ChemEquil.h

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/**
 *  @file ChemEquil.h Chemical equilibrium.
 */

// This file is part of Cantera. See License.txt in the top-level directory or
// at http://www.cantera.org/license.txt for license and copyright information.

#ifndef CT_CHEM_EQUIL_H
#define CT_CHEM_EQUIL_H

// Cantera includes
#include "cantera/base/ct_defs.h"
#include "cantera/base/ctexceptions.h"
#include "cantera/thermo/ThermoPhase.h"
#include <functional>

namespace Cantera
{

class DenseMatrix;
/// map property strings to integers
int _equilflag(const char* xy);

/**
 *  Chemical equilibrium options. Used internally by class ChemEquil.
 */
class EquilOpt
{
public:
    EquilOpt() : relTolerance(1.e-8), absElemTol(1.0E-70),maxIterations(1000),
        iterations(0),
        maxStepSize(10.0), propertyPair(TP), contin(false) {}

    doublereal relTolerance; ///< Relative tolerance
    doublereal absElemTol; ///< Abs Tol in element number
    int maxIterations; ///< Maximum number of iterations
    int iterations; ///< Iteration counter

    /**
     * Maximum step size. Largest change in any element potential or
     * in log(T) allowed in one Newton step. Default: 10.0
     */
    doublereal maxStepSize;

    /**
     * Property pair flag. Determines which two thermodynamic properties
     * are fixed.
     */
    int propertyPair;

    /**
     * Continuation flag. Set true if the calculation should be initialized from
     * the last calculation. Otherwise, the calculation will be started from
     * scratch and the initial composition and element potentials estimated.
     */
    bool contin;
};

/**
 * @defgroup equil Chemical Equilibrium
 */

/**
 * Class ChemEquil implements a chemical equilibrium solver for single-phase
 * solutions. It is a "non-stoichiometric" solver in the terminology of Smith
 * and Missen, meaning that every intermediate state is a valid chemical
 * equilibrium state, but does not necessarily satisfy the element constraints.
 * In contrast, the solver implemented in class MultiPhaseEquil uses a
 * "stoichiometric" algorithm, in which each intermediate state satisfies the
 * element constraints but is not a state of chemical equilibrium. Non-
 * stoichiometric methods are faster when they converge, but stoichiometric ones
 * tend to be more robust and can be used also for problems with multiple
 * condensed phases. As expected, the ChemEquil solver is faster than
 * MultiPhaseEquil for many single-phase equilibrium problems (particularly if
 * there are only a few elements but very many species), but can be less stable.
 * Problem situations include low temperatures where only a few species have
 * non-zero mole fractions, precisely stoichiometric compositions (e.g. 2 H2 +
 * O2). In general, if speed is important, this solver should be tried first,
 * and if it fails then use MultiPhaseEquil.
 * @ingroup equil
 */
class ChemEquil
{
public:
    ChemEquil();

    //! Constructor combined with the initialization function
    /*!
     * This constructor initializes the ChemEquil object with everything it
     * needs to start solving equilibrium problems.
     *
     * @param s ThermoPhase object that will be used in the equilibrium calls.
     */
    ChemEquil(thermo_t& s);

    virtual ~ChemEquil();

    /*!
     * Equilibrate a phase, holding the elemental composition fixed at the
     * initial value found within the ThermoPhase object *s*.
     *
     * The value of two specified properties are obtained by querying the
     * ThermoPhase object. The properties must be already contained within the
     * current thermodynamic state of the system.
     */
    int equilibrate(thermo_t& s, const char* XY, int loglevel = 0);

    /*!
     * Compute the equilibrium composition for two specified properties and the
     * specified element moles.
     *
     * The two specified properties are obtained by querying the ThermoPhase
     * object. The properties must be already contained within the current
     * thermodynamic state of the system.
     *
     * @param s phase object to be equilibrated
     * @param XY property pair to hold constant
     * @param elMoles specified vector of element abundances.
     * @param loglevel Specify amount of debug logging (0 to disable)
     * @return Successful returns are indicated by a return value of 0.
     *     Unsuccessful returns are indicated by a return value of -1 for lack
     *     of convergence or -3 for a singular Jacobian.
     */
    int equilibrate(thermo_t& s, const char* XY, vector_fp& elMoles,
                    int loglevel = 0);

    //! @deprecated To be removed after Cantera 2.4.
    const vector_fp& elementPotentials() const {
        return m_lambda;
    }

    /**
     * Options controlling how the calculation is carried out.
     * @see EquilOptions
     */
    EquilOpt options;

protected:
    //! Pointer to the ThermoPhase object used to initialize this object.
    /*!
     * This ThermoPhase object must be compatible with the ThermoPhase objects
     * input from the equilibrate function. Currently, this means that the 2
     * ThermoPhases have to have consist of the same species and elements.
     */
    thermo_t* m_phase;

    //! number of atoms of element m in species k.
    doublereal nAtoms(size_t k, size_t m) const {
        return m_comp[k*m_mm + m];
    }

    /*!
     * Prepare for equilibrium calculations.
     * @param s object representing the solution phase.
     */
    void initialize(thermo_t& s);

    /*!
     * Set mixture to an equilibrium state consistent with specified element
     * potentials and temperature.
     *
     * @param s mixture to be updated
     * @param x vector of non-dimensional element potentials
     * \f[ \lambda_m/RT \f].
     * @param t temperature in K.
     */
    void setToEquilState(thermo_t& s,
                         const vector_fp& x, doublereal t);

    //! Estimate the initial mole numbers. This version borrows from the
    //! MultiPhaseEquil solver.
    int setInitialMoles(thermo_t& s, vector_fp& elMoleGoal, int loglevel = 0);

    //! Generate a starting estimate for the element potentials.
    int estimateElementPotentials(thermo_t& s, vector_fp& lambda,
                                  vector_fp& elMolesGoal, int loglevel = 0);

    /*!
     * Do a calculation of the element potentials using the Brinkley method,
     * p. 129 Smith and Missen.
     *
     * We have found that the previous estimate may not be good enough to
     * avoid drastic numerical issues associated with the use of a numerically
     * generated Jacobian used in the main algorithm.
     *
     * The Brinkley algorithm, here, assumes a constant T, P system and uses a
     * linearized analytical Jacobian that turns out to be very stable even
     * given bad initial guesses.
     *
     * The pressure and temperature to be used are in the ThermoPhase object
     * input into the routine.
     *
     * The initial guess for the element potentials used by this routine is
     * taken from the input vector, x.
     *
     * elMoles is the input element abundance vector to be matched.
     *
     * Nonideal phases are handled in principle. This is done by calculating
     * the activity coefficients and adding them into the formula in the
     * correct position. However, these are treated as a RHS contribution
     * only. Therefore, convergence might be a problem. This has not been
     * tested. Also molality based unit systems aren't handled.
     *
     * On return, int return value contains the success code:
     * - 0 - successful
     * - 1 - unsuccessful, max num iterations exceeded
     * - -3 - unsuccessful, singular Jacobian
     *
     * NOTE: update for activity coefficients.
     */
    int estimateEP_Brinkley(thermo_t& s, vector_fp& lambda, vector_fp& elMoles);

    //! Find an acceptable step size and take it.
    /*!
     * The original implementation employed a line search technique that
     * enforced a reduction in the norm of the residual at every successful
     * step. Unfortunately, this method created false convergence errors near
     * the end of a significant number of steps, usually special conditions
     * where there were stoichiometric constraints.
     *
     * This new method just does a delta damping approach, based on limiting
     * the jump in the dimensionless element potentials. Mole fractions are
     * limited to a factor of 2 jump in the values from this method. Near
     * convergence, the delta damping gets out of the way.
     */
    int dampStep(thermo_t& s, vector_fp& oldx,
                 double oldf, vector_fp& grad, vector_fp& step, vector_fp& x,
                 double& f, vector_fp& elmols, double xval, double yval);

    /**
     *  Evaluates the residual vector F, of length #m_mm
     */
    void equilResidual(thermo_t& s, const vector_fp& x,
                       const vector_fp& elmtotal, vector_fp& resid,
                       double xval, double yval, int loglevel = 0);

    void equilJacobian(thermo_t& s, vector_fp& x,
                       const vector_fp& elmols, DenseMatrix& jac,
                       double xval, double yval, int loglevel = 0);

    void adjustEloc(thermo_t& s, vector_fp& elMolesGoal);

    //! Update internally stored state information.
    void update(const thermo_t& s);

    /**
     * Given a vector of dimensionless element abundances, this routine
     * calculates the moles of the elements and the moles of the species.
     *
     * @param[in] x = current dimensionless element potentials..
     */
    double calcEmoles(thermo_t& s, vector_fp& x,
                      const double& n_t, const vector_fp& Xmol_i_calc,
                      vector_fp& eMolesCalc, vector_fp& n_i_calc,
                      double pressureConst);

    size_t m_mm; //!< number of elements in the phase
    size_t m_kk; //!< number of species in the phase
    size_t m_skip;

    //! This is equal to the rank of the stoichiometric coefficient matrix when
    //! it is computed. It's initialized to #m_mm.
    size_t m_nComponents;

    std::function<double(ThermoPhase&)> m_p1, m_p2;

    //! Current value of the mole fractions in the single phase. length = #m_kk.
    vector_fp m_molefractions;

    //! Current value of the dimensional element potentials. length = #m_mm
    //! @deprecated To be removed after Cantera 2.4.
    vector_fp m_lambda;

    //! Current value of the sum of the element abundances given the current
    //! element potentials.
    doublereal m_elementTotalSum;

    //! Current value of the element mole fractions. Note these aren't the goal
    //! element mole fractions.
    vector_fp m_elementmolefracs;
    vector_fp m_reswork;
    vector_fp m_jwork1;
    vector_fp m_jwork2;

    //! Storage of the element compositions. natom(k,m) = m_comp[k*m_mm+ m];
    vector_fp m_comp;
    doublereal m_temp, m_dens;
    doublereal m_p0;

    //! Index of the element id corresponding to the electric charge of each
    //! species. Equal to -1 if there is no such element id.
    size_t m_eloc;

    vector_fp m_startSoln;

    vector_fp m_grt;
    vector_fp m_mu_RT;

    //! Dimensionless values of the Gibbs free energy for the standard state of
    //! each species, at the temperature and pressure of the solution (the star
    //! standard state).
    vector_fp m_muSS_RT;
    std::vector<size_t> m_component;

    //! element fractional cutoff, below which the element will be zeroed.
    double m_elemFracCutoff;
    bool m_doResPerturb;

    std::vector<size_t> m_orderVectorElements;
    std::vector<size_t> m_orderVectorSpecies;

    //! Verbosity of printed output. No messages when m_loglevel == 0. More
    //! output as level increases.
    int m_loglevel;
};

}

#endif