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adimensional_system.cpp
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/* =============================================================================
Copyright (c) 2014-2017 F. Georget <fabieng@princeton.edu> Princeton University
Copyright (c) 2017-2018 F. Georget <fabien.georget@epfl.ch> EPFL
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. Neither the name of the copyright holder 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 HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(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. *
============================================================================= */
#include "adimensional_system.hpp"
#include "adimensional_system_solution.hpp"
#include "specmicp_common/log.hpp"
#include "specmicp_common/physics/constants.hpp"
#include "specmicp_common/physics/laws.hpp"
#include <cmath>
#include <random>
#include <iostream>
// uncomment to activate the finite difference jacobian
// deprecated: use the cmake option instead
// #define SPECMICP_DEBUG_EQUATION_FD_JACOBIAN
namespace specmicp {
static const scalar_t log10 = std::log(10.0);
// Constructor
// ===========
// No previous solution
// --------------------
AdimensionalSystem::AdimensionalSystem(
RawDatabasePtr& ptrdata,
const AdimensionalSystemConstraints& constraints,
const AdimensionalSystemOptions& options,
const units::UnitsSet& units_set
):
AdimemsionalSystemNumbering(ptrdata),
OptionsHandler<AdimensionalSystemOptions>(options),
units::UnitBaseClass(units_set),
m_inert_volume_fraction(constraints.inert_volume_fraction),
m_second(ptrdata.get()),
m_equations(total_dofs(), ptrdata),
m_constraints(constraints)
{
specmicp_assert(ptrdata->is_valid());
m_fixed_values.setZero(ptrdata->nb_component()+ptrdata->nb_ssites()+1);
//number_eq(constraints);
}
// Previous solution
// -----------------
AdimensionalSystem::AdimensionalSystem(
RawDatabasePtr& ptrdata,
const AdimensionalSystemConstraints& constraints,
const AdimensionalSystemSolution& previous_solution,
const AdimensionalSystemOptions& options,
const units::UnitsSet& units_set
):
AdimemsionalSystemNumbering(ptrdata),
OptionsHandler<AdimensionalSystemOptions>(options),
units::UnitBaseClass(units_set),
m_inert_volume_fraction(constraints.inert_volume_fraction),
m_second(previous_solution, ptrdata.get()),
m_equations(total_dofs(), ptrdata),
m_constraints(constraints)
{
specmicp_assert(ptrdata->is_valid());
m_fixed_values.setZero(ptrdata->nb_component()+ptrdata->nb_ssites()+1);
//number_eq(constraints);
}
// Secondary variables constructor
// ===============================
// No previous solution
// --------------------
AdimensionalSystem::SecondaryVariables::SecondaryVariables(
database::DataContainer* data
):
secondary_molalities(Vector::Zero(data->nb_aqueous())),
loggamma(Vector::Zero(data->nb_component()+data->nb_aqueous())),
gas_fugacity(Vector::Zero(data->nb_gas())),
gas_concentration(Vector::Zero(data->nb_gas())),
sorbed_concentrations(Vector::Zero(data->nb_sorbed())),
molar_fractions(Vector::Zero(data->nb_solid_solutions())),
logactivity_solid_phases(Vector::Zero(data->nb_mineral()))
{}
// Previous solution
// -----------------
AdimensionalSystem::SecondaryVariables::SecondaryVariables(
const AdimensionalSystemSolution& previous_solution,
database::DataContainer* data
):
secondary_molalities(previous_solution.secondary_molalities),
loggamma(previous_solution.log_gamma),
gas_fugacity(previous_solution.gas_fugacities),
gas_concentration(Vector::Zero(previous_solution.gas_fugacities.rows())),
sorbed_concentrations(previous_solution.sorbed_molalities),
molar_fractions(Vector::Zero(data->nb_solid_solutions())),
logactivity_solid_phases(Vector::Zero(data->nb_mineral()))
{
// ToDo : initialization of solid solutions
}
// IdEquations constructor
// =======================
AdimensionalSystem::IdEquations::IdEquations(
index_t nb_dofs,
const RawDatabasePtr& data
):
ideq(nb_dofs, no_equation),
component_equation_type(data->nb_component()+data->nb_ssites()+1, no_equation),
fixed_activity_species(data->nb_component()+1, no_species),
active_aqueous(data->nb_aqueous(), false),
active_gas(data->nb_gas(), false),
active_sorbed(data->nb_sorbed()),
active_ssol(data->nb_solid_solutions(), true)
{}
// Equation numbering
// ==================
#define spc_tmp_HAS_SOLID_SOLUTION true
#define spc_tmp_NO_SOLID_SOLUTION false
template <>
void AdimensionalSystem::number_eq_minerals<spc_tmp_NO_SOLID_SOLUTION>(
const AdimensionalSystemConstraints& constraints,
index_t& neq
);
template <>
void AdimensionalSystem::number_eq_minerals<spc_tmp_HAS_SOLID_SOLUTION>(
const AdimensionalSystemConstraints& constraints,
index_t& neq
);
template <>
void AdimensionalSystem::number_eq_surfaces<SurfaceEquationType::Equilibrium>(
const AdimensionalSystemConstraints& constraints,
index_t& neq
);
template <>
void AdimensionalSystem::number_eq_surfaces<SurfaceEquationType::EDL>(
const AdimensionalSystemConstraints& constraints,
index_t& neq
);
// Note : this function also computes scaling factor that would be used in the computation
// ------
void AdimensionalSystem::number_eq(
)
{
const AdimensionalSystemConstraints& constraints = m_constraints;
index_t neq = 0;
// units
compute_scaling_factors();
// Water
// =====
if (constraints.water_equation != WaterEquationType::NoEquation) {
number_eq_water(constraints, neq);
}
// Aqueous components
// ==================
number_eq_aqueous_component(constraints, neq);
// Surface model
// =============
// only activate surface model if at least one concentration is positive
if (constraints.surface_model.model_type == SurfaceEquationType::Equilibrium) {
number_eq_surfaces<SurfaceEquationType::Equilibrium>(constraints, neq);
}
else if (constraints.surface_model.model_type == SurfaceEquationType::EDL) {
number_eq_surfaces<SurfaceEquationType::EDL>(constraints, neq);
}
else {
m_equations.type_equation(dof_surface_potential()) = static_cast<index_t>(SurfaceEquationType::NoEquation);
}
// Secondary species
// =================
// Secondary aqueous species
// -------------------------
bool solve_electron_equation = activate_secondary_species(constraints);
// Gas
// ---
activate_gas(constraints);
// Sorbed species
// --------------
if (surface_model() == SurfaceEquationType::NoEquation or constraints.immobile_disabled) {
for (index_t s: m_data->range_sorbed()) {
m_equations.set_sorbed_active(s, false);
}
}
else {
activate_sorbed_species(constraints);
}
// Electron equation
// -----------------
if (solve_electron_equation)
{
number_eq_electron(constraints, neq);
}
// Minerals
// ========
if (constraints.immobile_disabled) {
m_equations.nb_free_variables = neq;
} else {
if (get_options().solve_solid_solutions) {
number_eq_minerals<spc_tmp_HAS_SOLID_SOLUTION>(constraints, neq);
} else {
number_eq_minerals<spc_tmp_NO_SOLID_SOLUTION>(constraints, neq);
}
}
m_equations.nb_tot_variables = neq;
m_equations.nb_complementarity_variables = m_equations.nb_tot_variables - m_equations.nb_free_variables;
}
void AdimensionalSystem::number_eq_water(
const AdimensionalSystemConstraints& constraints,
index_t& neq
)
{
m_equations.type_equation(dof_water()) = static_cast<index_t>(constraints.water_equation);
if (constraints.water_equation == WaterEquationType::MassConservation)
{
m_fixed_values(dof_water()) = constraints.total_concentrations(dof_water());
if (constraints.water_partial_pressure.use_partial_pressure_model)
{
m_equations.use_water_pressure_model = true;
m_equations.water_pressure_model = constraints.water_partial_pressure.partial_pressure_model;
}
}
else if (constraints.water_equation == WaterEquationType::FixedSaturation)
{
m_fixed_values(dof_water()) = constraints.water_parameter;
}
else
{
specmicp_assert(constraints.water_equation == WaterEquationType::SaturatedSystem);
}
m_equations.add_equation(dof_water(), &neq);
}
void AdimensionalSystem::number_eq_aqueous_component(
const AdimensionalSystemConstraints& constraints,
index_t& neq
)
{
using EqT = AqueousComponentEquationType;
// First set the charge keeper
if (constraints.charge_keeper != no_species)
{
if (constraints.charge_keeper == 0 or constraints.charge_keeper > m_data->nb_component())
{
throw std::invalid_argument("The charge keeper must be an aqueous component. Invalid argument : "
+ std::to_string(constraints.charge_keeper));
}
m_equations.type_equation(dof_component(constraints.charge_keeper)) = static_cast<index_t>(EqT::ChargeBalance);
}
// Then go over fix fugacity gas
for (const auto& it: constraints.fixed_fugacity_cs)
{
if (m_equations.type_equation(dof_component(it.id_component)) != static_cast<index_t>(EqT::NoEquation))
{
throw std::invalid_argument("Component '" + m_data->components.get_label(it.id_component)
+ "' is already constrained, a fixed fugacity condition can not be applied");
}
m_equations.type_equation(dof_component(it.id_component)) = static_cast<int>(EqT::FixedFugacity);
m_fixed_values(it.id_component) = it.log_value;
m_equations.related_species(it.id_component) = it.id_gas;
}
// Then over the fixed activity species
for (const auto& it: constraints.fixed_activity_cs)
{
if (m_equations.type_equation(dof_component(it.id_component)) != static_cast<index_t>(EqT::NoEquation))
{
throw std::invalid_argument("Component '" + m_data->components.get_label(it.id_component)
+ "' is already constrained, a fixed activity condition can not be applied.");
}
m_equations.type_equation(dof_component(it.id_component)) = static_cast<index_t>(EqT::FixedActivity);
m_fixed_values(it.id_component) = it.log_value;
}
// Then the fixed molality components
for (const auto& it: constraints.fixed_molality_cs)
{
if (m_equations.type_equation(dof_component(it.id_component)) != static_cast<index_t>(EqT::NoEquation))
{
throw std::invalid_argument("Component '" + m_data->components.get_label(it.id_component)
+ "' is already constrained, a fixed molality condition can not be applied.");
}
m_equations.type_equation(dof_component(it.id_component)) = static_cast<index_t>(EqT::FixedMolality);
m_fixed_values(it.id_component) = it.log_value;
}
for (const auto& it: constraints.fixed_SI_cs)
{
if (m_equations.type_equation(dof_component(it.id_component)) != static_cast<index_t>(EqT::NoEquation))
{
throw std::invalid_argument("Component '"+ m_data->components.get_label(it.id_component)
+ "' is already constraint, a fixed saturation index condition can not be applied.");
}
m_equations.type_equation(dof_component(it.id_component)) = static_cast<index_t>(EqT::FixedSaturationIndex);
m_fixed_values(it.id_component) = it.saturation_index;
m_equations.related_species(it.id_component) = it.id_mineral;
}
// Finally number the equations
for (index_t component: m_data->range_aqueous_component())
{
// If no equation is assigned yet
if (m_equations.type_equation(dof_component(component)) == static_cast<index_t>(EqT::NoEquation))
{
// Mass is conserved for this component
//###FIXME: H[+], HO[-]
const scalar_t& total_concentration = constraints.total_concentrations(dof_component(component));
if (std::abs(total_concentration) > get_options().cutoff_total_concentration)
{
m_equations.type_equation(dof_component(component)) = static_cast<index_t>(EqT::MassConservation);
m_fixed_values(dof_component(component)) = total_concentration;
m_equations.add_equation(component, &neq);
}
else // add component to the nonactive component list
{
m_equations.add_non_active_component(component);
}
}
// If equation is already assigned
else
{
m_equations.add_equation(component, &neq);
}
}
if (stdlog::ReportLevel() >= logger::Debug and m_equations.nonactive_component.size() > 0)
{
// if in debug mode list the non active components
DEBUG << "Non active components :";
for (auto it: m_equations.nonactive_component)
{
DEBUG << " - " << it;
}
}
}
bool AdimensionalSystem::activate_secondary_species(
const AdimensionalSystemConstraints& constraints
)
{
bool include_half_cell_reaction = (constraints.electron_constraint.equation_type != ElectronEquationType::NoEquation);
bool solve_electron_equation {false};
for (auto j: m_data->range_aqueous())
{
bool can_exist { true };
if ( include_half_cell_reaction or not m_data->is_half_cell_reaction(j))
for (const auto& k: m_equations.nonactive_component)
{
if (m_data->nu_aqueous(j, k) != 0.0)
{
can_exist = false;
break;
}
}
else
{
can_exist = false;
}
m_equations.set_aqueous_active(j, can_exist);
if (can_exist and m_data->is_half_cell_reaction(j))
solve_electron_equation = true;
}
return solve_electron_equation;
}
void AdimensionalSystem::activate_gas(
const AdimensionalSystemConstraints& constraints)
{
for (index_t k: m_data->range_gas())
{
bool can_exist = true;
for (const index_t& n: m_equations.nonactive_component)
{
if (m_data->nu_gas(k, n) != 0.0)
{
can_exist = false;
break;
}
}
m_equations.set_gas_active(k, can_exist);
}
}
void AdimensionalSystem::activate_sorbed_species(
const AdimensionalSystemConstraints& constraints
)
{
// non active sorbed : no surface site or non active component
for (index_t s: m_data->range_sorbed()) {
if (surface_total_concentration(m_data->sorbed.surface_site(s)) == 0) {
m_equations.set_sorbed_active(s, false);
} else {
bool can_exist = true;
for (const index_t& k: m_equations.nonactive_component)
{
if (m_data->nu_sorbed(s, k) != 0.0)
{
can_exist = false;
break;
}
}
m_equations.set_sorbed_active(s, can_exist);
}
}
}
void AdimensionalSystem::number_eq_electron(
const AdimensionalSystemConstraints& constraints,
index_t& neq
)
{
m_equations.add_equation(dof_electron(), &neq);
m_equations.type_equation(dof_electron()) =
static_cast<index_t>(constraints.electron_constraint.equation_type);
if (constraints.electron_constraint.equation_type == ElectronEquationType::Equilibrium)
{
m_fixed_values(dof_electron()) = 0.0;
}
else if (constraints.electron_constraint.equation_type == ElectronEquationType::FixedpE)
{
m_fixed_values(dof_electron()) = constraints.electron_constraint.fixed_value;
m_equations.related_species(dof_electron()) = constraints.electron_constraint.species;
//assert(m_fixed_activity_species[dof_electron()] >= 0
// and m_fixed_activity_species[dof_electron()] < m_data->nb_aqueous());
//assert(m_data->is_half_cell_reaction(m_fixed_activity_species[dof_electron()]));
}
// scaling
if (get_options().scaling_electron == 0.0)
{
for (index_t component : m_data->range_aqueous_component())
{
if (aqueous_component_equation_type(component)
== AqueousComponentEquationType::MassConservation)
{
get_options().scaling_electron = total_concentration_bc(component);
break;
}
}
}
}
bool AdimensionalSystem::mineral_can_precipitate(
index_t m,
const AdimensionalSystemConstraints& constraints
)
{
bool can_precipitate = true; // true if all the components of the mineral
// are present in the system
// just check that the molar volume exist
auto molar_volume = m_data->molar_volume_mineral(m);
// Remove minerals that cannot precipitate
for (index_t& k: m_equations.nonactive_component)
{
if (m_data->nu_mineral(m, k) != 0.0 and molar_volume > 0.0)
{
can_precipitate = false;
break; // this is not a mineral that can precipitate
}
}
// check if no precipitation is set
// if upper bound is 0, deactivate the mineral
if (not constraints.mineral_constraints.empty())
{
for (const MineralConstraint& v: constraints.mineral_constraints)
{
if (v.id_mineral == m)
{
if (v.param == 0) {
can_precipitate = false;
}
}
}
}
// Not an equation if fixed saturation index
for (const auto& it : constraints.fixed_SI_cs) {
if (it.id_mineral == m) {
can_precipitate = false;
}
}
return can_precipitate;
}
template <>
void AdimensionalSystem::number_eq_minerals<spc_tmp_NO_SOLID_SOLUTION>(
const AdimensionalSystemConstraints& constraints,
index_t& neq
)
{
// above equations are 'free' (i.e. non constrained)
// following equations are complementarity conditions
m_equations.nb_free_variables = neq;
for (index_t m: m_data->range_mineral())
{
if (mineral_can_precipitate(m, constraints))
{
m_equations.add_equation(dof_mineral(m), &neq);
}
}
// Minerals => no precipitation
//
// /!\ must be set after equations ids are set
if (not constraints.mineral_constraints.empty())
{
for (const MineralConstraint& v: constraints.mineral_constraints)
{
if (v.equation_type == MineralConstraintType::NoPrecipitation)
{
index_t idm = v.id_mineral;
if (idm == no_species or ideq_min(idm) == no_equation) continue;
if (not m_equations.is_box_constrained) {
m_equations.activate_box_constrained(neq);
}
m_equations.set_box_constrained(ideq_min(idm), v.param);
}
}
}
}
template <>
void AdimensionalSystem::number_eq_minerals<spc_tmp_HAS_SOLID_SOLUTION>(
const AdimensionalSystemConstraints& constraints,
index_t& neq
)
{
std::vector<bool> can_precipitate(m_data->nb_mineral(), true);
for (index_t m: m_data->range_mineral())
{
can_precipitate[m] = mineral_can_precipitate(m, constraints);
}
for (auto i: m_data->range_solid_solutions())
{
for (auto m=m_data->members_solid_solution(i);m;++m) {
specmicp_assert(can_precipitate[m.index()] = true);
m_equations.add_equation(dof_mineral(m.index()), &neq);
++m_equations.nb_free_variables;
}
}
// above equations are 'free' (i.e. non constrained)
m_equations.nb_free_variables = neq;
// following equations are complementarity conditions
for (index_t m: m_data->range_mineral())
{
if (can_precipitate[m] and ideq_min(m)==no_equation)
// can precipitate and not part of solid solution
{
m_equations.add_equation(dof_mineral(m), &neq);
}
}
// Minerals => no precipitation
//
// /!\ must be set after equations ids are set
if (not constraints.mineral_constraints.empty())
{
for (const MineralConstraint& v: constraints.mineral_constraints)
{
if (v.equation_type == MineralConstraintType::NoPrecipitation)
{
index_t idm = v.id_mineral;
if (idm == no_species or ideq_min(idm) == no_equation) continue;
if (not m_equations.is_box_constrained) {
m_equations.activate_box_constrained(neq);
}
m_equations.set_box_constrained(ideq_min(idm), v.param);
}
}
}
}
#undef spc_tmp_HAS_SOLID_SOLUTION
#undef spc_tmp_NO_SOLID_SOLUTION
template <>
void AdimensionalSystem::number_eq_surfaces<SurfaceEquationType::Equilibrium>(
const AdimensionalSystemConstraints& constraints,
index_t& neq
)
{
specmicp_assert(constraints.surface_model.total_ssite_concentrations.rows() == m_data->nb_ssites());
bool at_least_one = false;
for (index_t q: m_data->range_ssites()) {
const scalar_t tot_conc = constraints.surface_model.total_ssite_concentrations(q);
if (tot_conc > 0.0) {
// add the equation
m_equations.add_equation(dof_surface(q), &neq);
m_equations.type_equation(dof_surface(q)) = static_cast<index_t>(SurfaceEquationType::Equilibrium);
// setup the total concentration
m_fixed_values(dof_surface(q)) = tot_conc;
at_least_one = true;
} else {
m_equations.type_equation(dof_surface(q)) = static_cast<index_t>(SurfaceEquationType::NoEquation);
}
}
// No surface potential equation for this model
if (at_least_one) {
m_equations.type_equation(dof_surface_potential()) = static_cast<index_t>(SurfaceEquationType::Equilibrium);
} else {
m_equations.type_equation(dof_surface_potential()) = static_cast<index_t>(SurfaceEquationType::NoEquation);
}
m_fixed_values(dof_surface_potential()) = -1.0;
}
template <>
void AdimensionalSystem::number_eq_surfaces<SurfaceEquationType::EDL>(
const AdimensionalSystemConstraints& constraints,
index_t& neq
)
{
specmicp_assert(constraints.surface_model.total_ssite_concentrations.rows() == m_data->nb_ssites());
bool at_least_one = false;
for (index_t q: m_data->range_ssites()) {
const scalar_t tot_conc = constraints.surface_model.total_ssite_concentrations(q);
if (tot_conc > 0.0) {
// add the equation
m_equations.add_equation(dof_surface(q), &neq);
m_equations.type_equation(dof_surface(q)) = static_cast<index_t>(SurfaceEquationType::EDL);
// setup the total concentration
m_fixed_values(dof_surface(q)) = tot_conc;
at_least_one = true;
} else {
m_equations.type_equation(dof_surface(q)) = static_cast<index_t>(SurfaceEquationType::NoEquation);
}
}
if (at_least_one) {
m_equations.type_equation(dof_surface_potential()) = static_cast<index_t>(SurfaceEquationType::EDL);
m_equations.add_equation(dof_surface_potential(), &neq);
m_fixed_values(dof_surface_potential()) = constraints.surface_model.sorption_surface;
} else {
m_equations.type_equation(dof_surface_potential()) = static_cast<index_t>(SurfaceEquationType::NoEquation);
}
}
// Units
// =================
void AdimensionalSystem::set_units(const units::UnitsSet& unit_set)
{
units::UnitBaseClass::set_units(unit_set);
}
void AdimensionalSystem::compute_scaling_factors()
{
// /!\ scaling factors must be set at least once per call to this functions !
// the set should be = not *= because the scaling factors are typically set twice...
// One at creation, the other before solving
// (latter is necessary because units are always reset by solver)
m_scaling_molar_volume = m_data->scaling_molar_volume(get_units());
// Unit scaling for the gaseous total concentration
// transform mol/m^3 into the right unit (pressure are always in Pa)
switch (get_units().length) {
case units::LengthUnit::decimeter:
m_scaling_gas = 1e-3;
break;
case units::LengthUnit::centimeter:
m_scaling_gas = 1e-6;
break;
default:
m_scaling_gas = 1.0;
break;
}
if (get_units().quantity == units::QuantityUnit::millimoles) {
m_scaling_gas *= 1e3;
m_scaling_molality = 1e3;
}
}
// Sums
// ==========
// ----
scalar_t AdimensionalSystem::weigthed_sum_aqueous(index_t component) const
{
scalar_t sum = 0.0;
for (index_t aqueous: m_data->range_aqueous())
{
if (not is_aqueous_active(aqueous)) continue;
sum += m_data->nu_aqueous(aqueous,component)*secondary_molality(aqueous);
}
return sum;
}
scalar_t AdimensionalSystem::diff_weigthed_sum_aqueous(index_t diff_component, index_t component) const
{
scalar_t sum = 0.0;
for (index_t aqueous: m_data->range_aqueous())
{
if (not is_aqueous_active(aqueous)) continue;
sum += m_data->nu_aqueous(aqueous,diff_component)*m_data->nu_aqueous(aqueous,component)*secondary_molality(aqueous);
}
return sum;
}
// ----
scalar_t AdimensionalSystem::weigthed_sum_sorbed(index_t component) const
{
scalar_t sum = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
sum += m_data->nu_sorbed(s, component)*sorbed_species_concentration(s);
}
return sum;
}
scalar_t AdimensionalSystem::weigthed_sum_charge_sorbed() const
{
scalar_t sum = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
sum += m_data->charge_sorbed(s)*sorbed_species_concentration(s);
}
return sum;
}
scalar_t AdimensionalSystem::weigthed_sum_sorbed_ssite(index_t ssite) const
{
scalar_t sum = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
sum += m_data->nu_ssites(s, ssite)*sorbed_species_concentration(s);
}
return sum;
}
scalar_t AdimensionalSystem::diff_weigthed_sum_sorbed(index_t diff_component, index_t component) const
{
scalar_t sum = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
sum += m_data->nu_sorbed(s, diff_component)*m_data->nu_sorbed(s, component)*sorbed_species_concentration(s);
}
return sum;
}
scalar_t AdimensionalSystem::diff_surface_weigthed_sum_sorbed(index_t diff_ssite, index_t component) const
{
scalar_t sum = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
sum += m_data->nu_sorbed(s, component)*m_data->nu_ssites(s, diff_ssite)*sorbed_species_concentration(s);
}
return sum;
}
scalar_t AdimensionalSystem::diff_weigthed_sum_sorbed_ssite(index_t diff_component, index_t ssite) const
{
scalar_t sum = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
sum += m_data->nu_sorbed(s, diff_component)*m_data->nu_ssites(s, ssite)*sorbed_species_concentration(s);
}
return sum;
}
scalar_t AdimensionalSystem::diff_surface_weigthed_sum_sorbed_ssite(index_t diff_ssite, index_t ssite) const
{
scalar_t sum = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
sum += m_data->nu_ssites(s, diff_ssite)*m_data->nu_ssites(s, ssite)*sorbed_species_concentration(s);
}
return sum;
}
// ----
scalar_t AdimensionalSystem::weigthed_sum_mineral(const Vector& x, index_t component) const
{
scalar_t sum = 0.0;
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation or m_data->nu_mineral(m, component) == 0.0) continue;
const auto concentration = volume_fraction_mineral(x, m)/molar_volume_mineral(m);
sum += m_data->nu_mineral(m, component)*concentration;
}
return sum;
}
// ----
scalar_t AdimensionalSystem::weigthed_sum_gas(index_t component) const
{
scalar_t sum = 0.0;
for (index_t k: m_data->range_gas())
{
if (not is_active_gas(k) or m_data->nu_gas(k, component) == 0.0) continue;
sum += m_data->nu_gas(k, component)*gas_concentration(k);
}
return sum;
}
scalar_t AdimensionalSystem::diff_weigthed_sum_gas(index_t diff_component, index_t component) const
{
scalar_t sum = 0.0;
for (index_t k: m_data->range_gas())
{
if (not is_active_gas(k) or m_data->nu_gas(k, component) == 0.0) continue;
sum += m_data->nu_gas(k, diff_component)*m_data->nu_gas(k, component)*gas_concentration(k);
}
return sum;
}
scalar_t AdimensionalSystem::edl_sqrt_surface_potential() const
{
scalar_t B=0;
const scalar_t RT = constants::gas_constant*temperature();
if (ionic_strength() != 0.0)
{
B = std::sqrt( 8*RT
* constants::vacuum_permittivity*constants::water_dielectric_constant_25
* ionic_strength()*density_water_SI()
);
} else {
B = std::sqrt( 8*RT
* constants::vacuum_permittivity*constants::water_dielectric_constant_25
* 0.00001*density_water_SI()
);
}
return B;
}
// ================ //
// //
// Residuals //
// //
// ================ //
scalar_t AdimensionalSystem::residual_water_conservation(const Vector& x) const
{
specmicp_assert(water_equation_type() == WaterEquationType::MassConservation);
scalar_t res = total_concentration_bc(0);
const scalar_t conc_w = density_water() * volume_fraction_water(x);
scalar_t aqconc = 1.0/m_data->molar_mass_basis(0) + weigthed_sum_aqueous(0);
if (surface_model() != SurfaceEquationType::NoEquation)
aqconc += weigthed_sum_sorbed(0);
res -= m_scaling_molality * conc_w * aqconc;
res -= weigthed_sum_mineral(x, 0);
if (m_data->nb_gas() > 0)
res -= weigthed_sum_gas(0);
if (m_equations.use_water_pressure_model and m_equations.solve_pressure_model)
{
// water pressure
const scalar_t aporosity = m_second.porosity;
scalar_t sat_w = volume_fraction_water(x) / aporosity;
if (sat_w < 1)
{
const scalar_t pressure = m_equations.water_pressure_model(sat_w);
res -= m_scaling_gas*(aporosity - volume_fraction_water(x))*(
pressure / (constants::gas_constant*temperature()));
}
}
res /= total_concentration_bc(0);
return res;
}
scalar_t AdimensionalSystem::residual_water_saturation(const Vector& x) const
{
specmicp_assert(water_equation_type() == WaterEquationType::SaturatedSystem);
scalar_t res = 1 - volume_fraction_water(x) - m_inert_volume_fraction;
for (index_t mineral: m_data->range_mineral())
{
res -= volume_fraction_mineral(x, mineral);
}
return res;
}
scalar_t AdimensionalSystem::residual_water_fixed_saturation(const Vector& x) const
{
specmicp_assert(water_equation_type() == WaterEquationType::FixedSaturation);
scalar_t porosity = 1 - m_inert_volume_fraction;
for (index_t mineral: m_data->range_mineral())
{
porosity -= volume_fraction_mineral(x, mineral);
}
scalar_t res = fixed_saturation_bc()*porosity - volume_fraction_water(x);
return res;
}
scalar_t AdimensionalSystem::residual_component(const Vector &x, index_t component) const
{
specmicp_assert(aqueous_component_equation_type(component)
== AqueousComponentEquationType::MassConservation);
const scalar_t conc_w = density_water()*volume_fraction_water(x);
scalar_t res = total_concentration_bc(component);
scalar_t aqconc = component_molality(x, component)
+ weigthed_sum_aqueous(component);
if (surface_model() != SurfaceEquationType::NoEquation) {
aqconc += weigthed_sum_sorbed(component);
}
res -= m_scaling_molality * conc_w * aqconc;
res -= weigthed_sum_mineral(x, component);
if (m_data->nb_gas() > 0)
res -= weigthed_sum_gas(component);
res /= total_concentration_bc(component);
return res;
}
scalar_t AdimensionalSystem::residual_fixed_activity(const Vector& x, index_t component) const
{
specmicp_assert(aqueous_component_equation_type(component)
== AqueousComponentEquationType::FixedActivity);
scalar_t res = (fixed_activity_bc(component)
- log_gamma_component(component)
- log_component_molality(x, component)
);
res /= fixed_activity_bc(component);
return res;
}
scalar_t AdimensionalSystem::residual_fixed_molality(const Vector& x, index_t component) const
{
specmicp_assert(aqueous_component_equation_type(component)
== AqueousComponentEquationType::FixedMolality);
scalar_t res = (fixed_molality_bc(component)
- log_component_molality(x, component)
);
res /= fixed_molality_bc(component);
return res;
}
scalar_t AdimensionalSystem::residual_fixed_fugacity(const Vector& x, index_t component) const
{
specmicp_assert(aqueous_component_equation_type(component)
== AqueousComponentEquationType::FixedFugacity);
index_t id_g = m_equations.fixed_activity_species[component];
scalar_t res = fixed_fugacity_bc(component) + m_data->logk_gas(id_g);
for (index_t component: m_data->range_aqueous_component())
{
if (m_data->nu_gas(id_g, component) == 0) continue;
res -= m_data->nu_gas(id_g, component)*(
log_gamma_component(component)
+ log_component_molality(x, component)
);
}
res /= fixed_fugacity_bc(component);
return res;
}
scalar_t AdimensionalSystem::residual_fixed_saturation_index(const Vector& x, index_t component) const
{
specmicp_assert(aqueous_component_equation_type(component)
== AqueousComponentEquationType::FixedSaturationIndex);
const index_t id_m = m_equations.fixed_activity_species[component];
scalar_t res = fixed_saturation_index_bc(component) + m_data->logk_mineral(id_m);
for (index_t component: m_data->range_aqueous_component())
{
if (m_data->nu_mineral(id_m, component) == 0) continue;
res -= m_data->nu_mineral(id_m, component)*(
log_gamma_component(component)
+ log_component_molality(x, component)
);
}
// No scaling because Fixed Saturation Index is usually small and often 0.0 !
//res /= fixed_saturation_index_bc(component);
return res;
}
scalar_t AdimensionalSystem::residual_mineral(const Vector& x, index_t m) const
{
specmicp_assert(ideq_min(m) != no_equation);
scalar_t res = m_data->logk_mineral(m) + m_second.logactivity_solid_phases(m);
for (index_t i: m_data->range_aqueous_component())
{
if (m_data->nu_mineral(m, i) != 0)
{
const auto log_activity_i = log_component_molality(x, i) + log_gamma_component(i);
res -= m_data->nu_mineral(m, i)*log_activity_i;
}
}
if (ideq_electron() != no_equation and m_data->is_mineral_half_cell_reaction(m))
res -= m_data->nu_mineral(m, m_data->electron_index())*log_activity_electron(x);
return res;
}
scalar_t AdimensionalSystem::residual_charge_conservation(const Vector& x) const
{
scalar_t res = 0.0;
for (index_t i: m_data->range_aqueous_component())
{
if (m_data->charge_component(i) != 0 and ideq_paq(i) != no_equation)
res += m_data->charge_component(i)*component_molality(x, i);
}
for (index_t j: m_data->range_aqueous())
{
if (m_data->charge_aqueous(j) == 0 and not is_aqueous_active(j)) continue;
res += m_data->charge_aqueous(j)*secondary_molality(j);
}
if (surface_model() != SurfaceEquationType::NoEquation)
{
res += weigthed_sum_charge_sorbed();
}
return m_scaling_molality*res;
}
scalar_t AdimensionalSystem::residual_surface(const Vector &x, index_t q) const
{
specmicp_assert(surface_model() != SurfaceEquationType::NoEquation);
const scalar_t conc_w = density_water()*volume_fraction_water(x);
const scalar_t tot_conc_surf = surface_total_concentration(q);
scalar_t res = tot_conc_surf;
res -= m_scaling_molality*conc_w*(free_sorption_site_concentration(x, q) + weigthed_sum_sorbed_ssite(q));
return res/tot_conc_surf;
}
scalar_t AdimensionalSystem::residual_surface_potential(const Vector& x) const
{
scalar_t A = density_water_SI()*volume_fraction_water(x)*weigthed_sum_charge_sorbed()
*constants::faraday_constant/sorption_surface_area();
scalar_t B = edl_sqrt_surface_potential();
const scalar_t RT = constants::gas_constant*temperature();
B *= std::sinh(surface_potential(x) * constants::faraday_constant/(2*RT));
//std::cout << (A-B) << "\n";
return (A - B)/density_water_SI();// /(density_water_SI()*volume_fraction_water(x));
}
scalar_t AdimensionalSystem::residual_electron(const Vector &x) const
{
specmicp_assert(electron_equation_type() == ElectronEquationType::Equilibrium);
const scalar_t conc_w = density_water()*volume_fraction_water(x);
scalar_t res = 0.0;
res -= conc_w * weigthed_sum_aqueous(m_data->electron_index());
if (surface_model() != SurfaceEquationType::NoEquation)
res -= conc_w * weigthed_sum_sorbed(m_data->electron_index());
res -= weigthed_sum_mineral(x, m_data->electron_index());
if (m_data->nb_gas() > 0)
res -= weigthed_sum_gas(m_data->electron_index());
return res/get_options().scaling_electron;
}
void AdimensionalSystem::get_residuals(const Vector& x, Vector& residual)
{
residual.resize(total_variables());
// initialisation of 'main' secondary variables
// They are especially nessary if the finite difference jacobian is used
// and for the linesearch
m_second.porosity = porosity(x);
set_volume_fraction_gas_phase(x);
set_secondary_concentration(x);
if (get_options().solve_solid_solutions)
compute_solid_solutions(x);
set_sorbed_concentrations(x);
set_pressure_fugacity(x);
//
// water
if (ideq_w() != no_equation)
{
switch (water_equation_type())
{
case WaterEquationType::MassConservation:
residual(ideq_w()) = residual_water_conservation(x);
break;
case WaterEquationType::SaturatedSystem:
residual(ideq_w()) = residual_water_saturation(x);
break;
case WaterEquationType::FixedSaturation:
residual(ideq_w()) = residual_water_fixed_saturation(x);
break;
case WaterEquationType::NoEquation:
break;
}
}
// aqueous component
for (index_t i: m_data->range_aqueous_component())
{
switch (aqueous_component_equation_type(i))
{
case AqueousComponentEquationType::NoEquation:
break;
case AqueousComponentEquationType::MassConservation:
residual(ideq_paq(i)) = residual_component(x, i);
break;
case AqueousComponentEquationType::ChargeBalance:
residual(ideq_paq(i)) = residual_charge_conservation(x);
break;
case AqueousComponentEquationType::FixedActivity:
residual(ideq_paq(i)) = residual_fixed_activity(x, i);
break;
case AqueousComponentEquationType::FixedFugacity:
residual(ideq_paq(i)) = residual_fixed_fugacity(x, i);
break;
case AqueousComponentEquationType::FixedMolality:
residual(ideq_paq(i)) = residual_fixed_molality(x, i);
break;
case AqueousComponentEquationType::FixedSaturationIndex:
residual(ideq_paq(i)) = residual_fixed_saturation_index(x, i);
break;
}
}
// surface
if (surface_model() != SurfaceEquationType::NoEquation)
{
for (index_t q: m_data->range_ssites()) {
if (ideq_surf(q) != no_equation)
residual(ideq_surf(q)) = residual_surface(x, q);
}
if (ideq_surf_pot() != no_equation) {
residual(ideq_surf_pot()) = residual_surface_potential(x);
}
}
// mineral
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) != no_equation) residual(ideq_min(m)) = residual_mineral(x, m);
}
// electron
if (ideq_electron() != no_equation ) residual(ideq_electron()) = residual_electron(x);
}
// ================ //
// //
// Jacobian //
// //
// ================ //
void AdimensionalSystem::get_jacobian(Vector& x, Matrix& jacobian)
// //non-optimized Finite difference, for test only
#ifdef SPECMICP_DEBUG_EQUATION_FD_JACOBIAN
{
finite_difference_jacobian(x, jacobian);
return;
}
#else // analytical jacobian
{
analytical_jacobian(x, jacobian);
return;
}
#endif
void AdimensionalSystem::finite_difference_jacobian(Vector& x, Matrix& jacobian)
{
const int neq = total_variables();
Eigen::VectorXd res(neq);
Eigen::VectorXd perturbed_res(neq);
jacobian.setZero(neq, neq);
get_residuals(x, res);
for (int j=0; j<neq; ++j)
{
double h = 1e-8*std::abs(x(j));
if (h<1e-16) h = 1e-8;
double tmp = x(j);
x(j) += h;
h = x(j) - tmp;
get_residuals(x, perturbed_res);
for (int i=0; i<neq; ++i)
{
jacobian(i, j) = (perturbed_res(i) - res(i))/h;
}
x(j) = tmp;
}
}
void AdimensionalSystem::analytical_jacobian(Vector& x, Matrix& jacobian)
{
const int neq = total_variables();
jacobian.setZero(neq, neq);
// water
jacobian_water(x, jacobian);
// aqueous component
jacobian_aqueous_components(x, jacobian);
// surface
if (surface_model() != SurfaceEquationType::NoEquation) {
jacobian_surface(x, jacobian);
if (ideq_surf_pot() != no_equation) jacobian_surface_potential(x, jacobian);
}
// mineral equilibrium
jacobian_minerals(x, jacobian);
// electron
if (ideq_electron() != no_equation) jacobian_electron(x, jacobian);
}
void AdimensionalSystem::jacobian_water(Vector& x, Matrix& jacobian)
{
if (water_equation_type() == WaterEquationType::MassConservation)
{
const index_t idw = ideq_w();
const scalar_t rho_w = density_water();
const scalar_t factor = total_concentration_bc(0);
scalar_t tmp = - 1.0
/m_data->molar_mass_basis(0);
tmp -= weigthed_sum_aqueous(0);
tmp -= weigthed_sum_sorbed(0);
tmp *= m_scaling_molality*rho_w;
tmp -= -weigthed_sum_gas(0);
if (m_equations.use_water_pressure_model and m_equations.solve_pressure_model )
{
// The jacobian of the pressure model is
// computed using finite difference
const scalar_t sat_w = volume_fraction_water(x)/ porosity(x);
if (sat_w >= 1.0)
{
Vector residual;
get_residuals(x, residual);
// doesn't make sense to have a saturation
// bigger than one in this case
ERROR << "Saturation greater that one detected : "
<< sat_w
<< " - porosity : " << porosity(x)
<< " - tot vol frac : " << sum_volume_fraction_minerals(x)
<< ", skip pressure model \n current solution \n ---- \n"
<< x
<< "\n ---- \n"
<< "residuals \n ----- \n"
<< residual
<< "\n ------ \n";
}
else
{
// compute the perturbation
scalar_t sp = sat_w*(1.0 + eps_jacobian);
if (sp == 0.0) sp = eps_jacobian;
const scalar_t h = sp - sat_w;
// can we save one call here ? cache
const scalar_t pv_sds = m_equations.water_pressure_model(sp);
const scalar_t pv_s = m_equations.water_pressure_model(sat_w);
const scalar_t diff = (pv_sds - pv_s) / h;
// add the contribution
tmp -= m_scaling_gas/(constants::gas_constant*temperature()) *(
(1.0-sat_w)*diff - pv_s
);
}
}
jacobian(idw, idw) = tmp/factor;
// aqueous component
const scalar_t conc_w = density_water()*volume_fraction_water(x);
for (index_t k: m_data->range_aqueous_component())
{
if (ideq_paq(k) == no_equation) continue;
scalar_t tmp = 0.0;
tmp -= diff_weigthed_sum_aqueous(k, 0);
tmp -= diff_weigthed_sum_sorbed(k, 0);
// fixme gas
tmp *= m_scaling_molality*conc_w;
tmp -= diff_weigthed_sum_gas(k, 0);
jacobian(idw, ideq_paq(k)) = log10*tmp/factor;
}
// electron
if (ideq_electron() != no_equation)
{
scalar_t tmp = 0.0;
tmp -= diff_weigthed_sum_aqueous(m_data->electron_index(), 0);
tmp -= diff_weigthed_sum_sorbed(m_data->electron_index(), 0);
tmp*= m_scaling_molality*conc_w;
tmp -= diff_weigthed_sum_gas(m_data->electron_index(), 0);
jacobian(idw, ideq_electron()) = log10*tmp/factor;
}
// mineral
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation) continue;
jacobian(idw, ideq_min(m)) = -m_data->nu_mineral(m, 0)/molar_volume_mineral(m)/factor;
}
if (surface_model() != SurfaceEquationType::NoEquation)
{
// sorption sites
for (index_t q: m_data->range_ssites())
{
if (ideq_surf(q) == no_equation) continue;
scalar_t tmp=diff_surface_weigthed_sum_sorbed(q,0);
tmp *= -m_scaling_molality*conc_w;
jacobian(idw,ideq_surf(q)) = log10*tmp/factor;
}
// surface potential
if (ideq_surf_pot() != no_equation)
{
scalar_t tmp = 0;
for (index_t p: m_data->range_sorbed()) {
if (m_data->nu_sorbed(p, 0) == 0 )continue;
tmp += m_data->nu_sorbed(p, 0) *
m_data->charge_sorbed(p) *
m_second.sorbed_concentrations(p);
}
tmp *= constants::faraday_constant/(constants::gas_constant*temperature());
tmp *= m_scaling_molality*conc_w;
jacobian(idw, ideq_surf_pot()) = tmp/factor;
}
}
}
else if (water_equation_type() == WaterEquationType::SaturatedSystem)
{
const index_t idw = ideq_w();
jacobian(idw, idw) = -1;
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation) continue;
jacobian(idw, ideq_min(m)) = -1;
}
}
else if (water_equation_type() == WaterEquationType::FixedSaturation)
{
const index_t idw = ideq_w();
jacobian(idw, idw) = -1;
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation) continue;
jacobian(idw, ideq_min(m)) = - fixed_saturation_bc();
}
}
}
void AdimensionalSystem::jacobian_aqueous_components(Vector& x, Matrix& jacobian)
{
for (index_t i: m_data->range_aqueous_component())
{
const index_t idp = ideq_paq(i);
if (idp == no_equation) continue;
switch (aqueous_component_equation_type(i))
{
case AqueousComponentEquationType::NoEquation:
continue;
// Mass balance equation
// =====================
case AqueousComponentEquationType::MassConservation:
{
const scalar_t conc_w = density_water()*volume_fraction_water(x);
const scalar_t factor = total_concentration_bc(i);
// Aqueous components
for (index_t k: m_data->range_aqueous_component())
{
if (ideq_paq(k) == no_equation) continue;
scalar_t tmp_iip = 0;
if (k == i) tmp_iip -= component_molality(x, i);
tmp_iip -= diff_weigthed_sum_aqueous(k, i) + diff_weigthed_sum_sorbed(k, i);
tmp_iip *= m_scaling_molality*conc_w;
tmp_iip -= diff_weigthed_sum_gas(k, i);
jacobian(idp, ideq_paq(k)) = log10*tmp_iip/factor;
}
// Minerals
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation) continue;
jacobian(idp, ideq_min(m)) = - m_data->nu_mineral(m, i)/molar_volume_mineral(m)/factor;
}
// Water
if (ideq_w() != no_equation)
{
scalar_t tmp_iw = (
- component_molality(x, i)
- weigthed_sum_aqueous(i)
- weigthed_sum_sorbed(i)
);
tmp_iw *= m_scaling_molality*density_water();
jacobian(idp, ideq_w()) = tmp_iw/factor;
}
// Surface
if (surface_model() != SurfaceEquationType::NoEquation)
{
// sorption sites
for (index_t q: m_data->range_ssites())
{
if (ideq_surf(q) == no_equation) continue;
scalar_t tmp=diff_surface_weigthed_sum_sorbed(q,i);
tmp *= -m_scaling_molality*conc_w;
jacobian(idp, ideq_surf(q)) = log10*tmp/factor;
}
// surface potential
if (ideq_surf_pot() != no_equation)
{
scalar_t tmp = 0.0;
for (index_t p: m_data->range_sorbed()) {
if (not is_active_sorbed(p) or m_data->nu_sorbed(p, i) == 0) continue;
tmp += -m_data->nu_sorbed(p, i) *
m_data->charge_sorbed(p) *
m_second.sorbed_concentrations(p);
}
tmp *= constants::faraday_constant/(
constants::gas_constant*temperature());
tmp *= -m_scaling_molality*conc_w;
jacobian(idp, ideq_surf_pot()) = tmp/factor;
}
}
if (ideq_electron() != no_equation)
{
scalar_t tmp = 0.0;
tmp -= diff_weigthed_sum_aqueous(m_data->electron_index(), i);
tmp -= diff_weigthed_sum_sorbed(m_data->electron_index(), i);
tmp*= m_scaling_molality*conc_w;
tmp -= diff_weigthed_sum_gas(m_data->electron_index(), i);
jacobian(idp, ideq_electron()) = log10*tmp/factor;
}
break;
}
// Charge balance equation
// =======================
case AqueousComponentEquationType::ChargeBalance:
{
// Aqueous components
for (index_t k: m_data->range_aqueous_component())
{
const index_t idc = ideq_paq(k);
if (idc == no_equation) continue;
scalar_t tmp_drdb = 0.0;
if (m_data->charge_component(k) != 0.0)
tmp_drdb = m_data->charge_component(k)*component_molality(x,k);
// Secondary species
for (index_t j: m_data->range_aqueous())
{
if ( not is_aqueous_active(j)
or m_data->nu_aqueous(j, k) == 0.0
or m_data->charge_aqueous(j) == 0.0
)
continue;
tmp_drdb += m_data->nu_aqueous(j, k)
* m_data->charge_aqueous(j)
* secondary_molality(j);
}
// sorbed species
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)
or m_data->nu_sorbed(s, k) == 0.0
or m_data->charge_sorbed(s) == 0.0
) continue;
tmp_drdb += m_data->nu_sorbed(s, k)
* m_data->charge_sorbed(s)
* sorbed_species_concentration(s);
}
jacobian(idp, idc) = m_scaling_molality*log10*tmp_drdb;
}
if (surface_model() != SurfaceEquationType::NoEquation)
{
// Sorption sites
for (index_t q: m_data->range_ssites())
{
const index_t idq = ideq_surf(q);
if (idq == no_equation) continue;
scalar_t tmp_drdlsq = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)
or m_data->nu_ssites(s, q) == 0.0
or m_data->charge_sorbed(s) == 0.0
) continue;
tmp_drdlsq += m_data->nu_ssites(s, q)
* m_data->charge_sorbed(s)
* sorbed_species_concentration(s);
}
jacobian(idp, idq) = m_scaling_molality*log10*tmp_drdlsq;
}
// Surface potential
if (ideq_surf_pot() != no_equation) {
scalar_t tmp_drdpsi = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)
or m_data->charge_sorbed(s) == 0.0
) continue;
tmp_drdpsi += - std::pow(m_data->charge_sorbed(s), 2)
* sorbed_species_concentration(s);
}
jacobian(idp, ideq_surf_pot()) = m_scaling_molality*tmp_drdpsi*
constants::faraday_constant /
(constants::gas_constant*temperature());
}
}
break;
}
// Fixed activity equation
// =======================
case AqueousComponentEquationType::FixedActivity:
{
jacobian(idp, idp) = -1.0/fixed_activity_bc(i);
break;
}
// Fixed fugacity equation
// =======================
case AqueousComponentEquationType::FixedFugacity:
{
index_t id_g = m_equations.fixed_activity_species[i];
for (index_t k: m_data->range_aqueous_component())
{
if (ideq_paq(k) == no_equation or m_data->nu_gas(id_g, k) == 0.0) continue;
jacobian(idp, ideq_paq(k)) = -m_data->nu_gas(id_g, k)/fixed_fugacity_bc(i);
}
break;
} // end case
// Fixed molality component
// ========================
case AqueousComponentEquationType::FixedMolality:
{
jacobian(idp, idp) = -1.0/fixed_molality_bc(i);
break;
}
// Fixed saturation index
// ======================
case AqueousComponentEquationType::FixedSaturationIndex:
{
const auto id_m = m_equations.fixed_activity_species[i];
for (auto k: m_data->range_aqueous_component())
{
if (ideq_paq(k) == no_equation or m_data->nu_mineral(id_m, k) == 0.0) continue;
jacobian(idp, ideq_paq(k)) = -m_data->nu_mineral(id_m, k);
}
break;
}
} // end switch
}
}
void AdimensionalSystem::jacobian_minerals(Vector& x, Matrix& jacobian)
{
for (index_t m: m_data->range_mineral())
{
const index_t idm = ideq_min(m);
if (idm == no_equation) continue;
for (index_t i: m_data->range_aqueous_component())
{
if (ideq_paq(i) == no_equation) continue;
jacobian(idm, ideq_paq(i)) = -m_data->nu_mineral(m, i);
}
if (ideq_electron() != no_equation and m_data->is_mineral_half_cell_reaction(m))
jacobian(idm, ideq_electron()) = -m_data->nu_mineral(m, m_data->electron_index());
if (get_options().solve_solid_solutions) {
index_t ids = m_data->id_solid_solution_of_mineral(m);
if (ids != no_species) {
scalar_t tot_c = 0;
for (auto it=m_data->members_solid_solution(ids); it; ++it) {
tot_c += ( volume_fraction_mineral(x, it.index())
/m_data->molar_volume_mineral(it.index()) );
//std::cout << volume_fraction_mineral(x, it.index()) << " - ";
}
//std::cout << "p " << tot_c << std::endl;
if (tot_c > 0) {
for (auto it=m_data->members_solid_solution(ids); it; ++it) {
auto mc = it.index();
auto idmc = ideq_min(mc);
//std::cout << m_data->get_label_mineral(mc) << " =-= "
// << mc << " -=- " << idmc << std::endl;
jacobian(idm, idmc) += 1.0/std::pow(10, m_second.logactivity_solid_phases(mc)) *(
tot_c- (volume_fraction_mineral(x, mc)
/m_data->molar_volume_mineral(mc)))/std::pow(tot_c, 2);
}
}
}
}
}
}
void AdimensionalSystem::jacobian_surface(Vector& x, Matrix& jacobian)
{
for (index_t q: m_data->range_ssites())
{
const index_t idq = ideq_surf(q);
if (idq == no_equation) continue;
const scalar_t factor = m_scaling_molality*density_water()/surface_total_concentration(q);
// Water
if (ideq_w() != no_equation) {
scalar_t tmp = free_sorption_site_concentration(x, q)+weigthed_sum_sorbed_ssite(q);
jacobian(idq, ideq_w()) = -factor*tmp;
}
// Aqueous component
for (index_t i: m_data->range_aqueous_component()) {
const index_t idc = ideq_paq(i);
if (idc == no_equation) continue;
scalar_t tmp = log10*volume_fraction_water(x)*diff_weigthed_sum_sorbed_ssite(i, q);
jacobian(idq, idc) = -factor*tmp;
}
// Surface site
for (index_t qp: m_data->range_ssites()) {
const index_t idqp = ideq_surf(qp);
if (idqp == no_equation) continue;
scalar_t tmp = diff_surface_weigthed_sum_sorbed_ssite(qp, q);
if (qp == q) {
tmp += free_sorption_site_concentration(x, q);
}
jacobian(idq, idqp) = -factor*volume_fraction_water(x)*log10*tmp;
}
// Surface potential
if (ideq_surf_pot() != no_equation) {
scalar_t tmp = 0;
for (index_t p: m_data->range_sorbed()) {
if (not is_active_sorbed(p) or m_data->nu_ssites(p, q) == 0) continue;
tmp += m_data->nu_ssites(p, q) *
m_data->charge_sorbed(p) *
m_second.sorbed_concentrations(p);
}
tmp *= - constants::faraday_constant/(constants::gas_constant*temperature());
jacobian(idq, ideq_surf_pot()) = -factor*volume_fraction_water(x)*tmp;
}
// Mineral
// Electron
}
}
void AdimensionalSystem::jacobian_surface_potential(Vector& x, Matrix& jacobian)
{
const index_t idqs = ideq_surf_pot();
const scalar_t factor_A = constants::faraday_constant/sorption_surface_area();
specmicp_assert(idqs != no_equation);
// water
if (ideq_w() != no_equation) {
jacobian(idqs, ideq_w()) = factor_A*weigthed_sum_charge_sorbed();
}
// aq. compoments
for (index_t i: m_data->range_aqueous_component()) {
const index_t idc = ideq_paq(i);
if (idc == no_equation) continue;
scalar_t tmp = 0;
for (index_t p: m_data->range_sorbed()) {
if (m_data->nu_sorbed(p, i) == 0 ) continue;
tmp += m_data->nu_sorbed(p, i) *
m_data->charge_sorbed(p) *
m_second.sorbed_concentrations(p);
}
jacobian(idqs, idc) = factor_A*volume_fraction_water(x)*log10*tmp;
}
// surface site
{
for (index_t q: m_data->range_ssites()) {
if (ideq_surf(q) == no_equation) continue;
scalar_t tmp = 0.0;
for (index_t p: m_data->range_sorbed()) {
if (not is_active_sorbed(p) or m_data->nu_ssites(p, q)==0.0) continue;
tmp += m_data->charge_sorbed(p) * m_data->nu_ssites(p, q)*m_second.sorbed_concentrations(p);
}
jacobian(idqs, ideq_surf(q)) = factor_A*volume_fraction_water(x)*log10*tmp;
}
}
// surface potential
{
const scalar_t RT = constants::gas_constant*temperature();
scalar_t dB = constants::faraday_constant/(2*RT)*edl_sqrt_surface_potential();
dB *= std::cosh(surface_potential(x)*constants::faraday_constant/(2*RT) );
//
scalar_t dA = 0.0;
for (index_t p: m_data->range_sorbed()) {
if (not is_active_sorbed(p)) continue;
dA += -std::pow(m_data->charge_sorbed(p),2) *
m_second.sorbed_concentrations(p);
}
dA *= factor_A*density_water_SI()*volume_fraction_water(x)*constants::faraday_constant/(RT);
jacobian(idqs, idqs) = (dA-dB)/(density_water_SI());
}
}
void AdimensionalSystem::jacobian_electron(Vector& x, Matrix& jacobian)
{
const auto ide = ideq_electron();
const auto dofe = m_data->electron_index();
const scalar_t conc_w = density_water()*volume_fraction_water(x);
const scalar_t factor = get_options().scaling_electron;
// Aqueous components
for (index_t k: m_data->range_aqueous_component())
{
if (ideq_paq(k) == no_equation) continue;
scalar_t tmp_eip = 0;
tmp_eip -= diff_weigthed_sum_aqueous(k, dofe);
tmp_eip -= diff_weigthed_sum_sorbed(k, dofe);
tmp_eip *= conc_w;
tmp_eip -= diff_weigthed_sum_gas(k, dofe);
jacobian(ide, ideq_paq(k)) = log10*tmp_eip/factor;
}
// Minerals
for (index_t m: m_data->range_mineral())
{
if (ideq_min(m) == no_equation) continue;
jacobian(ide, ideq_min(m)) = - m_data->nu_mineral(m, dofe)/molar_volume_mineral(m)/factor;
}
// Water
if (ideq_w() != no_equation)
{
scalar_t tmp_iw = 0;
tmp_iw -= weigthed_sum_aqueous(dofe);
tmp_iw -= weigthed_sum_sorbed(dofe);
tmp_iw *= density_water();
jacobian(ide, ideq_w()) = tmp_iw/factor;
}
// Surface
// if (ideq_surf() != no_equation)
// {
// scalar_t tmp_s = -conc_w*diff_surface_weigthed_sum_sorbed(dofe);
// jacobian(ide, ideq_surf()) = tmp_s/factor;
// }
// Electron
if (ideq_electron() != no_equation)
{
scalar_t tmp = 0.0;
tmp -= diff_weigthed_sum_aqueous(dofe, dofe);
tmp -= diff_weigthed_sum_sorbed(dofe, dofe);
tmp*= conc_w;
tmp -= diff_weigthed_sum_gas(dofe, dofe);
jacobian(ide, ide) = log10*tmp/factor;
}
}
// ========================== //
// //
// Secondary variables //
// //
// ========================== //
void AdimensionalSystem::set_secondary_variables(const Vector& x)
{
m_second.porosity = 1 - sum_volume_fraction_minerals(x) - m_inert_volume_fraction;
if (surface_model() != SurfaceEquationType::NoEquation) {
set_sorbed_concentrations(x);
}
set_secondary_concentration(x);
compute_log_gamma(x);
set_volume_fraction_gas_phase(x);
set_pressure_fugacity(x);
if (get_options().solve_solid_solutions)
compute_solid_solutions(x);
}
void AdimensionalSystem::compute_solid_solutions(const Vector& x)
{
m_second.logactivity_solid_phases.setZero();
for (auto id: m_data->range_solid_solutions()) {
if (not m_equations.active_ssol[id]) continue;
scalar_t tot_c = 0;
for (auto it=m_data->members_solid_solution(id); it; ++it) {
tot_c += ( volume_fraction_mineral(x, it.index())
/m_data->molar_volume_mineral(it.index()) );
}
if (tot_c > 1e-10) {
for (auto it=m_data->members_solid_solution(id); it; ++it) {
auto m = it.index();
m_second.logactivity_solid_phases(m) = std::log10(
(volume_fraction_mineral(x, m)
/m_data->molar_volume_mineral(m))/tot_c);
}
}
}
}
void AdimensionalSystem::set_volume_fraction_gas_phase(const Vector& x)
{
m_second.volume_fraction_gas = m_second.porosity - volume_fraction_water(x);
}
void AdimensionalSystem::set_pressure_fugacity(const Vector& x)
{
const auto rt = constants::gas_constant*temperature();
for (index_t k: m_data->range_gas())
{
if (not is_active_gas(k)) continue;
scalar_t logp = -m_data->logk_gas(k);
for (index_t i: m_data->range_aqueous_component())
{
if (m_data->nu_gas(k, i) == 0.0) continue;
const auto log_activity_i = log_component_molality(x, i) + log_gamma_component(i);
logp += m_data->nu_gas(k, i) * log_activity_i;
}
if (ideq_electron() != no_equation and m_data->is_gas_half_cell_reaction(k))
logp += m_data->nu_gas(k, m_data->electron_index())*log_activity_electron(x);
m_second.gas_fugacity(k) = pow10(logp);
const scalar_t pressure = gas_fugacity(k)*gas_total_pressure();
const scalar_t concentration = m_scaling_gas*volume_fraction_gas_phase()*pressure/rt;
m_second.gas_concentration(k) = concentration;
}
}
void AdimensionalSystem::set_secondary_concentration(const Vector& x)
{
for (index_t j: m_data->range_aqueous())
{
if (not is_aqueous_active(j))
{
m_second.secondary_molalities(j) = 0.0;
continue;
}
scalar_t logconc = -m_data->logk_aqueous(j) - log_gamma_secondary(j);
for (index_t k: m_data->range_aqueous_component())
{
if (m_data->nu_aqueous(j, k) == 0) continue;
const auto log_activity_k = log_component_molality(x, k) + log_gamma_component(k);
logconc += m_data->nu_aqueous(j, k)*log_activity_k;
}
if (ideq_electron() != no_equation and m_data->is_half_cell_reaction(j))
logconc += m_data->nu_aqueous(j, m_data->electron_index())*log_activity_electron(x);
m_second.secondary_molalities(j) = pow10(logconc);
}
}
void AdimensionalSystem::set_sorbed_concentrations(const Vector& x)
{
for (index_t s: m_data->range_sorbed())
{
index_t q = m_data->sorbed.surface_site(s);
if (not is_active_sorbed(s))
{
m_second.sorbed_concentrations(s) = 0.0;
continue;
}
scalar_t logconc = -m_data->logk_sorbed(s) +
m_data->sorbed.nu_ssite(s)*log_free_sorption_site_concentration(x, q);
for (index_t k: m_data->range_aqueous_component())
{
if (m_data->nu_sorbed(s, k) != 0.0) {
const auto log_activity_k = log_component_molality(x, k) + log_gamma_component(k);
logconc += m_data->nu_sorbed(s, k)*log_activity_k;
}
}
if (ideq_electron() != no_equation and m_data->is_sorbed_half_cell_reaction(s))
logconc += m_data->nu_sorbed(s, m_data->electron_index())*log_activity_electron(x);
m_second.sorbed_concentrations(s) = pow10(logconc);
if (surface_model() == SurfaceEquationType::EDL) {
m_second.sorbed_concentrations(s) *= std::exp(
-m_data->charge_sorbed(s)*surface_potential(x)*constants::faraday_constant /
(constants::gas_constant*temperature()));
}
}
}
void AdimensionalSystem::set_ionic_strength(const Vector& x)
{
scalar_t ionic = 0;
for (index_t i: m_data->range_aqueous_component())
{
if (ideq_paq(i) == no_equation or m_data->charge_component(i) == 0) continue;
ionic += component_molality(x, i)*std::pow(m_data->charge_component(i),2);
}
for (index_t j: m_data->range_aqueous())
{
if (not is_aqueous_active(j) or m_data->charge_aqueous(j) == 0) continue;
ionic += secondary_molality(j)*std::pow(m_data->charge_aqueous(j),2);
}
ionic_strength() = ionic/2;
}
void AdimensionalSystem::compute_log_gamma(const Vector& x)
{
set_ionic_strength(x);
const scalar_t ion_str = ionic_strength();
const scalar_t sqrti = std::sqrt(ionic_strength());
vector_debye_huckel_component(ion_str, sqrti);
vector_debye_huckel_aqueous(ion_str, sqrti);
}
void AdimensionalSystem::vector_debye_huckel_component(
scalar_t ionic_strength,
scalar_t sqrt_ionic
)
{
Vector& log_gamma = m_second.loggamma;
Matrix& ionic_param = m_data->components.m_ionic_param.m_matrix;
using IoParam = database::IonicModelParameters;
for (auto i: m_data->range_aqueous_component())
{
const scalar_t zisquare = std::pow(ionic_param(i, IoParam::charge_ind), 2);
log_gamma(i) = - ( constants::Adebye * zisquare * sqrt_ionic);
log_gamma(i) /= ( 1 + ionic_param(i, IoParam::adebye_ind)*constants::Bdebye*sqrt_ionic);
log_gamma(i) += ionic_param(i, IoParam::bdebye_ind)*ionic_strength;
}
}
void AdimensionalSystem::vector_debye_huckel_aqueous(
scalar_t ionic_strength,
scalar_t sqrt_ionic
)
{
Vector& log_gamma = m_second.loggamma;
Matrix& ionic_param = m_data->aqueous.m_ionic_param.m_matrix;
using IoParam = database::IonicModelParameters;
const index_t offset = m_data->nb_component();
for (auto j: m_data->range_aqueous())
{
const scalar_t zisquare = std::pow(ionic_param(j, IoParam::charge_ind), 2);
log_gamma(offset+j) = - (constants::Adebye * zisquare * sqrt_ionic);
log_gamma(offset+j) /= ( 1 + ionic_param(j, IoParam::adebye_ind)*constants::Bdebye*sqrt_ionic);
log_gamma(offset+j) += ionic_param(j, IoParam::bdebye_ind)*ionic_strength;
}
}
bool AdimensionalSystem::hook_start_iteration(const Vector& x, scalar_t norm_residual)
{
//std::cout << get_options().solve_solid_solutions << std::endl;
if (not get_options().non_ideality)
{
set_secondary_variables(x);
// we still need to compute secondary species !
// if (norm_residual < nb_free_variables()*get_options().start_non_ideality_computation)
// {
// set_secondary_variables(x);
// }
return true;
}
not_in_linesearch = true;
scalar_t previous_norm = m_second.loggamma.norm();
if (previous_norm == 0) previous_norm = 1.0;
bool may_have_converged = false;
if (norm_residual < nb_free_variables()*get_options().start_non_ideality_computation)
{
m_equations.solve_pressure_model = true;
// Use fixed point iterations for non-ideality
for (int i=0; i<get_options().non_ideality_max_iter; ++i)
{
set_secondary_variables(x);
compute_log_gamma(x);
// convergence check
if ( (std::abs(previous_norm - m_second.loggamma.norm())/previous_norm <
get_options().non_ideality_tolerance)
//and (std::abs(previous_norm_2 - m_second.logactivity_solid_phases.norm())/previous_norm_2 <
// get_options().non_ideality_tolerance)
) {
may_have_converged = true;
break;
}
previous_norm = m_second.loggamma.norm();
}
}
else {
m_equations.solve_pressure_model = false;
}
return may_have_converged;
}
double AdimensionalSystem::max_lambda(const Vector& x, const Vector& update)
{
if (ideq_w() != no_equation)
{
return 1.0/std::max(
1.0, -update(0)/(get_options().under_relaxation_factor*x(0))
);
}
else
{
return 1.0;
}
}
AdimensionalSystemSolution AdimensionalSystem::unsafe_get_solution(
Vector& xtot,
const Vector& x
)
{
return AdimensionalSystemSolution(xtot,
m_second.secondary_molalities,
m_second.loggamma,
m_second.ionic_strength,
m_second.gas_fugacity,
m_second.sorbed_concentrations,
m_inert_volume_fraction);
}
AdimensionalSystemSolution AdimensionalSystem::get_solution(
Vector& xtot,
const Vector& x
)
{
// make sure secondary variables are ok
double previous_norm = m_second.loggamma.norm();
set_volume_fraction_gas_phase(x);
set_pressure_fugacity(x);
set_secondary_concentration(x);
if (surface_model() != SurfaceEquationType::NoEquation) {
set_sorbed_concentrations(x);
}
if (get_options().non_ideality)
{
compute_log_gamma(x);
if (get_options().solve_solid_solutions) {
compute_solid_solutions(x);
}
double error = std::abs(previous_norm - m_second.loggamma.norm());
if (error > 1e-6)
{
WARNING << "Activity coefficient have not converged !" << std::endl
<< "output can not be trusted\n Difference : "
+std::to_string(error);
}
}
// Set the correct value for the water volume fraction
if (ideq_w() == no_equation)
{
xtot(dof_water()) = volume_fraction_water(x);
}
return unsafe_get_solution(xtot, x);
}
// Water, saturation and density
// ==============================
scalar_t AdimensionalSystem::density_water() const {
return laws::density_water(get_units());
}
scalar_t AdimensionalSystem::density_water_SI() const {
return laws::density_water(units::SI_units);
}
scalar_t AdimensionalSystem::volume_fraction_water(const Vector& x) const
{
if (ideq_w() != no_equation)
return x(ideq_w());
else
return porosity(x);
}
scalar_t AdimensionalSystem::volume_fraction_mineral(const Vector& x, index_t mineral) const
{
specmicp_assert(mineral >= 0 and mineral < m_data->nb_mineral());
if (ideq_min(mineral) == no_equation) return 0.0;
else return x(ideq_min(mineral));
}
scalar_t AdimensionalSystem::sum_volume_fraction_minerals(const Vector& x) const
{
scalar_t sum_saturations = 0.0;
for (index_t mineral: m_data->range_mineral())
{
sum_saturations += volume_fraction_mineral(x, mineral);
}
return sum_saturations;
}
// Starting guess
// ==============
void AdimensionalSystem::reasonable_starting_guess(Vector &xtot)
{
xtot.resize(total_dofs());
xtot(dof_water()) = get_options().restart_water_volume_fraction;
for (index_t i: m_data->range_aqueous_component())
{
xtot(dof_component(i)) = -6.0;
}
if (surface_model() != SurfaceEquationType::NoEquation) {
for (index_t q: m_data->range_ssites()) {
if (ideq_surf(q) != no_equation)
xtot(dof_surface(q)) = std::log10(0.1*surface_total_concentration(q));
else
xtot(dof_surface(q)) = -HUGE_VAL;
}
if (surface_model() == SurfaceEquationType::EDL) {
xtot(dof_surface_potential()) = 1e-3;
} else {
xtot(dof_surface_potential()) = -HUGE_VAL;
}
}
if (ideq_electron() != no_equation)
xtot(dof_electron()) = -4;
else
xtot(dof_electron()) = -HUGE_VAL;
xtot.segment(offset_minerals(), m_data->nb_mineral()).setZero();
if (get_options().solve_solid_solutions)
{
for (auto d: m_data->range_solid_solutions())
{
for (auto m=m_data->members_solid_solution(d);m;++m)
{
xtot(dof_mineral(m)) = 0.1;
}
}
}
m_second = SecondaryVariables(m_data.get());
}
void AdimensionalSystem::reasonable_restarting_guess(Vector& xtot)
{
static std::mt19937 gen(std::random_device{}());
std::uniform_real_distribution<> dis(-2, 2);
xtot(dof_water()) = get_options().restart_water_volume_fraction;
for (index_t i: m_data->range_aqueous_component())
{
//if (xtot(dof_component(i)) > 0 or xtot(dof_component(i)) < -9)
xtot(i) = get_options().restart_concentration + dis(gen);
}
if (surface_model() != SurfaceEquationType::NoEquation) {
for (index_t q: m_data->range_ssites()) {
if (ideq_surf(q) != no_equation)
xtot(dof_surface(q)) = std::log10(0.1*surface_total_concentration(q));
else
xtot(dof_surface(q)) = -HUGE_VAL;
}
if (surface_model() == SurfaceEquationType::EDL) {
xtot(dof_surface_potential()) = 1e-3;
} else {
xtot(dof_surface_potential()) = -HUGE_VAL;
}
}
if (ideq_electron() != no_equation)
xtot(dof_electron()) = -4;
else
xtot(dof_electron()) = -HUGE_VAL;
xtot.segment(offset_minerals(), m_data->nb_mineral()).setZero();
if (get_options().solve_solid_solutions)
{
for (auto d: m_data->range_solid_solutions())
{
for (auto m=m_data->members_solid_solution(d);m;++m)
{
xtot(dof_mineral(m)) = 0.1;
}
}
}
m_second = SecondaryVariables(m_data.get());
}
} // end namespace specmicp

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