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adimensional_system.cpp
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/*-------------------------------------------------------------------------------
Copyright (c) 2014,2015 F. 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:
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 <cmath>
#include "adimensional_system.hpp"
#include "../../utils/log.hpp"
#include "../../physics/constants.hpp"
#include "../../physics/laws.hpp"
#include "adimensional_system_solution.hpp"
#include <random>
#include <iostream>
// uncomment to activate the finite difference jacobian
// #define SPECMICP_DEBUG_EQUATION_FD_JACOBIAN
namespace specmicp {
//constexpr scalar_t log10f() const {return std::log(10.0);}
//constexpr scalar_t log10 = log10f();
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),
m_equations(total_dofs(), ptrdata)
{
specmicp_assert(ptrdata->is_valid());
m_fixed_values.setZero(ptrdata->nb_component()+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),
m_equations(total_dofs(), ptrdata)
{
specmicp_assert(ptrdata->is_valid());
m_fixed_values.setZero(ptrdata->nb_component()+1);
number_eq(constraints);
}
// Secondary variables constructor
// ===============================
// No previous solution
// --------------------
AdimensionalSystem::SecondaryVariables::SecondaryVariables(
const RawDatabasePtr& 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()))
{}
// Previous solution
// -----------------
AdimensionalSystem::SecondaryVariables::SecondaryVariables(
const AdimensionalSystemSolution& previous_solution
):
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)
{}
// IdEquations constructor
// =======================
AdimensionalSystem::IdEquations::IdEquations(
index_t nb_dofs,
const RawDatabasePtr& data
):
ideq(nb_dofs, no_equation),
component_equation_type(data->nb_component()+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())
{}
// Equation numbering
// ==================
// Note : this function also computes scaling factor that would be used in the computation
// ------
void AdimensionalSystem::number_eq(
const AdimensionalSystemConstraints& constraints
)
{
index_t neq = 0;
// Water
// =====
if (constraints.water_equation != WaterEquationType::NoEquation)
{
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;
}
}
m_equations.add_equation(dof_water(), &neq);
}
// Aqueous components
// ==================
number_eq_aqueous_component(constraints, neq);
// Surface model
// =============
if (constraints.surface_model.model_type == SurfaceEquationType::Equilibrium)
{
// add the equation
m_equations.add_equation(dof_surface(), &neq);
m_equations.type_equation(dof_surface()) = static_cast<index_t>(constraints.surface_model.model_type);
// setup the total concentration
m_fixed_values(dof_surface()) = constraints.surface_model.concentration;
}
// Secondary species
// =================
// Secondary aqueous species
// -------------------------
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;
//std::cout << m_data->labels_aqueous[j] << "can exist ? " << can_exist << " - logk : " << m_data->logk_aqueous(j) << std::endl;
}
// Gas
// ---
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);
}
// Unit scaling for the gaseous total concentration
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;
}
// Sorbed species
// --------------
for (index_t s: m_data->range_sorbed())
{
// Check if the surface model is computed
if (constraints.surface_model.model_type != SurfaceEquationType::Equilibrium)
{
m_equations.set_sorbed_active(s, false);
continue;
}
// If so, check that all components of the sorbed species exist
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);
}
// Electron equation
// -----------------
if (solve_electron_equation)
{
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;
}
}
}
}
// above equations are 'free' (i.e. non constrained)
m_equations.nb_free_variables = neq;
// following equations are complementarity conditions
// Minerals
// ========
m_scaling_molar_volume = m_data->scaling_molar_volume(get_units().length);
for (index_t m: m_data->range_mineral())
{
bool can_precipitate = true;
// 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
}
}
if (can_precipitate)
{
m_equations.add_equation(dof_mineral(m), &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_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;
}
// 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;
}
}
}
// ================ //
// //
// Residuals //
// //
// ================ //
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 += log10*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::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 += log10*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 component) const
{
scalar_t sum = 0.0;
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
sum += log10*m_data->nb_sorption_sites(s)*m_data->nu_sorbed(s, component)*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 = saturation_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 += log10*m_data->nu_gas(k, diff_component)*m_data->nu_gas(k, component)*gas_concentration(k);
}
return sum;
}
scalar_t AdimensionalSystem::residual_water(const Vector& x) const
{
scalar_t res {0.0};
if (water_equation_type() == WaterEquationType::MassConservation)
{
const scalar_t conc_w = density_water() * saturation_water(x);
res = total_concentration_bc(0);
res -= conc_w/m_data->molar_mass_basis(0);
res -= conc_w*weigthed_sum_aqueous(0);
if (ideq_surf() != no_equation)
res -= conc_w*weigthed_sum_sorbed(0);
res -= weigthed_sum_mineral(x, 0);
if (m_data->nb_gas() > 0)
res -= weigthed_sum_gas(0);
if (m_equations.use_water_pressure_model)
{
const scalar_t porosity = m_second.porosity;
scalar_t sat_w = saturation_water(x) / porosity;
if (sat_w < 1)
{
const scalar_t pressure = m_equations.water_pressure_model(sat_w);
res -= m_scaling_gas*(porosity - saturation_water(x))*(pressure
/ (constants::gas_constant*temperature()));
}
}
res /= total_concentration_bc(0);
}
else if (water_equation_type() == WaterEquationType::SaturatedSystem)
{
res = 1 - saturation_water(x) - m_inert_volume_fraction;
for (index_t mineral: m_data->range_mineral())
{
res -= saturation_mineral(x, mineral);
}
}
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()*saturation_water(x);
scalar_t res = total_concentration_bc(component);
res -= conc_w*component_molality(x, component);
res -= conc_w*weigthed_sum_aqueous(component);
if (ideq_surf() != no_equation)
res -= conc_w*weigthed_sum_sorbed(component);
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_mineral(const Vector& x, index_t m) const
{
specmicp_assert(ideq_min(m) != no_equation);
scalar_t res = m_data->logk_mineral(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);
}
return res;
}
scalar_t AdimensionalSystem::residual_surface(const Vector &x) const
{
specmicp_assert(ideq_surf() != no_equation);
const scalar_t conc_w = density_water()*saturation_water(x);
scalar_t res = surface_total_concentration() - conc_w*free_sorption_site_concentration(x);
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
res -= conc_w*m_data->nb_sorption_sites(s)*sorbed_species_concentration(s);
}
return res/surface_total_concentration();
}
scalar_t AdimensionalSystem::residual_electron(const Vector &x) const
{
specmicp_assert(electron_equation_type() == ElectronEquationType::Equilibrium);
const scalar_t conc_w = density_water()*saturation_water(x);
scalar_t res = 0.0;
res -= conc_w * weigthed_sum_aqueous(m_data->electron_index());
if (ideq_surf() != no_equation)
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 = 1- sum_saturation_minerals(x);
m_second.saturation_gas = m_second.porosity - saturation_water(x);
set_secondary_concentration(x);
set_sorbed_concentrations(x);
//
// water
if (ideq_w() != no_equation) residual(ideq_w()) = residual_water(x);
// 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;
}
}
// surface
if (ideq_surf() != no_equation) residual(ideq_surf()) = residual_surface(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);
// std::cout << residual << std::endl;
}
// ================ //
// //
// 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==0) 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 (ideq_surf() != no_equation) jacobian_surface(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 *= rho_w;
tmp -= -weigthed_sum_gas(0);
if (m_equations.use_water_pressure_model)
{
const scalar_t porosity = (1-sum_saturation_minerals(x)-m_inert_volume_fraction);
const scalar_t sat_w = saturation_water(x)/ porosity;
if (sat_w < 1)
// TODO bound checking
{
scalar_t sp = sat_w*(1.0 + eps_jacobian);
if (sp == 0.0) sp = eps_jacobian;
const scalar_t h = sp - sat_w;
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;
tmp -= m_scaling_gas/(constants::gas_constant*temperature()) *(
(1-sat_w)*diff - pv_s
);
}
}
jacobian(idw, idw) = tmp/factor;
const scalar_t conc_w = density_water()*saturation_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 *= conc_w;
tmp -= diff_weigthed_sum_gas(k, 0);
jacobian(idw, ideq_paq(k)) = tmp/factor;
}
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*= conc_w;
tmp -= diff_weigthed_sum_gas(m_data->electron_index(), 0);
jacobian(idw, ideq_electron()) = tmp/factor;
}
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;
}
}
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;
}
}
}
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()*saturation_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)*log10;
tmp_iip -= diff_weigthed_sum_aqueous(k, i);
tmp_iip -= diff_weigthed_sum_sorbed(k, i);
tmp_iip *= conc_w;
tmp_iip -= diff_weigthed_sum_gas(k, i);
jacobian(idp, ideq_paq(k)) = 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);
tmp_iw -= weigthed_sum_aqueous(i);
tmp_iw -= weigthed_sum_sorbed(i);
tmp_iw *= density_water();
jacobian(idp, ideq_w()) = tmp_iw/factor;
}
// Surface
if (ideq_surf() != no_equation)
{
scalar_t tmp_s = -conc_w*diff_surface_weigthed_sum_sorbed(i);
jacobian(idp, ideq_surf()) = tmp_s/factor;
}
// Electron
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*= conc_w;
tmp -= diff_weigthed_sum_gas(m_data->electron_index(), i);
jacobian(idp, ideq_electron()) = 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);
// 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;
scalar_t tmp_value = m_data->nu_aqueous(j, k)*m_data->charge_aqueous(j);
tmp_value *= secondary_molality(j)/component_molality(x, k);
tmp_drdb += tmp_value;
}
jacobian(idp, idc) += component_molality(x,k)*log10*tmp_drdb;
}
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;
}
} // 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());
}
}
void AdimensionalSystem::jacobian_surface(Vector& x, Matrix& jacobian)
{
const index_t ids = ideq_surf();
const scalar_t factor = surface_total_concentration();
const scalar_t conc_w = density_water()*saturation_water(x);
specmicp_assert(ids != no_equation);
scalar_t tmp_s = - free_sorption_site_concentration(x);
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
tmp_s -= m_data->nb_sorption_sites(s)* m_data->nb_sorption_sites(s)*sorbed_species_concentration(s);
}
jacobian(ids, ids) = conc_w*log10 * tmp_s / factor;
// water
const index_t idw = ideq_w();
if (idw != no_equation)
{
const scalar_t rho_w = density_water();
scalar_t tmp_w = - free_sorption_site_concentration(x);
for (index_t s: m_data->range_sorbed())
{
if (not is_active_sorbed(s)) continue;
tmp_w -= m_data->nb_sorption_sites(s)*sorbed_species_concentration(s);
}
jacobian(ids, idw) = rho_w * tmp_w / factor;
}
// component
for (index_t k: m_data->range_aqueous_component())
{
const index_t idk = ideq_paq(k);
if (idk == no_equation) continue;
scalar_t tmp_k = - conc_w*diff_surface_weigthed_sum_sorbed(k);
jacobian(ids, idk) = tmp_k/factor;
}
if (ideq_electron() != no_equation)
{
scalar_t tmp_e = - conc_w*diff_surface_weigthed_sum_sorbed(m_data->electron_index());
jacobian(ids, ideq_electron()) = tmp_e/factor;
}
// water
}
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()*saturation_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)) = 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) = tmp/factor;
}
}
// ========================== //
// //
// Secondary variables //
// //
// ========================== //
void AdimensionalSystem::set_secondary_variables(const Vector& x)
{
m_second.porosity = 1 - sum_saturation_minerals(x) - m_inert_volume_fraction;
set_saturation_gas_phase(x);
set_pressure_fugacity(x);
if (ideq_surf() != no_equation) set_sorbed_concentrations(x);
set_secondary_concentration(x);
compute_log_gamma(x);
}
void AdimensionalSystem::set_saturation_gas_phase(const Vector& x)
{
m_second.saturation_gas = m_second.porosity - saturation_water(x);
//m_second.saturation_gas = 1 - saturation_water(x) - sum_saturation_minerals(x) - m_inert_volume_fraction;
}
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*saturation_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())
{
if (not is_active_sorbed(s))
{
m_second.sorbed_concentrations(s) = 0.0;
continue;
}
scalar_t logconc = -m_data->logk_sorbed(s) +
m_data->nb_sorption_sites(s)*(log_free_sorption_site_concentration(x));
for (index_t k: m_data->range_aqueous_component())
{
if (m_data->nu_sorbed(s, k) == 0.0) continue;
const auto activity_k = log_component_molality(x, k) + log_gamma_component(k);
logconc += m_data->nu_sorbed(s, k)*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);
}
}
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 sqrti = std::sqrt(ionic_strength());
for (index_t i: m_data->range_aqueous_component())
{
if (ideq_paq(i) == no_equation)
{
log_gamma_component(i) = 0.0;
continue;
}
log_gamma_component(i) = laws::extended_debye_huckel(
ionic_strength(), sqrti,
m_data->charge_component(i),
m_data->a_debye_component(i),
m_data->b_debye_component(i)
);
}
for (index_t j: m_data->range_aqueous())
{
if (not is_aqueous_active(j))
{
log_gamma_secondary(j) = 0.0;
continue;
}
log_gamma_secondary(j) = laws::extended_debye_huckel(
ionic_strength(), sqrti,
m_data->charge_aqueous(j),
m_data->a_debye_aqueous(j),
m_data->b_debye_aqueous(j)
);
}
}
bool AdimensionalSystem::hook_start_iteration(const Vector& x, scalar_t norm_residual)
{
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;
bool may_have_converged = false;
if (norm_residual < nb_free_variables()*get_options().start_non_ideality_computation)
{
// 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) {
may_have_converged = true;
break;
}
previous_norm = m_second.loggamma.norm();
}
}
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::get_solution(Vector& xtot, const Vector& x)
{
double previous_norm = m_second.loggamma.norm();
set_saturation_gas_phase(x);
set_pressure_fugacity(x);
set_secondary_concentration(x);
if (ideq_surf() != no_equation) set_sorbed_concentrations(x);
if (get_options().non_ideality)
{
compute_log_gamma(x);
if (std::abs(previous_norm - m_second.loggamma.norm()) > 1e-6)
{
WARNING << "Activity coefficient have not converged !" << std::endl
<< "output can not be trusted\n Difference : "
+std::to_string(std::abs(previous_norm - m_second.loggamma.norm()));
}
}
// Set the correct value for the water total saturation
if (ideq_w() == no_equation)
{
xtot(dof_water()) = saturation_water(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);
}
// Water, saturation and density
// ==============================
scalar_t AdimensionalSystem::density_water() const {
return laws::density_water(units::celsius(25.0), length_unit(), mass_unit());
}
scalar_t AdimensionalSystem::saturation_water(const Vector& x) const
{
if (ideq_w() != no_equation)
return x(ideq_w());
else
return 1.0 - sum_saturation_minerals(x) - m_inert_volume_fraction;
}
scalar_t AdimensionalSystem::saturation_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_saturation_minerals(const Vector& x) const
{
scalar_t sum_saturations = 0.0;
for (index_t mineral: m_data->range_mineral())
{
sum_saturations += saturation_mineral(x, mineral);
}
return sum_saturations;
}
// Starting guess
// ==============
void AdimensionalSystem::reasonable_starting_guess(Vector &xtot)
{
xtot.resize(total_dofs());
xtot(dof_water()) = 0.8;
for (index_t i: m_data->range_aqueous_component())
{
xtot(dof_component(i)) = -4.0;
}
if (ideq_surf() != no_equation)
xtot(dof_surface()) = std::log10(0.8*surface_total_concentration());
else
xtot(dof_surface()) = -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();
m_second = SecondaryVariables(m_data);
}
void AdimensionalSystem::reasonable_restarting_guess(Vector& xtot)
{
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_real_distribution<> dis(-2, 2);
xtot(dof_water()) = 0.5;
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 (ideq_surf() != no_equation)
xtot(dof_surface()) = std::log10(0.8*surface_total_concentration());
else
xtot(dof_surface()) = -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();
m_second = SecondaryVariables(m_data);
}
} // end namespace specmicp

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