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)
	Construct from components. More...

	chemPointISAT (const chemPointISAT< CompType, ThermoType > &p, binaryNode< CompType, ThermoType > *node)
	Construct from another chemPoint and reference to a binary node. More...

	chemPointISAT (chemPointISAT< CompType, ThermoType > &p)
	Construct from another chemPoint. More...

TDACChemistryModel< CompType, ThermoType > &	chemistry ()
	Access to the TDACChemistryModel. More...

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 ()
	Increases the number of retrieves the chempoint has generated. More...

void	resetNumRetrieve ()
	Resets the number of retrieves at each time step. More...

void	increaseNLifeTime ()
	Increases the "counter" of the chP life. More...

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)
	To RETRIEVE the mapping from the stored chemPoint phi, the query. More...

bool	grow (const scalarField &phiq)
	More details about the minimum-volume ellipsoid covering an. More...

bool	checkSolution (const scalarField &phiq, const scalarField &Rphiq)
	If phiq is not in the EOA, then the mapping is computed. More...

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' describind 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 140 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`
	)

Construct from components.

Definition at line 201 of file chemPointISAT.C.

References TDACChemistryModel< ReactionThermo, ThermoType >::completeToSimplifiedIndex(), Foam::max(), Foam::multiply(), SVD::S(), TDACChemistryModel< ReactionThermo, ThermoType >::simplifiedToCompleteIndex(), Matrix< Form, Type >::T(), SVD::U(), and SVD::V().

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◆ chemPointISAT() [2/3]

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

Construct from another chemPoint and reference to a binary node.

◆ chemPointISAT() [3/3]

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

Construct from another chemPoint.

Definition at line 320 of file chemPointISAT.C.

References chemPointISAT< CompType, ThermoType >::tolerance().

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Member Function Documentation

◆ chemistry()

TDACChemistryModel<CompType, ThermoType>& chemistry ( )

inline

Access to the TDACChemistryModel.

Definition at line 275 of file chemPointISAT.H.

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

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◆ nGrowth()

label nGrowth ( )

inline

Definition at line 280 of file chemPointISAT.H.

Referenced by ISAT< CompType, ThermoType >::~ISAT().

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◆ completeSpaceSize()

label& completeSpaceSize ( )

inline

Definition at line 285 of file chemPointISAT.H.

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

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◆ phi()

const scalarField& phi ( ) const

inline

Definition at line 290 of file chemPointISAT.H.

Referenced by binaryTree< CompType, ThermoType >::balance(), binaryNode< CompType, ThermoType >::calcA(), binaryNode< CompType, ThermoType >::calcV(), and ISAT< CompType, ThermoType >::~ISAT().

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◆ Rphi()

const scalarField& Rphi ( ) const

inline

Definition at line 295 of file chemPointISAT.H.

Referenced by ISAT< CompType, ThermoType >::~ISAT().

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◆ scaleFactor()

const scalarField& scaleFactor ( )

inline

Definition at line 300 of file chemPointISAT.H.

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

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◆ tolerance()

const scalar& tolerance ( )

inline

Definition at line 305 of file chemPointISAT.H.

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

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◆ changeTolerance()

static void changeTolerance ( scalar newTol )

inlinestatic

Definition at line 310 of file chemPointISAT.H.

◆ node()

binaryNode<CompType, ThermoType>*& node ( )

inline

Definition at line 315 of file chemPointISAT.H.

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

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◆ A() [1/2]

const scalarSquareMatrix& A ( ) const

inline

Definition at line 320 of file chemPointISAT.H.

Referenced by ISAT< CompType, ThermoType >::~ISAT().

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◆ A() [2/2]

scalarSquareMatrix& A ( )

inline

Definition at line 325 of file chemPointISAT.H.

◆ LT() [1/2]

const scalarSquareMatrix& LT ( ) const

inline

Definition at line 330 of file chemPointISAT.H.

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

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◆ LT() [2/2]

scalarSquareMatrix& LT ( )

inline

Definition at line 335 of file chemPointISAT.H.

◆ nActiveSpecies()

label nActiveSpecies ( )

inline

Definition at line 340 of file chemPointISAT.H.

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

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◆ completeToSimplifiedIndex()

List<label>& completeToSimplifiedIndex ( )

inline

Definition at line 345 of file chemPointISAT.H.

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

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◆ simplifiedToCompleteIndex() [1/2]

List<label>& simplifiedToCompleteIndex ( )

inline

Definition at line 350 of file chemPointISAT.H.

References chemPointISAT< CompType, ThermoType >::increaseNLifeTime(), chemPointISAT< CompType, ThermoType >::increaseNumRetrieve(), and chemPointISAT< CompType, ThermoType >::resetNumRetrieve().

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◆ increaseNumRetrieve()

void increaseNumRetrieve ( )

Increases the number of retrieves the chempoint has generated.

Definition at line 789 of file chemPointISAT.C.

Referenced by ISAT< CompType, ThermoType >::retrieve(), and chemPointISAT< CompType, ThermoType >::simplifiedToCompleteIndex().

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◆ resetNumRetrieve()

void resetNumRetrieve ( )

Resets the number of retrieves at each time step.

Definition at line 796 of file chemPointISAT.C.

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

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◆ increaseNLifeTime()

void increaseNLifeTime ( )

Increases the "counter" of the chP life.

Definition at line 803 of file chemPointISAT.C.

Referenced by chemPointISAT< CompType, ThermoType >::simplifiedToCompleteIndex().

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◆ simplifiedToCompleteIndex() [2/2]

Foam::label simplifiedToCompleteIndex ( const label i )

Definition at line 812 of file chemPointISAT.C.

◆ timeTag()

const label& timeTag ( )

inline

Definition at line 366 of file chemPointISAT.H.

Referenced by ISAT< CompType, ThermoType >::retrieve(), and ISAT< CompType, ThermoType >::~ISAT().

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◆ lastTimeUsed()

label& lastTimeUsed ( )

inline

Definition at line 371 of file chemPointISAT.H.

◆ toRemove()

bool& toRemove ( )

inline

Definition at line 376 of file chemPointISAT.H.

Referenced by ISAT< CompType, ThermoType >::retrieve(), and ISAT< CompType, ThermoType >::~ISAT().

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◆ maxNumNewDim()

label& maxNumNewDim ( )

inline

Definition at line 381 of file chemPointISAT.H.

◆ numRetrieve()

const label& numRetrieve ( )

inline

Definition at line 386 of file chemPointISAT.H.

◆ nLifeTime()

const label& nLifeTime ( )

inline

Definition at line 391 of file chemPointISAT.H.

◆ variableTimeStep()

bool variableTimeStep ( ) const

inline

Definition at line 396 of file chemPointISAT.H.

References chemPointISAT< CompType, ThermoType >::checkSolution(), chemPointISAT< CompType, ThermoType >::grow(), chemPointISAT< CompType, ThermoType >::inEOA(), and TDACChemistryModel< ReactionThermo, ThermoType >::variableTimeStep().

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

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◆ inEOA()

bool inEOA ( const scalarField & phiq )

To RETRIEVE the mapping from the stored chemPoint phi, the query.

point phiq has to be in the EOA of phi. To test if phiq is in the ellipsoid: ||L^T.dphi|| <= 1

Definition at line 365 of file chemPointISAT.C.

References chemPointISAT< CompType, ThermoType >::checkSolution(), Foam::endl(), Foam::Info, Foam::max(), phi, Foam::sqr(), and Foam::sqrt().

Referenced by ISAT< CompType, ThermoType >::retrieve(), binaryTree< CompType, ThermoType >::secondaryBTSearch(), and chemPointISAT< CompType, ThermoType >::variableTimeStep().

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◆ grow()

bool grow ( const scalarField & phiq )

More details about the minimum-volume ellipsoid covering an.

ellispoid E and a point p are found in [1]. Here is the main steps to obtain the modified matrix L' describind 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'^T = (L.G)(L.G)^T, L'^T is then obtained by QR decomposition of (L.G)^T = G^T.L^T [1] Stephen B. Pope, "Algorithms for ellipsoids", FDA 08-01, Cornell University, 2008

add new column and line for the new active species transfer last two lines of the previous matrix (p and T) to the end

(change the diagonal position) !set all element of the new lines and columns to zero except diagonal /*! (=1/(tolerance*scaleFactor))

Definition at line 604 of file chemPointISAT.C.

References DynamicList< T, SizeInc, SizeMult, SizeDiv >::append(), forAll, phi, and List< T >::size().

Referenced by chemPointISAT< CompType, ThermoType >::variableTimeStep(), and ISAT< CompType, ThermoType >::~ISAT().

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◆ checkSolution()

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

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 thecomputed results with the one obtained by linear interpolation. The error eps is calculated: eps = ||B.(dR - dRl)||, with dR = Rphiq - Rphi, dRl = A.dphi and B the diagonal scale factor matrix. If eps <= tolerance, the EOA is too conservative and a GROW is performed, otherwise, the newly computed mapping is associated to the initial composition and added to the tree.

Definition at line 533 of file chemPointISAT.C.

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

Referenced by chemPointISAT< CompType, ThermoType >::inEOA(), chemPointISAT< CompType, ThermoType >::variableTimeStep(), and ISAT< CompType, ThermoType >::~ISAT().

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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 >