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/*-------------------------------------------------------
Copyright (c) 2014,2015 Fabien Georget <fabieng@princeton.edu>, Princeton University
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
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documentation and/or other materials provided with the distribution.
* Neither the name of the Princeton University nor the
names of its contributors may be used to endorse or promote products
derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
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(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
---------------------------------------------------------*/
#ifndef SPECMICP_ADIMENSIONALSYSTEM_HPP
#define SPECMICP_ADIMENSIONALSYSTEM_HPP
//! \file adimensional_system.hpp The MiCP program to solve speciation
#include "common.hpp"
#ifndef SPECMICP_DATABASE_HPP
#include "database.hpp"
#endif
#include "micpsolver/micpprog.hpp"
#include "physics/units.hpp"
#include "utils/options_handler.hpp"
#include "adimensional_system_numbering.hpp"
#include "adimensional_system_structs.hpp"
//! \namespace specmicp main namespace for the SpecMiCP solver
namespace specmicp {
class AdimensionalSystemSolution;
//! \brief The equilibrium speciation problem
//!
//! Represent the equilibrium speciation problem as a Mixed Complementarity program
//!
//! The main variables are :
//! - \f$S^t_w\f$ the volume fraction of water (total saturation)
//! - \f$b_i\f$ the molality of aqueous component
//! - \f$S^t_m\f$ the volume fraction of mineral
//!
//! The solid phase equilibrium is solved by using a complementarity formulation
//! \f[ S^t_m \geq 0, \; - \mathrm{SI}_m \geq 0 , \; \mathrm{and} \; - S^t_m \mathrm{SI}_m = 0 \f]
//!
//! The secondary variables (molalities of secondary aqueous species, gas fugacities, ionic strength, ...)
//! are solved using a fixed point iteration at the beginning of each iteration.
//!
class AdimensionalSystem :
public micpsolver::MiCPProg<AdimensionalSystem>,
public AdimemsionalSystemNumbering,
public OptionsHandler<AdimensionalSystemOptions>,
private units::UnitBaseClass
{
public:
//! \brief Create a reduced system
//!
//! \param ptrdata Shared pointer to the thermodynamic database
//! \param constraints Constraints to apply to the system
//! \param options Numerical options, mainly related to the secondary variables
//! \param units_set The set of units
AdimensionalSystem(RawDatabasePtr& ptrdata,
const AdimensionalSystemConstraints& constraints,
const AdimensionalSystemOptions& options=AdimensionalSystemOptions(),
const units::UnitsSet& units_set=units::UnitsSet()
);
//! \brief Create a reduced system, initialize the system using a previous solution
//!
//! \param ptrdata Shared pointer to the thermodynamic database
//! \param constraints Constraints to apply to the system
//! \param previous_solution The previous solution to use for initialization
//! \param options Numerical options, mainly related to the secondary variables
//! \param units_set The set of units
AdimensionalSystem(
RawDatabasePtr& ptrdata,
const AdimensionalSystemConstraints& constraints,
const AdimensionalSystemSolution& previous_solution,
const AdimensionalSystemOptions& options=AdimensionalSystemOptions(),
const units::UnitsSet& units_set=units::UnitsSet()
);
// Variables
// ==========
//! \brief Return the total number of variables
index_t total_variables() const {return m_equations.nb_tot_variables;}
//! \brief Return the number of 'free' variables (not subject to complementarity conditions)
index_t nb_free_variables() const {return m_equations.nb_free_variables;}
//! \brief Return the number of variables subjected to the complementarity conditions
index_t nb_complementarity_variables() const {return m_equations.nb_complementarity_variables;}
//! \brief Return a pointer to the database
RawDatabasePtr get_database() {return m_data;}
// The linear system
// ==================
//! \brief Return the residual for the water conservation equation
//!
//! \param x Vector of the main variables
scalar_t residual_water(const Vector& x) const;
//! \brief Return the residual for the conservation equation of component (i)
//!
//! For water (i==0) use the method : 'residual_water'
//! \param x Vector of the main variables
//! \param i Index of the component (in the database)
scalar_t residual_component(const Vector& x, index_t i) const;
//! \brief Compute the residual for the surface sorption
//! \param x Vector of the main variables
scalar_t residual_surface(const Vector& x) const;
//! \brief Equilibrium condition for the minerals
//! \param x Vector of the main variables
//! \param i Index of the component (in the database)
scalar_t residual_mineral(const Vector& x, index_t m) const;
//! \brief Return the residual of the charge conservation equation
//!
//! This equation may be used instead of a mass conservation equation to
//! explicitely enforce the electroneutrality.
//! The component corresponding to this equation is called the charge keeper
//! \param x Vector of the main variables
scalar_t residual_charge_conservation(const Vector& x) const;
//! \brief Return the residual corresponding to a fixed fugacity equation
//! \param x Vector of the main variables
//! \param component Index of the corresponding component (in the database)
scalar_t residual_fixed_fugacity(const Vector& x, index_t component) const;
//! \brief Return the residual corresponding to a fixed activity equation
//!
//! If 'component ' is charged, then a charge keeper should be set.
//! \param x Vector of the main variables
//! \param component Index of the corresponding component (in the database)
scalar_t residual_fixed_activity(const Vector& x, index_t component) const;
//! \brief Return the residuals
//!
//! \param x Vector of the main variables
//! \param[out] residual Vector containing the residuals
void get_residuals(const Vector& x, Vector& residual);
//! \brief Return the jacobian
//!
//! \param x Vector of the main variables
//! \param[out] jacobian Dense matrix representing the jacobian
void get_jacobian(Vector& x,
Matrix& jacobian);
// Getters
// #######
// Equation id access
// ==================
//! \brief Return the equation id
//! \param i Index of the main variable (in the set of the main variables)
index_t ideq(index_t i) const {return m_equations.ideq[i];}
//! \brief Return the equation number for conservation of water
index_t ideq_w() const {return m_equations.ideq[dof_water()];}
//! \brief Return the equation number of component 'i'
//! \param i Index of the component (in the database)
index_t ideq_paq(index_t i) const {
specmicp_assert(i < m_data->nb_component());
return m_equations.ideq[dof_component(i)];
}
//! \brief Return the equation number of the electron equation
index_t ideq_electron() const {
return m_equations.ideq[dof_electron()];
}
//! \brief Return the equation number of the free surface concentration
index_t ideq_surf() const {
return m_equations.ideq[dof_surface()];
}
//! \brief Return the equation number of mineral 'm'
//! \param m Index of the mineral (in the database)
index_t ideq_min(index_t m) const {
specmicp_assert(m < m_data->nb_mineral());
return m_equations.ideq[dof_mineral(m)];
}
// Equation type
// -------------
//! \brief Return the type of equation used for the solvent
//!
//! Can be no equation, mass conservation, saturation of the system, ...
//!
//! \sa #WaterEquationType, #aqueous_component_equation_type, #AqueousComponentEquationType
WaterEquationType water_equation_type() const {
return static_cast<WaterEquationType>(m_equations.type_equation(dof_water()));
}
//! \brief Return the type of equation for aqueous species 'component'
//!
//! For water used the method #water_equation_type
//! \param component Index of the aqueous component (in the database)
//!
//! \sa #AqueousComponentEquationType, water_equation_type, #WaterEquationType
AqueousComponentEquationType aqueous_component_equation_type(index_t component) const {
specmicp_assert(component > 0 and component < m_data->nb_component());
return static_cast<AqueousComponentEquationType>(m_equations.type_equation(dof_component(component)));
}
//! \brief Return the type of equation for the electron
ElectronEquationType electron_equation_type() const {
return static_cast<ElectronEquationType>(m_equations.type_equation(dof_electron()));
}
//! \brief Return true if an equation exist for this component
//!
//! \param component Index of the component (in the database)
bool is_active_component(index_t component) const {
specmicp_assert(component < m_data->nb_component() and component > no_species);
return m_equations.id_equation(dof_component(component)) != no_equation;
}
//! \brief Return the surface model
SurfaceEquationType surface_model() const {
if (ideq_surf() == no_equation)
return SurfaceEquationType::NoEquation;
return SurfaceEquationType::Equilibrium;
}
// Variables
// =========
// Primary
// -------
//! \brief Return the saturation of water
//!
//! \param x Vector of the main variables
scalar_t saturation_water(const Vector& x) const;
//! \brief Return the density of water
scalar_t density_water() const;
//! \brief Return the volume fraction of a mineral
//!
//! \param x Vector of the main variables
//! \param mineral Index of the mineral (in the database)
scalar_t saturation_mineral(const Vector& x, index_t mineral) const;
//! \brief Return the volume of minerals
//!
//! \param mineral Index of the mineral (in the database)
scalar_t molar_volume_mineral(index_t mineral) const {
return m_scaling_molar_volume*m_data->unsafe_molar_volume_mineral(mineral);
}
//! \brief Return the sum of saturation of the minerals
//!
//! This corresponds to the volume fraction of the solid phases (minus the inert phase)
//! \param x Vector of the main variables
scalar_t sum_saturation_minerals(const Vector& x) const;
//! \brief Return the log_10 of the component molality
//!
//! \param x Vector of the main variables
//! \param component Index of the aqueous component (in the database)
scalar_t log_component_molality(const Vector& x, index_t component) const {
specmicp_assert(ideq_paq(component) != no_equation and component < m_data->nb_component());
return x(ideq_paq(component));
}
//! \brief Return the molality of 'component'
//!
//! \param x Vector of the main variables
//! \param component Index of the aqueous component (in the database)
scalar_t component_molality(const Vector& x, index_t component) const {
return pow10(log_component_molality(x, component));
}
//! \brief Return the concentration of free sorption site
scalar_t free_sorption_site_concentration(const Vector& x) const {
return pow10(log_free_sorption_site_concentration(x));
}
//! \brief Return the log_10 of the free sorption site concentration
scalar_t log_free_sorption_site_concentration(const Vector& x) const {
specmicp_assert(ideq_surf() != no_equation);
return x(ideq_surf());
}
// Secondary
// ---------
//! \brief Return the concentration of secondary species 'aqueous'
//!
//! \param aqueous Index of the secondary aqueous species (in the database)
scalar_t secondary_molality(index_t aqueous) const {
if (not is_aqueous_active(aqueous)) return 0.0;
return m_second.secondary_molalities(dof_aqueous(aqueous));
}
//! \brief Return true if 'aqueous' is active
//!
//! i.e. Return true if all its component are present in the system
//! \param aqueous Index of the secondary aqueous species (in the database)
bool is_aqueous_active(index_t aqueous) const {
return m_equations.active_aqueous[dof_aqueous(aqueous)];
}
//! \brief Return log_10(γ_i) where i is a component
//!
//! γ is the activity coefficient
//! \param component Index of the aqueous component (in the database)
scalar_t log_gamma_component(index_t component) const {
return m_second.loggamma(dof_component_gamma(component));
}
//! \brief Return log_10(γ_j) where j is a secondary aqueous species
//!
//! γ is the activity coefficient
//! \param aqueous Index of the secondary aqueous species (in the database)
scalar_t log_gamma_secondary(index_t aqueous) const {
return m_second.loggamma(dof_aqueous_gamma(aqueous));
}
//! \brief Return the ionic strength
scalar_t ionic_strength() const noexcept {
return m_second.ionic_strength;
}
//! \brief Return the total concentration of 'component'
//!
//! Only use this method if the mass is conserved for 'component'
//! \param component Index of the aqueous component (in the database)
scalar_t total_concentration_bc(index_t component) const {
specmicp_assert((component > 0 and aqueous_component_equation_type(component)
== AqueousComponentEquationType::MassConservation)
or
( water_equation_type() == WaterEquationType::MassConservation));
return m_fixed_values(component);
}
//! \brief Return the fixed activity of 'component'
//!
//! Only use this method if 'component' has a fixed activity constraint
//! \param component Index of the aqueous component (in the database)
scalar_t fixed_activity_bc(index_t component) const {
specmicp_assert(aqueous_component_equation_type(component)
== AqueousComponentEquationType::FixedActivity);
return m_fixed_values(component);
}
//! \brief Return the fixed fugacity value for 'component'
scalar_t fixed_fugacity_bc(index_t component) const {
specmicp_assert(aqueous_component_equation_type(component)
== AqueousComponentEquationType::FixedFugacity);
return m_fixed_values(component);
}
// Gas
// ---
//! \brief Return the fugacity of 'gas'
//!
//! \param gas Index of the gas (in the database)
scalar_t gas_fugacity(index_t gas) const {
return m_second.gas_fugacity(gas);
}
//! \brief Return true if gas is active
//!
//! \param gas Index of the gas (in the database)
bool is_active_gas(index_t gas) const {
return m_equations.active_gas[gas];
}
//! \brief Return the volume fraction (total saturation) of the gas phase
scalar_t saturation_gas_phase() const noexcept {
return m_second.saturation_gas;
}
// Sorbed species
// --------------
//! \brief Return the surface total concentration
const scalar_t& surface_total_concentration() const {
return m_fixed_values(dof_surface());
}
//! \brief Return true if 'sorbed' is an active species
//! \param sorbed Index of the sorbed species (in the database)
bool is_active_sorbed(index_t sorbed) const {
return m_equations.active_sorbed[sorbed];
}
//! \brief Return the molality of the sorbed species 'sorbed'
//! \param sorbed Index of the sorbed species (in the database)
const scalar_t& sorbed_species_concentration(index_t sorbed) const {
return m_second.sorbed_concentrations(sorbed);
}
// Pressure and temperature
// ------------------------
//! \brief Return the gas pressure
//!
//! This is a fixed value (1 atm)
scalar_t gas_total_pressure() const {
return units::convert_pressure(1.01325e5, length_unit());
}
//! \brief Return the temperature
//!
//! This is a fixed value (25°C)
scalar_t temperature() const noexcept {
return 273.16+25;
}
// Solution
// =================
//! \brief Return the equilibrium state of the system, the Solution of the speciation problem
//!
//! \param xtot the complete set of main variables
//! \param x the reduced set of main variables, only the variables with an equation
AdimensionalSystemSolution get_solution(Vector& xtot, const Vector& x);
// Algorithm
// #########
//! \brief Compute the ionic strength
//!
//! \param x Vector of the main variables
void set_ionic_strength(const Vector& x);
//! \brief Compute the activity coefficients
//!
//! \param x Vector of the main variables
void compute_log_gamma(const Vector& x);
//! \brief Compute the secondary aqueous species molalities
//!
//! \param x Vector of the main variables
void set_secondary_concentration(const Vector& x);
//! \brief Compute the secondary variables
//!
//! \param x Vector of the main variables
void set_secondary_variables(const Vector& x);
//! \brief Compute the gas phase volume fraction
//!
//! \param x Vector of the main variables
void set_saturation_gas_phase(const Vector& x);
//! \brief Compute the fugacity for all the gas
//!
//! \param x Vector of the main variables
void set_pressure_fugacity(const Vector& x);
//! \brief Compute the sorbed species concentrations
//!
//! \param x Vector of the main variables
void set_sorbed_concentrations(const Vector& x);
//! \brief This function is called at the beginning of each iteration by the solver
//!
//! It does the fixed-point iteration to compute the secondary variables
//! \param x Vector of the main variables
//! \param norm_residual Norm of the current residuals
bool hook_start_iteration(const Vector &x, scalar_t norm_residual);
//! \brief Return a scale factor to avoid negative mass during Newton's iteration
//!
//! \param x Vector of the main variables
//! \param update Update of the current iteration
double max_lambda(const Vector &x, const Vector &update);
//! \brief Return the component that does not exist in the solution (inactive dof)
const std::vector<index_t>& get_non_active_component() {return m_equations.nonactive_component;}
//! \brief A reasonable (well... maybe...) starting guess
//!
//! \param xtot Vector of the main variables
//! \sa #reasonable_starting_guess
void reasonable_starting_guess(Vector& xtot);
//! \brief A reasonable (maybe...) restarting guess
//!
//! \param xtot Vector of the main variables
//! \sa #reasonable_restarting_guess
void reasonable_restarting_guess(Vector& xtot);
//! \brief Return true if 'component' is the charge keeper
//!
//! The charge keeper is the component added or removed to satisfy the charge balance
//! \param component Index of the aqueous component (in the database)
bool is_charge_keeper(index_t component)
{
return (aqueous_component_equation_type(component) == AqueousComponentEquationType::ChargeBalance);
}
//! \brief Compute the jacobian analytically
void analytical_jacobian(Vector& x, Matrix& jacobian);
//! \brief Compute the jacobian using finite difference
void finite_difference_jacobian(Vector& x, Matrix& jacobian);
//! \brief Set the units
void set_units(const units::UnitsSet& unit_set) {
units::UnitBaseClass::set_units(unit_set);
m_scaling_molar_volume = m_data->scaling_molar_volume(unit_set.length);
}
// Private Members and attributes
// ##############################
private:
// Jacobian
// ########
//! \brief Compute the water equation contribution to the Jacobian
//! \param x Reduced vector of the main variables
//! \param jacobian Dense matrix containing the jacobian
void jacobian_water(Vector& x, Matrix& jacobian);
//! \brief Compute the aqueous components equation contribution to the Jacobian
//! \param x Reduced vector of the main variables
//! \param jacobian Dense matrix containing the jacobian
void jacobian_aqueous_components(Vector& x, Matrix& jacobian);
//! \brief Compute the mineral equations contribution to the Jacobian
//! \param x Reduced vector of the main variables
//! \param jacobian Dense matrix containing the jacobian
void jacobian_minerals(Vector& x, Matrix& jacobian);
//! \brief Compute the contribution of the surface sorption equation to te Jacobian
//! \param x Reduced vector of the main variables
//! \param jacobian Dense matrix containing the jacobian
void jacobian_surface(Vector& x, Matrix& jacobian);
// Equation numbering
// ##################
//! \brief Number the equations
//! \param constraints the constraints to apply to the system
//! \sa number_eq_aqueous_component
void number_eq(const AdimensionalSystemConstraints& constraints);
//! \brief Number the equations for the aqueous components
//! \param constraints the constraints to apply to the system
//! \param[in,out] neq the number of equations in the system
//! \sa number_eq
void number_eq_aqueous_component(
const AdimensionalSystemConstraints& constraints,
index_t& neq
);
// Setter
// ######
// main variables
// --------------
// they are set by the solver
// Secondary variables
// -------------------
//! \brief Return a reference to log_10(γ_i) where i is a component
scalar_t& log_gamma_component(index_t component) {
return m_second.loggamma(dof_component_gamma(component));
}
//! \brief Return a reference to log_10(γ_j) where j is a secondary aqueous species
scalar_t& log_gamma_secondary(index_t aqueous) {
return m_second.loggamma(dof_aqueous_gamma(aqueous));
}
//! \brief Return a reference to the ionic strength
scalar_t& ionic_strength() {
return m_second.ionic_strength;
}
// Attributes
// ##########
//! \struct AdimensionalSystem::SecondaryVariables
//! \brief Contains information about the secondary variables
struct SecondaryVariables {
scalar_t ionic_strength {0.0}; //!< The ionic Strength
scalar_t saturation_gas {0.0}; //!< The gas saturation
Vector secondary_molalities; //!< The secondary molalities
Vector loggamma; //!< The log of activity coefficients
Vector gas_fugacity; //!< The gas fugacities
Vector sorbed_concentrations; //!< The sorbed concentrations
//! \brief Initialization without a previous solution
SecondaryVariables(const RawDatabasePtr& data);
//! \brief Initialization with a previous solution
SecondaryVariables(const AdimensionalSystemSolution& previous_solution);
};
//! \struct IdEquations
//! \brief BookKeeper for the equations id and type
struct IdEquations {
index_t nb_tot_variables;
index_t nb_free_variables;
index_t nb_complementarity_variables;
std::vector<index_t> ideq;
std::vector<index_t> component_equation_type;
std::vector<index_t> fixed_activity_species;
std::vector<index_t> nonactive_component;
std::vector<bool> active_aqueous;
std::vector<bool> active_gas;
std::vector<bool> active_sorbed;
//! \brief Initialize the data structure
IdEquations(index_t nb_dofs, const RawDatabasePtr& data);
//! \brief Return the equation id
const index_t& id_equation(index_t dof) const {
return ideq[dof];
}
//! \brief Return a reference to the equation id
index_t& id_equation(index_t dof) {
return ideq[dof];
}
//! \brief Return a reference to the type of equation of 'dof'
index_t& type_equation(index_t dof) {
return component_equation_type[dof];
}
//! \brief Return the equation type for 'dof'
index_t type_equation(index_t dof) const {
return component_equation_type[dof];
}
//! \brief Return the related species for dof
//!
//! The exact meaning of this relation is dependant upon the equation type
index_t& related_species(index_t dof) {
return fixed_activity_species[dof];
}
//! \brief Add a non active component to the system
void add_non_active_component(index_t id) {
nonactive_component.push_back(id);
}
//! \brief Add an equation
void add_equation(index_t id, index_t *neq) {
ideq[id] = *neq;
++(*neq);
}
//! \brief Set the active flag of aqueous species 'id' to 'is_active'
void set_aqueous_active(index_t id, bool is_active) {
active_aqueous[id] = is_active;
}
//! \brief Set the active flag of gas 'id' to 'is_active'
void set_gas_active(index_t id, bool is_active) {
active_gas[id] = is_active;
}
//! \brief Set the active flag of sorbed species 'id' to 'is_active'
void set_sorbed_active(index_t id, bool is_active) {
active_sorbed[id] = is_active;
}
};
bool not_in_linesearch;
scalar_t m_inert_volume_fraction;
scalar_t m_scaling_molar_volume;
Vector m_fixed_values;
SecondaryVariables m_second;
IdEquations m_equations;
};
} // end namespace specmicp
#endif // SPECMICP_ADIMENSIONALSYSTEM_HPP
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