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) |
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.
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 |
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Construct from components.
Definition at line 199 of file chemPointISAT.C.
References A, chemistry, D, Foam::max(), Foam::multiply(), SVD::S(), Matrix< Form, Type >::T(), SVD::U(), and SVD::V().
chemPointISAT | ( | const chemPointISAT< CompType, ThermoType > & | p, |
binaryNode< CompType, ThermoType > * | node | ||
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Construct from another chemPoint and reference to a binary node.
chemPointISAT | ( | Foam::chemPointISAT< CompType, ThermoType > & | p | ) |
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Access to the TDACChemistryModel.
Definition at line 319 of file chemPointISAT.H.
Referenced by binaryNode< CompType, ThermoType >::calcV().
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Definition at line 324 of file chemPointISAT.H.
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Definition at line 329 of file chemPointISAT.H.
Referenced by binaryNode< CompType, ThermoType >::calcV().
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Definition at line 334 of file chemPointISAT.H.
Referenced by binaryNode< CompType, ThermoType >::calcA(), and binaryNode< CompType, ThermoType >::calcV().
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Definition at line 339 of file chemPointISAT.H.
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Definition at line 344 of file chemPointISAT.H.
Referenced by binaryNode< CompType, ThermoType >::calcV().
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Definition at line 349 of file chemPointISAT.H.
Referenced by binaryNode< CompType, ThermoType >::calcV().
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Definition at line 354 of file chemPointISAT.H.
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Definition at line 359 of file chemPointISAT.H.
Referenced by binaryTree< CompType, ThermoType >::deleteLeaf(), and binaryTree< CompType, ThermoType >::insertNewLeaf().
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Definition at line 364 of file chemPointISAT.H.
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Definition at line 369 of file chemPointISAT.H.
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Definition at line 374 of file chemPointISAT.H.
Referenced by binaryNode< CompType, ThermoType >::calcV().
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Definition at line 379 of file chemPointISAT.H.
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Definition at line 384 of file chemPointISAT.H.
Referenced by binaryNode< CompType, ThermoType >::calcV().
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Definition at line 389 of file chemPointISAT.H.
Referenced by binaryNode< CompType, ThermoType >::calcV().
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Definition at line 394 of file chemPointISAT.H.
void increaseNumRetrieve | ( | ) |
Increases the number of retrieves the chempoint has generated.
Definition at line 788 of file chemPointISAT.C.
void resetNumRetrieve | ( | ) |
Resets the number of retrieves at each time step.
Definition at line 795 of file chemPointISAT.C.
Referenced by binaryTree< CompType, ThermoType >::resetNumRetrieve().
void increaseNLifeTime | ( | ) |
Increases the "counter" of the chP life.
Definition at line 802 of file chemPointISAT.C.
Foam::label simplifiedToCompleteIndex | ( | const label | i | ) |
Definition at line 811 of file chemPointISAT.C.
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Definition at line 416 of file chemPointISAT.H.
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Definition at line 421 of file chemPointISAT.H.
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Definition at line 426 of file chemPointISAT.H.
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Definition at line 431 of file chemPointISAT.H.
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Definition at line 436 of file chemPointISAT.H.
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Definition at line 441 of file chemPointISAT.H.
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Definition at line 446 of file chemPointISAT.H.
References TDACChemistryModel< ReactionThermo, ThermoType >::variableTimeStep().
Referenced by binaryNode< CompType, ThermoType >::binaryNode().
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 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().
bool grow | ( | const scalarField & | phiq | ) |
More details about the minimum-volume ellipsoid covering an.
ellipsoid 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 599 of file chemPointISAT.C.
References DynamicList< T, SizeMin >::append(), forAll, gamma, phi, UList< T >::size(), Foam::sqr(), Foam::sqrt(), and Foam::Zero.
bool checkSolution | ( | const scalarField & | phiq, |
const scalarField & | Rphiq | ||
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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 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 528 of file chemPointISAT.C.
References A, phi, Foam::sqr(), and Foam::sqrt().
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