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...

	CrankNicolsonDdtScheme (const CrankNicolsonDdtScheme &)=delete
	Disallow default bitwise copy construction. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual tmp< scalarField >	meshPhi (const GeometricField< Type, fvPatchField, volMesh > &, const label patchi)

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

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

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...

	ddtScheme (const ddtScheme &)
	Disallow default bitwise copy construction. More...

virtual	~ddtScheme ()
	Destructor. More...

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

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

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

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

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

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

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

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 refCount
	refCount ()
	Construct null initialising 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 stabilise 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 110 of file CrankNicolsonDdtScheme.H.

Member Typedef Documentation

◆ fluxFieldType

typedef ddtScheme<Type>::fluxFieldType fluxFieldType

Definition at line 283 of file CrankNicolsonDdtScheme.H.

Constructor & Destructor Documentation

◆ CrankNicolsonDdtScheme() [1/3]

CrankNicolsonDdtScheme ( const fvMesh & mesh )

Construct from mesh.

Definition at line 281 of file CrankNicolsonDdtScheme.C.

References polyMesh::moving(), and fvMesh::V00().

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◆ CrankNicolsonDdtScheme() [2/3]

CrankNicolsonDdtScheme	(	const fvMesh &	mesh,
		Istream &	is
	)

Construct from mesh and Istream.

Definition at line 297 of file CrankNicolsonDdtScheme.C.

References dict, Foam::exit(), Foam::FatalIOError, FatalIOErrorInFunction, CrankNicolsonDdtScheme< Type >::fvcDdt(), token::isNumber(), Function1< Type >::New(), token::number(), CrankNicolsonDdtScheme< Type >::ocCoeff(), and Istream::putBack().

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◆ CrankNicolsonDdtScheme() [3/3]

CrankNicolsonDdtScheme ( const CrankNicolsonDdtScheme< Type > & )

delete

Disallow default bitwise copy construction.

Member Function Documentation

◆ TypeName()

TypeName ( "CrankNicolson" )

Runtime type information.

◆ mesh()

const fvMesh& mesh ( ) const

inline

Return mesh reference.

Definition at line 219 of file CrankNicolsonDdtScheme.H.

References ddtScheme< Type >::mesh().

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

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◆ ocCoeff()

scalar ocCoeff ( ) const

inline

Return the current off-centreing coefficient.

Definition at line 225 of file CrankNicolsonDdtScheme.H.

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

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

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◆ fvcDdt() [1/5]

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

virtual

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
	)

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() [1/3]

◆ CrankNicolsonDdtScheme() [2/3]

◆ CrankNicolsonDdtScheme() [3/3]

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() [1/2]

◆ meshPhi() [2/2]

◆ operator=()

◆ ddt0_()

◆ fvcDdtUfCorr() [3/4]

◆ fvcDdtPhiCorr() [3/4]

◆ fvcDdtUfCorr() [4/4]

◆ fvcDdtPhiCorr() [4/4]

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