C.

References dimensioned::dimensions(), Foam::dimTime, Foam::stringOps::evaluate(), mesh, dimensioned::name(), tmp::ref(), timeName, and Foam::Zero.

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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 398 of file CrankNicolsonDdtScheme.C.

References GeometricField::boundaryField(), Foam::stringOps::evaluate(), Foam::fv::ff(), 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 485 of file CrankNicolsonDdtScheme.C.

References GeometricField::boundaryField(), dimensioned::dimensions(), Foam::stringOps::evaluate(), Foam::fv::ff(), mesh, GeometricField::oldTime(), GeometricField::primitiveField(), 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 575 of file CrankNicolsonDdtScheme.C.

References GeometricField::boundaryField(), dimensioned::dimensions(), Foam::stringOps::evaluate(), Foam::fv::ff(), mesh, GeometricField::oldTime(), GeometricField::primitiveField(), 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 675 of file CrankNicolsonDdtScheme.C.

References Foam::constant::atomic::alpha, GeometricField::boundaryField(), dimensioned::dimensions(), Foam::stringOps::evaluate(), Foam::fv::ff(), mesh, dimensioned::name(), GeometricField::oldTime(), GeometricField::primitiveField(), 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 805 of file CrankNicolsonDdtScheme.C.

References Foam::dimTime, Foam::dimVol, Foam::stringOps::evaluate(), 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 888 of file CrankNicolsonDdtScheme.C.

References Foam::dimTime, Foam::dimVol, Foam::stringOps::evaluate(), 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 970 of file CrankNicolsonDdtScheme.C.

References Foam::dimTime, Foam::dimVol, Foam::stringOps::evaluate(), 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 1060 of file CrankNicolsonDdtScheme.C.

References Foam::constant::atomic::alpha, dimensioned::dimensions(), Foam::dimTime, Foam::dimVol, Foam::stringOps::evaluate(), 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 1171 of file CrankNicolsonDdtScheme.C.

References Foam::stringOps::evaluate(), 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 1232 of file CrankNicolsonDdtScheme.C.

References Foam::fvc::dotInterpolate(), Foam::stringOps::evaluate(), 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 1295 of file CrankNicolsonDdtScheme.C.

References Foam::abort(), ddtCorr, Foam::dimVelocity, Foam::stringOps::evaluate(), 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 1452 of file CrankNicolsonDdtScheme.C.

References Foam::abort(), ddtCorr, Foam::dimArea, Foam::dimVelocity, Foam::fvc::dotInterpolate(), Foam::stringOps::evaluate(), Foam::FatalError, FatalErrorInFunction, 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 1597 of file CrankNicolsonDdtScheme.C.

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

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◆ ddt0_()

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

Definition at line 103 of file CrankNicolsonDdtScheme.C.

References IOobject::AUTO_WRITE, Foam::dimTime, mesh, IOobject::MUST_READ, Foam::name(), IOobject::NO_READ, runTime, regIOobject::store(), timeName, and Foam::Zero.

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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
	)

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

◆ fluxFieldType

Constructor & Destructor Documentation

◆ CrankNicolsonDdtScheme() [1/2]

◆ CrankNicolsonDdtScheme() [2/2]

Member Function Documentation

◆ 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()

◆ ddt0_()

◆ fvcDdtUfCorr() [3/4]

◆ fvcDdtPhiCorr() [3/4]

◆ fvcDdtUfCorr() [4/4]

◆ fvcDdtPhiCorr() [4/4]

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