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CrankNicolsonDdtScheme< Type > Class Template Reference

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

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Public Types

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

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 fvMeshmesh () 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< fluxFieldTypefvcDdtUfCorr (const GeometricField< Type, fvPatchField, volMesh > &U, const GeometricField< Type, fvsPatchField, surfaceMesh > &Uf)
 
tmp< fluxFieldTypefvcDdtPhiCorr (const GeometricField< Type, fvPatchField, volMesh > &U, const fluxFieldType &phi)
 
tmp< fluxFieldTypefvcDdtUfCorr (const volScalarField &rho, const GeometricField< Type, fvPatchField, volMesh > &U, const GeometricField< Type, fvsPatchField, surfaceMesh > &Uf)
 
tmp< fluxFieldTypefvcDdtPhiCorr (const volScalarField &rho, const GeometricField< Type, fvPatchField, volMesh > &U, const fluxFieldType &phi)
 
tmp< surfaceScalarFieldmeshPhi (const GeometricField< Type, fvPatchField, volMesh > &)
 
template<>
tmp< surfaceScalarFieldfvcDdtUfCorr (const GeometricField< scalar, fvPatchField, volMesh > &U, const GeometricField< scalar, fvsPatchField, surfaceMesh > &Uf)
 
template<>
tmp< surfaceScalarFieldfvcDdtPhiCorr (const volScalarField &U, const surfaceScalarField &phi)
 
template<>
tmp< surfaceScalarFieldfvcDdtUfCorr (const volScalarField &rho, const volScalarField &U, const surfaceScalarField &Uf)
 
template<>
tmp< surfaceScalarFieldfvcDdtPhiCorr (const volScalarField &rho, const volScalarField &U, const surfaceScalarField &phi)
 
- Public Member Functions inherited from ddtScheme< Type >
virtual const wordtype () 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 fvMeshmesh () const
 Return mesh reference. More...
 
tmp< surfaceScalarFieldfvcDdtPhiCoeff (const GeometricField< Type, fvPatchField, volMesh > &U, const fluxFieldType &phi, const fluxFieldType &phiCorr)
 
tmp< surfaceScalarFieldfvcDdtPhiCoeff (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...
 

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 fvMeshmesh_
 

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

Definition at line 288 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 FatalIOErrorIn.

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Member Function Documentation

TypeName ( "CrankNicolson"  )

Runtime type information.

const fvMesh& mesh ( ) const
inline

Return mesh reference.

Definition at line 224 of file CrankNicolsonDdtScheme.H.

References ddtScheme< Type >::mesh().

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scalar ocCoeff ( ) const
inline

Return the off-centreing coefficient.

Definition at line 230 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
tmp< GeometricField< Type, fvPatchField, volMesh > > fvcDdt ( const GeometricField< Type, fvPatchField, volMesh > &  vf)
virtual
tmp< GeometricField< Type, fvPatchField, volMesh > > fvcDdt ( const dimensionedScalar rho,
const GeometricField< Type, fvPatchField, volMesh > &  vf 
)
virtual
tmp< GeometricField< Type, fvPatchField, volMesh > > fvcDdt ( const volScalarField rho,
const GeometricField< Type, fvPatchField, volMesh > &  vf 
)
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 > &  vf)
virtual
tmp< fvMatrix< Type > > fvmDdt ( const dimensionedScalar rho,
const GeometricField< Type, fvPatchField, volMesh > &  vf 
)
virtual
tmp< fvMatrix< Type > > fvmDdt ( const volScalarField rho,
const GeometricField< Type, fvPatchField, volMesh > &  vf 
)
virtual
tmp< fvMatrix< Type > > fvmDdt ( const volScalarField alpha,
const volScalarField rho,
const GeometricField< Type, fvPatchField, volMesh > &  psi 
)
virtual
tmp< typename CrankNicolsonDdtScheme< Type >::fluxFieldType > fvcDdtUfCorr ( const GeometricField< Type, fvPatchField, volMesh > &  U,
const GeometricField< Type, fvsPatchField, surfaceMesh > &  Uf 
)
virtual
tmp< typename CrankNicolsonDdtScheme< Type >::fluxFieldType > fvcDdtPhiCorr ( const GeometricField< Type, fvPatchField, volMesh > &  U,
const fluxFieldType phi 
)
virtual
tmp< typename CrankNicolsonDdtScheme< Type >::fluxFieldType > fvcDdtUfCorr ( const volScalarField rho,
const GeometricField< Type, fvPatchField, volMesh > &  U,
const GeometricField< Type, fvsPatchField, surfaceMesh > &  Uf 
)
virtual
tmp< typename CrankNicolsonDdtScheme< Type >::fluxFieldType > fvcDdtPhiCorr ( const volScalarField rho,
const GeometricField< Type, fvPatchField, volMesh > &  U,
const fluxFieldType phi 
)
virtual
tmp< surfaceScalarField > meshPhi ( const GeometricField< Type, fvPatchField, volMesh > &  vf)
virtual

Implements ddtScheme< Type >.

Definition at line 1436 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: