Leaf of the binary tree. The chemPoint stores the composition 'phi', the mapping of this composition Rphi, the mapping gradient matrix A and the matrix describing the Ellipsoid Of Accuracy (EOA). More...

Public Member Functions
	chemPointISAT (TDACChemistryModel< CompType, ThermoType > &chemistry, const scalarField &phi, const scalarField &Rphi, const scalarSquareMatrix &A, const scalarField &scaleFactor, const scalar &tolerance, const label &completeSpaceSize, const dictionary &coeffsDict, binaryNode< CompType, ThermoType > *node=nullptr)

	chemPointISAT (const chemPointISAT< CompType, ThermoType > &p, binaryNode< CompType, ThermoType > *node)

	chemPointISAT (chemPointISAT< CompType, ThermoType > &p)

TDACChemistryModel< CompType, ThermoType > &	chemistry ()

label	nGrowth ()

label &	completeSpaceSize ()

const scalarField &	phi () const

const scalarField &	Rphi () const

const scalarField &	scaleFactor ()

const scalar &	tolerance ()

binaryNode< CompType, ThermoType > *&	node ()

const scalarSquareMatrix &	A () const

scalarSquareMatrix &	A ()

const scalarSquareMatrix &	LT () const

scalarSquareMatrix &	LT ()

label	nActiveSpecies ()

List< label > &	completeToSimplifiedIndex ()

List< label > &	simplifiedToCompleteIndex ()

void	increaseNumRetrieve ()

void	resetNumRetrieve ()

void	increaseNLifeTime ()

label	simplifiedToCompleteIndex (const label i)

const label &	timeTag ()

label &	lastTimeUsed ()

bool &	toRemove ()

label &	maxNumNewDim ()

const label &	numRetrieve ()

const label &	nLifeTime ()

bool	variableTimeStep () const

bool	inEOA (const scalarField &phiq)

bool	grow (const scalarField &phiq)

bool	checkSolution (const scalarField &phiq, const scalarField &Rphiq)

Static Public Member Functions
static void	changeTolerance (scalar newTol)

Detailed Description

template<class CompType, class ThermoType>
class Foam::chemPointISAT< CompType, ThermoType >

Leaf of the binary tree. The chemPoint stores the composition 'phi', the mapping of this composition Rphi, the mapping gradient matrix A and the matrix describing the Ellipsoid Of Accuracy (EOA).

1)When the chemPoint is created the region of accuracy is approximated by an ellipsoid E centered in 'phi' (obtained with the constant): E = {x| ||L^T.(x-phi)|| <= 1}, with x a point in the composition space and L^T the transpose of an upper triangular matrix describing the EOA (see below: "Computation of L" ).

2)To RETRIEVE the mapping from the chemPoint phi, the query point phiq has to be in the EOA of phi. It follows that, dphi=phiq-phi and to test if phiq is in the ellipsoid there are two methods. First, compare r=||dphi|| with rmin and rmax. If r < rmin, phiq is in the EOA. If r > rmax, phiq is out of the EOA. This operations is O(completeSpaceSize) and is performed first. If rmin < r < rmax, then the second method is used: ||L^T.dphi|| <= 1 to be in the EOA.

If phiq is in the EOA, Rphiq is obtained by linear interpolation: Rphiq= Rphi + A.dphi.

3)If phiq is not in the EOA, then the mapping is computed. But as the EOA is a conservative approximation of the region of accuracy surrounding the point phi, we could expand it by comparing the computed results with the one obtained by linear interpolation. The error epsGrow is calculated: epsGrow = ||B.(dR - dRl)||, with dR = Rphiq - Rphi, dRl = A.dphi and B the diagonal scale factor matrix. If epsGrow <= tolerance, the EOA is too conservative and a GROW is perforned otherwise, the newly computed mapping is associated to the initial composition and added to the tree.

4)To GROW the EOA, we expand it to include the previous EOA and the query point phiq. The rank-one matrix method is used. The EOA is transformed to a hypersphere centered at the origin. Then it is expanded to include the transformed point phiq' on its boundary. Then the inverse transformation give the modified matrix L' (see below: "Grow the EOA").

Computation of L : In [1], the EOA of the constant approximation is given by E = {x| ||B.A/tolerance.(x-phi)|| <= 1}, with B a scale factor diagonal matrix, A the mapping gradient matrix and tolerance the absolute tolerance. If we take the QR decomposition of (B.A)/tolerance= Q.R, with Q an orthogonal matrix and R an upper triangular matrix such that the EOA is described by (phiq-phi0)^T.R^T.R.(phiq-phi0) <= 1 L^T = R, both Cholesky decomposition of A^T.B^T.B.A/tolerance^2 This representation of the ellipsoid is used in [2] and in order to avoid large value of semi-axe length in certain direction, a Singular Value Decomposition (SVD) is performed on the L matrix: L = UDV^T, with the orthogonal matrix U giving the directions of the principal axes and 1/di the inverse of the element of the diagonal matrix D giving the length of the principal semi-axes. To avoid very large value of those length, di' = max(di, 1/(alphaEOA*sqrt(tolerance))), with alphaEOA = 0.1 (see [2]) di' = max(di, 1/2), see [1]. The latter will be used in this implementation. And L' = UD'V^T, with D' the diagonal matrix with the modified di'.

Grow the EOA : More details about the minimum-volume ellipsoid covering an ellispoid E and a point p are found in [3]. Here is the main steps to obtain the modified matrix L' describing the new ellipsoid. 1) calculate the point p' in the transformed space : p' = L^T.(p-phi) 2) compute the rank-one decomposition: G = I + gamma.p'.p'^T, with gamma = (1/|p'|-1)*1/|p'|^2 3) compute L': L' = L.G.

References:

    [1] Pope, S. B. (1997).
    Computationally efficient implementation of combustion chemistry using
    in situ adaptive tabulation.
    Combustion Theory and Modelling, 1, 41-63.

    [2] Lu, L., & Pope, S. B. (2009).
    An improved algorithm for in situ adaptive tabulation.
    Journal of Computational Physics, 228(2), 361-386.

    [3] Pope, S. B. (2008).
    Algorithms for ellipsoids.
    Cornell University Report No. FDA, 08-01.

Definition at line 136 of file chemPointISAT.H.

Constructor & Destructor Documentation

◆ chemPointISAT() [1/3]

chemPointISAT	(	TDACChemistryModel< CompType, ThermoType > &	chemistry,
		const scalarField &	phi,
		const scalarField &	Rphi,
		const scalarSquareMatrix &	A,
		const scalarField &	scaleFactor,
		const scalar &	tolerance,
		const label &	completeSpaceSize,
		const dictionary &	coeffsDict,
		binaryNode< CompType, ThermoType > *	node = `nullptr`
	)

Definition at line 199 of file chemPointISAT.C.

References A, chemistry, D, Foam::max(), Foam::multiply(), SVD::S(), Matrix::T(), SVD::U(), and SVD::V().

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◆ chemPointISAT() [2/3]

chemPointISAT	(	const chemPointISAT< CompType, ThermoType > &	p,
		binaryNode< CompType, ThermoType > *	node
	)

◆ chemPointISAT() [3/3]

chemPointISAT ( Foam::chemPointISAT< CompType, ThermoType > & p )

Definition at line 318 of file chemPointISAT.C.

References p.

Member Function Documentation

◆ chemistry()

TDACChemistryModel<CompType, ThermoType>& chemistry ( )

inline

Definition at line 271 of file chemPointISAT.H.

Referenced by binaryNode< CompType, ThermoType >::calcV().

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◆ nGrowth()

label nGrowth ( )

inline

Definition at line 276 of file chemPointISAT.H.

◆ completeSpaceSize()

label& completeSpaceSize ( )

inline

Definition at line 281 of file chemPointISAT.H.

Referenced by binaryNode< CompType, ThermoType >::calcV().

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◆ phi()

const scalarField& phi ( ) const

inline

Definition at line 286 of file chemPointISAT.H.

Referenced by binaryNode< CompType, ThermoType >::calcA(), and binaryNode< CompType, ThermoType >::calcV().

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◆ Rphi()

const scalarField& Rphi ( ) const

inline

Definition at line 291 of file chemPointISAT.H.

◆ scaleFactor()

const scalarField& scaleFactor ( )

inline

Definition at line 296 of file chemPointISAT.H.

Referenced by binaryNode< CompType, ThermoType >::calcV().

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◆ tolerance()

const scalar& tolerance ( )

inline

Definition at line 301 of file chemPointISAT.H.

Referenced by binaryNode< CompType, ThermoType >::calcV().

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◆ changeTolerance()

static void changeTolerance ( scalar newTol )

inlinestatic

Definition at line 306 of file chemPointISAT.H.

◆ node()

binaryNode<CompType, ThermoType>*& node ( )

inline

Definition at line 311 of file chemPointISAT.H.

Referenced by binaryTree< CompType, ThermoType >::deleteLeaf(), and binaryTree< CompType, ThermoType >::insertNewLeaf().

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◆ A() [1/2]

const scalarSquareMatrix& A ( ) const

inline

Definition at line 316 of file chemPointISAT.H.

◆ A() [2/2]

scalarSquareMatrix& A ( )

inline

Definition at line 321 of file chemPointISAT.H.

◆ LT() [1/2]

const scalarSquareMatrix& LT ( ) const

inline

Definition at line 326 of file chemPointISAT.H.

Referenced by binaryNode< CompType, ThermoType >::calcV().

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◆ LT() [2/2]

scalarSquareMatrix& LT ( )

inline

Definition at line 331 of file chemPointISAT.H.

◆ nActiveSpecies()

label nActiveSpecies ( )

inline

Definition at line 336 of file chemPointISAT.H.

Referenced by binaryNode< CompType, ThermoType >::calcV().

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◆ completeToSimplifiedIndex()

List<label>& completeToSimplifiedIndex ( )

inline

Definition at line 341 of file chemPointISAT.H.

Referenced by binaryNode< CompType, ThermoType >::calcV().

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◆ simplifiedToCompleteIndex() [1/2]

List<label>& simplifiedToCompleteIndex ( )

inline

Definition at line 346 of file chemPointISAT.H.

◆ increaseNumRetrieve()

void increaseNumRetrieve

Definition at line 785 of file chemPointISAT.C.

◆ resetNumRetrieve()

void resetNumRetrieve

Definition at line 792 of file chemPointISAT.C.

Referenced by binaryTree< CompType, ThermoType >::resetNumRetrieve().

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◆ increaseNLifeTime()

void increaseNLifeTime

Definition at line 799 of file chemPointISAT.C.

◆ simplifiedToCompleteIndex() [2/2]

Foam::label simplifiedToCompleteIndex ( const label i )

Definition at line 808 of file chemPointISAT.C.

◆ timeTag()

const label& timeTag ( )

inline

Definition at line 362 of file chemPointISAT.H.

◆ lastTimeUsed()

label& lastTimeUsed ( )

inline

Definition at line 367 of file chemPointISAT.H.

◆ toRemove()

bool& toRemove ( )

inline

Definition at line 372 of file chemPointISAT.H.

◆ maxNumNewDim()

label& maxNumNewDim ( )

inline

Definition at line 377 of file chemPointISAT.H.

◆ numRetrieve()

const label& numRetrieve ( )

inline

Definition at line 382 of file chemPointISAT.H.

◆ nLifeTime()

const label& nLifeTime ( )

inline

Definition at line 387 of file chemPointISAT.H.

◆ variableTimeStep()

bool variableTimeStep ( ) const

inline

Definition at line 392 of file chemPointISAT.H.

References TDACChemistryModel::variableTimeStep().

Referenced by binaryNode< CompType, ThermoType >::binaryNode().

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◆ inEOA()

bool inEOA ( const scalarField & phiq )

Definition at line 363 of file chemPointISAT.C.

References Foam::endl(), Foam::Info, Foam::max(), Foam::nl, phi, Foam::sqr(), Foam::sqrt(), and Foam::Zero.

Referenced by binaryTree< CompType, ThermoType >::secondaryBTSearch().

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◆ grow()

bool grow ( const scalarField & phiq )

Definition at line 599 of file chemPointISAT.C.

References DynamicList::append(), forAll, gamma, phi, DynamicList::setSize(), Foam::sqr(), Foam::sqrt(), and Foam::Zero.

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◆ checkSolution()

bool checkSolution	(	const scalarField &	phiq,
		const scalarField &	Rphiq
	)

Definition at line 528 of file chemPointISAT.C.

References A, phi, Foam::sqr(), and Foam::sqrt().

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

src/thermophysicalModels/chemistryModel/chemistryModel/TDACChemistryModel/tabulation/ISAT/chemPointISAT/chemPointISAT.H
src/thermophysicalModels/chemistryModel/chemistryModel/TDACChemistryModel/tabulation/ISAT/chemPointISAT/chemPointISAT.C

Public Member Functions

Static Public Member Functions

Detailed Description

template<class CompType, class ThermoType> class Foam::chemPointISAT< CompType, ThermoType >

Constructor & Destructor Documentation

◆ chemPointISAT() [1/3]

◆ chemPointISAT() [2/3]

◆ chemPointISAT() [3/3]

Member Function Documentation

◆ chemistry()

◆ nGrowth()

◆ completeSpaceSize()

◆ phi()

◆ Rphi()

◆ scaleFactor()

◆ tolerance()

◆ changeTolerance()

◆ node()

◆ A() [1/2]

◆ A() [2/2]

◆ LT() [1/2]

◆ LT() [2/2]

◆ nActiveSpecies()

◆ completeToSimplifiedIndex()

◆ simplifiedToCompleteIndex() [1/2]

◆ increaseNumRetrieve()

◆ resetNumRetrieve()

◆ increaseNLifeTime()

◆ simplifiedToCompleteIndex() [2/2]

◆ timeTag()

◆ lastTimeUsed()

◆ toRemove()

◆ maxNumNewDim()

◆ numRetrieve()

◆ nLifeTime()

◆ variableTimeStep()

◆ inEOA()

◆ grow()

◆ checkSolution()

template<class CompType, class ThermoType>
class Foam::chemPointISAT< CompType, ThermoType >