Cantera
2.3.0

Method to solve a pseudo steady state surface problem. More...
#include <solveSP.h>
Public Member Functions  
solveSP (ImplicitSurfChem *surfChemPtr, int bulkFunc=BULK_ETCH)  
Constructor for the object. More...  
~solveSP ()  
Destructor. Deletes the integrator. More...  
int  solveSurfProb (int ifunc, doublereal time_scale, doublereal TKelvin, doublereal PGas, doublereal reltol, doublereal abstol) 
Main routine that actually calculates the pseudo steady state of the surface problem. More...  
Public Attributes  
int  m_ioflag 
Private Member Functions  
solveSP (const solveSP &right)  
Unimplemented private copy constructor. More...  
solveSP &  operator= (const solveSP &right) 
Unimplemented private assignment operator. More...  
void  print_header (int ioflag, int ifunc, doublereal time_scale, int damping, doublereal reltol, doublereal abstol) 
Printing routine that optionally gets called at the start of every invocation. More...  
void  printIteration (int ioflag, doublereal damp, int label_d, int label_t, doublereal inv_t, doublereal t_real, size_t iter, doublereal update_norm, doublereal resid_norm, bool do_time, bool final=false) 
Printing routine that gets called after every iteration. More...  
doublereal  calc_t (doublereal netProdRateSolnSP[], doublereal XMolSolnSP[], int *label, int *label_old, doublereal *label_factor, int ioflag) 
Calculate a conservative delta T to use in a pseudosteady state algorithm. More...  
void  calcWeights (doublereal wtSpecies[], doublereal wtResid[], const Array2D &Jac, const doublereal CSolnSP[], const doublereal abstol, const doublereal reltol) 
Calculate the solution and residual weights. More...  
void  updateState (const doublereal *cSurfSpec) 
Update the surface states of the surface phases. More...  
void  updateMFSolnSP (doublereal *XMolSolnSP) 
Update mole fraction vector consisting of unknowns in surface problem. More...  
void  updateMFKinSpecies (doublereal *XMolKinSp, int isp) 
Update the mole fraction vector for a specific kinetic species vector corresponding to one InterfaceKinetics object. More...  
void  evalSurfLarge (const doublereal *CSolnSP) 
Update the vector that keeps track of the largest species in each surface phase. More...  
void  fun_eval (doublereal *resid, const doublereal *CSolnSP, const doublereal *CSolnOldSP, const bool do_time, const doublereal deltaT) 
Main Function evaluation. More...  
void  resjac_eval (DenseMatrix &jac, doublereal *resid, doublereal *CSolnSP, const doublereal *CSolnSPOld, const bool do_time, const doublereal deltaT) 
Main routine that calculates the current residual and Jacobian. More...  
Private Attributes  
ImplicitSurfChem *  m_SurfChemPtr 
Pointer to the manager of the implicit surface chemistry problem. More...  
std::vector< InterfaceKinetics * > &  m_objects 
Vector of interface kinetics objects. More...  
size_t  m_neq 
Total number of equations to solve in the implicit problem. More...  
int  m_bulkFunc 
This variable determines how the bulk phases are to be handled. More...  
size_t  m_numSurfPhases 
Number of surface phases in the surface problem. More...  
size_t  m_numTotSurfSpecies 
Total number of surface species in all surface phases. More...  
std::vector< size_t >  m_indexKinObjSurfPhase 
Mapping between the surface phases and the InterfaceKinetics objects. More...  
std::vector< size_t >  m_nSpeciesSurfPhase 
Vector of length number of surface phases containing the number of surface species in each phase. More...  
std::vector< SurfPhase * >  m_ptrsSurfPhase 
Vector of surface phase pointers. More...  
std::vector< size_t >  m_eqnIndexStartSolnPhase 
Index of the start of the unknowns for each solution phase. More...  
std::vector< size_t >  m_kinObjPhaseIDSurfPhase 
Phase ID in the InterfaceKinetics object of the surface phase. More...  
size_t  m_numBulkPhasesSS 
Total number of volumetric condensed phases included in the steady state problem handled by this routine. More...  
std::vector< size_t >  m_numBulkSpecies 
Vector of number of species in the m_numBulkPhases phases. More...  
size_t  m_numTotBulkSpeciesSS 
Total number of species in all bulk phases. More...  
std::vector< ThermoPhase * >  m_bulkPhasePtrs 
Vector of bulk phase pointers, length is equal to m_numBulkPhases. More...  
std::vector< size_t >  m_kinSpecIndex 
Index between the equation index and the position in the kinetic species array for the appropriate kinetics operator. More...  
std::vector< size_t >  m_kinObjIndex 
Index between the equation index and the index of the InterfaceKinetics object. More...  
std::vector< size_t >  m_spSurfLarge 
Vector containing the indices of the largest species in each surface phase. More...  
doublereal  m_atol 
The absolute tolerance in real units. units are (kmol/m2) More...  
doublereal  m_rtol 
The relative error tolerance. More...  
doublereal  m_maxstep 
maximum value of the time step. units = seconds More...  
size_t  m_maxTotSpecies 
Maximum number of species in any single kinetics operator > also maxed wrt the total # of solution species. More...  
vector_fp  m_netProductionRatesSave 
Temporary vector with length equal to max m_maxTotSpecies. More...  
vector_fp  m_numEqn1 
Temporary vector with length equal to max m_maxTotSpecies. More...  
vector_fp  m_numEqn2 
Temporary vector with length equal to max m_maxTotSpecies. More...  
vector_fp  m_CSolnSave 
Temporary vector with length equal to max m_maxTotSpecies. More...  
vector_fp  m_CSolnSP 
Solution vector. length MAX(1, m_neq) More...  
vector_fp  m_CSolnSPInit 
Saved initial solution vector. length MAX(1, m_neq) More...  
vector_fp  m_CSolnSPOld 
Saved solution vector at the old time step. length MAX(1, m_neq) More...  
vector_fp  m_wtResid 
Weights for the residual norm calculation. length MAX(1, m_neq) More...  
vector_fp  m_wtSpecies 
Weights for the species concentrations norm calculation. More...  
vector_fp  m_resid 
Residual for the surface problem. More...  
vector_fp  m_XMolKinSpecies 
Vector of mole fractions. length m_maxTotSpecies. More...  
DenseMatrix  m_Jac 
Jacobian. More...  
Method to solve a pseudo steady state surface problem.
The following class handles solving the surface problem. The calculation uses Newton's method to obtain the surface fractions of the surface and bulk species by requiring that the surface species production rate = 0 and that the either the bulk fractions are proportional to their production rates or they are constants.
Currently, the bulk mole fractions are treated as constants. Implementation of their being added to the unknown solution vector is delayed.
Lets introduce the unknown vector for the "surface problem". The surface problem is defined as the evaluation of the surface site fractions for multiple surface phases. The unknown vector will consist of the vector of surface concentrations for each species in each surface vector. Species are grouped first by their surface phases
The unknown solution vector is defined as follows:
C_i_j  kindexSP 

C_0_0  0 
C_1_0  1 
C_2_0  2 
. . .  ... 
C_N01_0  N01 
C_0_1  N0 
C_1_1  N0+1 
C_2_1  N0+2 
. . .  ... 
C_N11_1  NO+N11 
Note there are a couple of different types of species indices floating around in the formulation of this object.
kindexSP: This is the species index in the contiguous vector of unknowns for the surface problem.
Note, in the future, BULK_DEPOSITION systems will be added, and the solveSP unknown vector will get more complicated. It will include the mole fraction and growth rates of specified bulk phases
Indices which relate to individual kinetics objects use the suffix KSI (kinetics species index).
This routine is typically used within a residual calculation in a large code. It's typically invoked millions of times for large calculations, and it must work every time. Therefore, requirements demand that it be robust but also efficient.
The solution methodology is largely determined by the ifunc
parameter, that is input to the solution object. This parameter may have one of the values defined in Surface Problem Solver Methods.
The time step is determined from sdot[], so that the time step doesn't ever change the value of a variable by more than 100%.
This algorithm does use a damped Newton's method to relax the equations. Damping is based on a "delta damping" technique. The solution unknowns are not allowed to vary too much between iterations.
EXTRA_ACCURACY
: A constant that is the ratio of the required update norm in this Newton iteration compared to that in the nonlinear solver. A value of 0.1 is used so surface species are safely overconverged.
Functions called:
ct_dgetrf
– First half of LAPACK direct solve of a full Matrixct_dgetrs
– Second half of LAPACK direct solve of a full matrix. Returns solution vector in the righthandside vector, resid. solveSP  (  ImplicitSurfChem *  surfChemPtr, 
int  bulkFunc = BULK_ETCH 

) 
Constructor for the object.
surfChemPtr  Pointer to the ImplicitSurfChem object that defines the surface problem to be solved. 
bulkFunc  Integer representing how the bulk phases should be handled. See Surface Problem Bulk Phase Mode. Currently, only the default value of BULK_ETCH is supported. 
Definition at line 23 of file solveSP.cpp.
int solveSurfProb  (  int  ifunc, 
doublereal  time_scale,  
doublereal  TKelvin,  
doublereal  PGas,  
doublereal  reltol,  
doublereal  abstol  
) 
Main routine that actually calculates the pseudo steady state of the surface problem.
The actual converged solution is returned as part of the internal state of the InterfaceKinetics objects.
Uses Newton's method to get the surface fractions of the surface and bulk species by requiring that the surface species production rate = 0 and that the bulk fractions are proportional to their production rates.
ifunc  Determines the type of solution algorithm to be used. See Surface Problem Solver Methods for possible values. 
time_scale  Time over which to integrate the surface equations, where applicable 
TKelvin  Temperature (kelvin) 
PGas  Pressure (pascals) 
reltol  Relative tolerance to use 
abstol  absolute tolerance. 
Definition at line 113 of file solveSP.cpp.
References solveSP::calc_t(), solveSP::calcWeights(), solveSP::evalSurfLarge(), solveSP::fun_eval(), solveSP::m_CSolnSP, solveSP::m_CSolnSPInit, solveSP::m_CSolnSPOld, solveSP::m_Jac, solveSP::m_neq, solveSP::m_netProductionRatesSave, solveSP::m_nSpeciesSurfPhase, solveSP::m_numEqn1, solveSP::m_numSurfPhases, solveSP::m_ptrsSurfPhase, solveSP::m_resid, solveSP::m_wtResid, solveSP::m_wtSpecies, solveSP::m_XMolKinSpecies, solveSP::print_header(), solveSP::printIteration(), solveSP::resjac_eval(), SFLUX_INITIALIZE, SFLUX_JACOBIAN, SFLUX_TRANSIENT, Cantera::solve(), solveSP::updateState(), Cantera::writelog(), and Cantera::writelogf().

private 
Printing routine that optionally gets called at the start of every invocation.
Definition at line 637 of file solveSP.cpp.
References BULK_DEPOSITION, BULK_ETCH, solveSP::m_bulkFunc, SFLUX_INITIALIZE, SFLUX_JACOBIAN, SFLUX_RESIDUAL, SFLUX_TRANSIENT, Cantera::writelog(), and Cantera::writelogf().
Referenced by solveSP::solveSurfProb().

private 
Printing routine that gets called after every iteration.
Definition at line 686 of file solveSP.cpp.
References solveSP::m_kinObjIndex, solveSP::m_kinSpecIndex, solveSP::m_objects, Cantera::writelog(), and Cantera::writelogf().
Referenced by solveSP::solveSurfProb().

private 
Calculate a conservative delta T to use in a pseudosteady state algorithm.
This routine calculates a pretty conservative 1/del_t based on MAX_i(sdot_i/(X_i*SDen0)). This probably guarantees diagonal dominance.
Small surface fractions are allowed to intervene in the del_t determination, no matter how small. This may be changed. Now minimum changed to 1.0e12,
Maximum time step set to time_scale.
netProdRateSolnSP  Output variable. Net production rate of all of the species in the solution vector. 
XMolSolnSP  output variable. Mole fraction of all of the species in the solution vector 
label  Output variable. Pointer to the value of the species index (kindexSP) that is controlling the time step 
label_old  Output variable. Pointer to the value of the species index (kindexSP) that controlled the time step at the previous iteration 
label_factor  Output variable. Pointer to the current factor that is used to indicate the same species is controlling the time step. 
ioflag  Level of the output requested. 
Definition at line 591 of file solveSP.cpp.
References Kinetics::getNetProductionRates(), Kinetics::kineticsSpeciesIndex(), solveSP::m_nSpeciesSurfPhase, solveSP::m_numEqn1, solveSP::m_numSurfPhases, solveSP::m_objects, Phase::molarDensity(), Kinetics::surfacePhaseIndex(), Kinetics::thermo(), and solveSP::updateMFSolnSP().
Referenced by solveSP::solveSurfProb().

private 
Calculate the solution and residual weights.
wtSpecies  Weights to use for the soln unknowns. These are in concentration units 
wtResid  Weights to sue for the residual unknowns. 
Jac  Jacobian. Row sum scaling is used for the Jacobian 
CSolnSP  Solution vector for the surface problem 
abstol  Absolute error tolerance 
reltol  Relative error tolerance 
Definition at line 558 of file solveSP.cpp.
References BULK_DEPOSITION, solveSP::m_bulkFunc, solveSP::m_bulkPhasePtrs, solveSP::m_neq, solveSP::m_nSpeciesSurfPhase, solveSP::m_numBulkPhasesSS, solveSP::m_numBulkSpecies, solveSP::m_numSurfPhases, and solveSP::m_ptrsSurfPhase.
Referenced by solveSP::solveSurfProb().

private 
Update the surface states of the surface phases.
Definition at line 296 of file solveSP.cpp.
References solveSP::m_nSpeciesSurfPhase, solveSP::m_numSurfPhases, and solveSP::m_ptrsSurfPhase.
Referenced by solveSP::fun_eval(), and solveSP::solveSurfProb().

private 
Update mole fraction vector consisting of unknowns in surface problem.
XMolSolnSP  Vector of mole fractions for the unknowns in the surface problem. 
Definition at line 305 of file solveSP.cpp.
References solveSP::m_eqnIndexStartSolnPhase, solveSP::m_numSurfPhases, and solveSP::m_ptrsSurfPhase.
Referenced by solveSP::calc_t().

private 
Update the mole fraction vector for a specific kinetic species vector corresponding to one InterfaceKinetics object.
XMolKinSp  Mole fraction vector corresponding to a particular kinetic species for a single InterfaceKinetics Object This is a vector over all the species in all of the phases in the InterfaceKinetics object 
isp  ID of the InterfaceKinetics Object. 
Definition at line 313 of file solveSP.cpp.
References Phase::getMoleFractions(), Kinetics::kineticsSpeciesIndex(), solveSP::m_objects, Kinetics::nPhases(), and Kinetics::thermo().

private 
Update the vector that keeps track of the largest species in each surface phase.
CSolnSP  Vector of the current values of the surface concentrations in all of the surface species. 
Definition at line 322 of file solveSP.cpp.
References solveSP::m_nSpeciesSurfPhase, solveSP::m_numSurfPhases, and solveSP::m_spSurfLarge.
Referenced by solveSP::solveSurfProb().

private 
Main Function evaluation.
resid  output Vector of residuals, length = m_neq 
CSolnSP  Vector of species concentrations, unknowns in the problem, length = m_neq 
CSolnOldSP  Old Vector of species concentrations, unknowns in the problem, length = m_neq 
do_time  Calculate a time dependent residual 
deltaT  Delta time for time dependent problem. 
Definition at line 338 of file solveSP.cpp.
References BULK_DEPOSITION, Kinetics::getNetProductionRates(), Kinetics::kineticsSpeciesIndex(), solveSP::m_bulkFunc, solveSP::m_bulkPhasePtrs, solveSP::m_indexKinObjSurfPhase, solveSP::m_netProductionRatesSave, solveSP::m_nSpeciesSurfPhase, solveSP::m_numBulkPhasesSS, solveSP::m_numEqn1, solveSP::m_numSurfPhases, solveSP::m_numTotSurfSpecies, solveSP::m_objects, solveSP::m_ptrsSurfPhase, solveSP::m_spSurfLarge, Kinetics::surfacePhaseIndex(), and solveSP::updateState().
Referenced by solveSP::resjac_eval(), and solveSP::solveSurfProb().

private 
Main routine that calculates the current residual and Jacobian.
jac  Jacobian to be evaluated. 
resid  output Vector of residuals, length = m_neq 
CSolnSP  Vector of species concentrations, unknowns in the problem, length = m_neq. These are tweaked in order to derive the columns of the Jacobian. 
CSolnSPOld  Old Vector of species concentrations, unknowns in the problem, length = m_neq 
do_time  Calculate a time dependent residual 
deltaT  Delta time for time dependent problem. 
Definition at line 445 of file solveSP.cpp.
References solveSP::fun_eval(), solveSP::m_nSpeciesSurfPhase, solveSP::m_numSurfPhases, and solveSP::m_ptrsSurfPhase.
Referenced by solveSP::solveSurfProb().

private 

private 
Vector of interface kinetics objects.
Each of these is associated with one and only one surface phase.
Definition at line 317 of file solveSP.h.
Referenced by solveSP::calc_t(), solveSP::fun_eval(), solveSP::printIteration(), and solveSP::updateMFKinSpecies().

private 
Total number of equations to solve in the implicit problem.
Note, this can be zero, and frequently is
Definition at line 323 of file solveSP.h.
Referenced by solveSP::calcWeights(), and solveSP::solveSurfProb().

private 
This variable determines how the bulk phases are to be handled.
Possible values are given in Surface Problem Bulk Phase Mode.
Definition at line 329 of file solveSP.h.
Referenced by solveSP::calcWeights(), solveSP::fun_eval(), and solveSP::print_header().

private 
Number of surface phases in the surface problem.
This number is equal to the number of InterfaceKinetics objects in the problem. (until further noted)
Definition at line 336 of file solveSP.h.
Referenced by solveSP::calc_t(), solveSP::calcWeights(), solveSP::evalSurfLarge(), solveSP::fun_eval(), solveSP::resjac_eval(), solveSP::solveSurfProb(), solveSP::updateMFSolnSP(), and solveSP::updateState().

private 
Total number of surface species in all surface phases.
This is also the number of equations to solve for m_mode=0 system It's equal to the sum of the number of species in each of the m_numSurfPhases.
Definition at line 344 of file solveSP.h.
Referenced by solveSP::fun_eval().

private 
Mapping between the surface phases and the InterfaceKinetics objects.
Currently this is defined to be a 11 mapping (and probably assumed in some places) m_surfKinObjID[i] = i
Definition at line 352 of file solveSP.h.
Referenced by solveSP::fun_eval().

private 
Vector of length number of surface phases containing the number of surface species in each phase.
Length is equal to the number of surface phases, m_numSurfPhases
Definition at line 359 of file solveSP.h.
Referenced by solveSP::calc_t(), solveSP::calcWeights(), solveSP::evalSurfLarge(), solveSP::fun_eval(), solveSP::resjac_eval(), solveSP::solveSurfProb(), and solveSP::updateState().

private 
Vector of surface phase pointers.
This is created during the constructor Length is equal to the number of surface phases, m_numSurfPhases
Definition at line 366 of file solveSP.h.
Referenced by solveSP::calcWeights(), solveSP::fun_eval(), solveSP::resjac_eval(), solveSP::solveSurfProb(), solveSP::updateMFSolnSP(), and solveSP::updateState().

private 
Index of the start of the unknowns for each solution phase.
i_eqn = m_eqnIndexStartPhase[isp]
isp is the phase id in the list of phases solved by the surface problem.
i_eqn is the equation number of the first unknown in the solution vector corresponding to isp'th phase.
Definition at line 378 of file solveSP.h.
Referenced by solveSP::updateMFSolnSP().

private 
Phase ID in the InterfaceKinetics object of the surface phase.
For each surface phase, this lists the PhaseId of the surface phase in the corresponding InterfaceKinetics object
Length is equal to m_numSurfPhases

private 
Total number of volumetric condensed phases included in the steady state problem handled by this routine.
This is equal to or less than the total number of volumetric phases in all of the InterfaceKinetics objects. We usually do not include bulk phases. Bulk phases are only included in the calculation when their domain isn't included in the underlying continuum model conservation equation system.
This is equal to 0, for the time being
Definition at line 400 of file solveSP.h.
Referenced by solveSP::calcWeights(), and solveSP::fun_eval().

private 
Vector of number of species in the m_numBulkPhases phases.
Length is number of bulk phases
Definition at line 406 of file solveSP.h.
Referenced by solveSP::calcWeights().

private 

private 
Vector of bulk phase pointers, length is equal to m_numBulkPhases.
Definition at line 416 of file solveSP.h.
Referenced by solveSP::calcWeights(), and solveSP::fun_eval().

private 
Index between the equation index and the position in the kinetic species array for the appropriate kinetics operator.
Length = m_neq.
ksp = m_kinSpecIndex[ieq] ksp is the kinetic species index for the ieq'th equation.
Definition at line 426 of file solveSP.h.
Referenced by solveSP::printIteration().

private 
Index between the equation index and the index of the InterfaceKinetics object.
Length m_neq
Definition at line 433 of file solveSP.h.
Referenced by solveSP::printIteration().

private 
Vector containing the indices of the largest species in each surface phase.
k = m_spSurfLarge[i]
where k
is the local species index, i.e., it varies from 0 to (num species in phase  1) and i
is the surface phase index in the problem. Length is equal to m_numSurfPhases.
Definition at line 442 of file solveSP.h.
Referenced by solveSP::evalSurfLarge(), and solveSP::fun_eval().

private 

private 

private 

private 
Temporary vector with length equal to max m_maxTotSpecies.
Definition at line 458 of file solveSP.h.
Referenced by solveSP::fun_eval(), and solveSP::solveSurfProb().

private 
Temporary vector with length equal to max m_maxTotSpecies.
Definition at line 461 of file solveSP.h.
Referenced by solveSP::calc_t(), solveSP::fun_eval(), and solveSP::solveSurfProb().

private 

private 

private 
Solution vector. length MAX(1, m_neq)
Definition at line 470 of file solveSP.h.
Referenced by solveSP::solveSurfProb().

private 
Saved initial solution vector. length MAX(1, m_neq)
Definition at line 473 of file solveSP.h.
Referenced by solveSP::solveSurfProb().

private 
Saved solution vector at the old time step. length MAX(1, m_neq)
Definition at line 476 of file solveSP.h.
Referenced by solveSP::solveSurfProb().

private 
Weights for the residual norm calculation. length MAX(1, m_neq)
Definition at line 479 of file solveSP.h.
Referenced by solveSP::solveSurfProb().

private 
Weights for the species concentrations norm calculation.
length MAX(1, m_neq)
Definition at line 485 of file solveSP.h.
Referenced by solveSP::solveSurfProb().

private 
Residual for the surface problem.
The residual vector of length "dim" that, that has the value of "sdot" for surface species. The residuals for the bulk species are a function of the sdots for all species in the bulk phase. The last residual of each phase enforces {Sum(fractions) = 1}. After linear solve (dgetrf_ & dgetrs_), resid holds the update vector.
length MAX(1, m_neq)
Definition at line 497 of file solveSP.h.
Referenced by solveSP::solveSurfProb().

private 
Vector of mole fractions. length m_maxTotSpecies.
Definition at line 500 of file solveSP.h.
Referenced by solveSP::solveSurfProb().

private 
Jacobian.
m_neq by m_neq computed Jacobian matrix for the local Newton's method.
Definition at line 504 of file solveSP.h.
Referenced by solveSP::solveSurfProb().