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adimensional_system.cpp
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			/*-------------------------------------------------------

			- Module : specmicp
			- File : adim_system.cpp
			- Author : Fabien Georget

			Copyright (c) 2014, Fabien Georget <fabieng@princeton.edu>, Princeton University
			All rights reserved.

			Redistribution and use in source and binary forms, with or without
			modification, are permitted provided that the following conditions are met:
			* Redistributions of source code must retain the above copyright
			notice, this list of conditions and the following disclaimer.
			* Redistributions in binary form must reproduce the above copyright
			notice, this list of conditions and the following disclaimer in the
			documentation and/or other materials provided with the distribution.
			* Neither the name of the Princeton University nor the
			names of its contributors may be used to endorse or promote products
			derived from this software without specific prior written permission.

			THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
			ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
			WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
			DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
			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 "../equilibrium_data.hpp"

			#include "physics/constants.hpp"
			#include "physics/laws.hpp"

			#include "adimensional_system_solution.hpp"

			#include <random>

			// uncomment to activate the finite difference jacobian
			// #define SPECMICP_DEBUG_EQUATION_FD_JACOBIAN

			namespace specmicp {

			constexpr scalar_t log10 = std::log(10.0);

			// Constructor
			// ===========

			AdimensionalSystem::AdimensionalSystem(RawDatabasePtr ptrdata,
			const AdimensionalSystemConstraints& constraints,
			const AdimensionalSystemOptions& options)
			:
			AdimemsionalSystemNumbering(ptrdata),
			OptionsHandler<AdimensionalSystemOptions>(options),
			m_fixed_values(constraints.total_concentrations),
			m_secondary_conc(ptrdata->nb_aqueous),
			m_loggamma(ptrdata->nb_component+ptrdata->nb_aqueous),
			m_saturation_gas(0),
			m_gas_fugacity(ptrdata->nb_gas),
			m_sorbed_concentrations(ptrdata->nb_sorbed),
			m_inert_volume_fraction(constraints.inert_volume_fraction)
			{
			number_eq(constraints);
			m_secondary_conc.setZero();
			m_gas_fugacity.setZero();
			m_loggamma.setZero();
			m_sorbed_concentrations.setZero();
			}


			AdimensionalSystem::AdimensionalSystem(
			RawDatabasePtr ptrdata,
			const AdimensionalSystemConstraints& constraints,
			const AdimensionalSystemSolution& previous_solution,
			const AdimensionalSystemOptions& options
			):
			AdimemsionalSystemNumbering(ptrdata),
			OptionsHandler<AdimensionalSystemOptions>(options),
			m_fixed_values(constraints.total_concentrations),
			m_secondary_conc(previous_solution.secondary_molalities),
			m_loggamma(previous_solution.log_gamma),
			m_ionic_strength(previous_solution.ionic_strength),
			m_saturation_gas(0),
			m_gas_fugacity(previous_solution.gas_fugacities),
			m_sorbed_concentrations(previous_solution.sorbed_molalities),
			m_inert_volume_fraction(constraints.inert_volume_fraction)
			{
			number_eq(constraints);
			}

			// Equation numbering
			// ==================

			void AdimensionalSystem::number_eq(
			const AdimensionalSystemConstraints& constraints
			)
			{
			index_t neq = 0;
			m_ideq = std::vector<index_t>(total_dofs(), no_equation);
			m_component_equation_type = std::vector<int>(m_data->nb_component, no_equation);
			m_fixed_activity_species = std::vector<index_t>(m_data->nb_component, no_species);

			// Water
			// =====
			if (constraints.water_equation != WaterEquationType::NoEquation)
			{
			m_ideq[dof_water()] = neq;
			m_component_equation_type[dof_water()] = static_cast<int>(constraints.water_equation);
			++neq;
			}

			// Aqueous components
			// ==================
			number_eq_aqueous_component(constraints, neq);

			// Surface model
			// =============
			if (constraints.surface_model.model_type == SurfaceEquationType::Equilibrium)
			{
			// add the equation
			m_ideq[dof_surface()] = neq;
			++neq;
			// setup the total concentration
			m_surface_concentration = constraints.surface_model.concentration;
			}
			// above equations are 'free' (i.e. non constrained)
			m_nb_free_vars = neq;
			// following equations are complementarity conditions

			// Minerals
			// ========
			for (index_t m: m_data->range_mineral())
			{
			bool can_precipitate = true;
			// Remove minerals that cannot precipitate
			for (index_t& k: m_nonactive_component)
			{
			if (m_data->nu_mineral(m, k) != 0.0)
			{
			can_precipitate = false;
			break; // this is not a mineral that can precipitate
			}
			}
			if (can_precipitate)
			{
			m_ideq[dof_mineral(m)] = neq;
			++neq;
			}
			}
			m_nb_tot_vars = neq;
			m_nb_compl_vars = m_nb_tot_vars - m_nb_free_vars;

			// Secondary species
			// =================

			// Secondary aqueous species
			// -------------------------
			m_active_aqueous.reserve(m_data->nb_aqueous);
			for (index_t j: m_data->range_aqueous())
			{
			bool can_exist = true;
			for (const index_t& k: m_nonactive_component)
			{
			if (m_data->nu_aqueous(j, k) != 0)
			{
			can_exist = false;
			}
			}
			m_active_aqueous.push_back(can_exist);
			}
			m_active_gas.reserve(m_data->nb_gas);

			// Gas
			// ---
			for (index_t k: m_data->range_gas())
			{
			bool can_exist = true;
			for (const index_t& n: m_nonactive_component)
			{
			if (m_data->nu_gas(k, n) != 0.0)
			{
			can_exist = false;
			break;
			}
			}
			m_active_gas.push_back(can_exist);
			}

			// 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_active_sorbed.push_back(false);
			continue;
			}
			// If so, check that all components of the sorbed species exist
			bool can_exist = true;
			for (const index_t& k: m_nonactive_component)
			{
			if (m_data->nu_sorbed(s, k) != 0.0)
			{
			can_exist = false;
			break;
			}
			}
			m_active_sorbed.push_back(can_exist);
			}
			}


			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_component_equation_type[constraints.charge_keeper] = static_cast<int>(EqT::ChargeBalance);
			}
			// Then go over fix fugacity gas
			for (auto it=constraints.fixed_fugacity_cs.begin(); it!=constraints.fixed_fugacity_cs.end(); ++it)
			{
			if (m_component_equation_type[it->id_component] != static_cast<int>(EqT::NoEquation))
			{
			throw std::invalid_argument("Component '" + m_data->labels_basis[it->id_component]
			+ "' is already constrained, a fixed fugacity condition can not be applied");
			}
			m_component_equation_type[it->id_component] = static_cast<int>(EqT::FixedFugacity);
			m_fixed_values(it->id_component) = it->log_value;
			m_fixed_activity_species[it->id_component] = it->id_gas;
			}
			// Then over the fix activity species
			for (auto it=constraints.fixed_activity_cs.begin(); it!=constraints.fixed_activity_cs.end(); ++it)
			{
			if (m_component_equation_type[it->id_component] != static_cast<int>(EqT::NoEquation))
			{
			throw std::invalid_argument("Component '" + m_data->labels_basis[it->id_component]
			+ "' is already constrained, a fixed activity condition can not be applied.");
			}
			m_component_equation_type[it->id_component] = static_cast<int>(EqT::FixedActivity);
			m_fixed_values(it->id_component) = it->log_value;
			}
			// Finally number the equations
			for (index_t component: m_data->range_aqueous_component())
			{
			// Mass is conserved for this component
			//###FIXME: H[+], HO[-]
			if (m_component_equation_type[component] == static_cast<int>(EqT::NoEquation)
			and m_fixed_values(component) != 0.0)
			{
			m_component_equation_type[component] = static_cast<int>(EqT::MassConservation);
			m_ideq[component] = neq;
			++neq;
			}
			// Or this is another type of equation
			else if (m_component_equation_type[component] != static_cast<int>(EqT::NoEquation))
			{
			m_ideq[component] = neq;
			++neq;
			}
			// else add component to the nonactive component list
			else
			{
			m_nonactive_component.push_back(component);
			}
			}
			if (stdlog::ReportLevel() >= logger::Debug and m_nonactive_component.size() > 0)
			{
			// if in debug mode list the non active components
			DEBUG << "Non active components :";
			for (auto it: m_nonactive_component)
			{
			DEBUG << " - " << it;
			}
			}
			}

			// ================ //
			// //
			// Residuals //
			// //
			// ================ //

			scalar_t AdimensionalSystem::residual_water(const Vector& x) const
			{
			scalar_t res = 0;
			if (m_component_equation_type[dof_water()] == static_cast<int>(WaterEquationType::MassConservation))
			{
			const scalar_t conc_w = density_water()*saturation_water(x);
			res = total_concentration_bc(0) - conc_w/m_data->molar_mass_basis_si(0);
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j)) continue;
			res -= conc_wm_data->nu_aqueous(j, 0)m_secondary_conc(j);
			}
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			res -= conc_wm_data->nu_sorbed(s, 0)sorbed_species_concentration(s);
			}
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation or m_data->nu_mineral(m, 0) == 0.0) continue;
			res -= m_data->nu_mineral(m, 0)*saturation_mineral(x, m)/molar_volume_mineral(m);
			}
			for (index_t k: m_data->range_gas())
			{
			if (m_data->nu_gas(k, 0) == 0.0) continue;
			res -= m_data->nu_gas(k, 0)saturation_gas_phase()gas_fugacity(k)*gas_total_pressure()/(
			constants::gas_constant*temperature());
			}
			res /= total_concentration_bc(0);
			}
			else if (m_component_equation_type[dof_water()] == static_cast<int>(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) - conc_w*component_molality(x, component);
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j)) continue;
			res -= conc_wm_data->nu_aqueous(j, component)secondary_molality(j);
			}
			if (ideq_surf() != no_equation)
			{
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			res -= conc_wm_data->nu_sorbed(s, component)sorbed_species_concentration(s);
			}
			}
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation) continue;
			res -= m_data->nu_mineral(m, component)*saturation_mineral(x, m)/molar_volume_mineral(m);
			}
			for (index_t k: m_data->range_gas())
			{
			if (m_data->nu_gas(k, component) == 0.0) continue;
			res -= m_data->nu_gas(k, component)saturation_gas_phase()gas_fugacity(k)*gas_total_pressure()/(
			constants::gas_constant*temperature());
			}
			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_fugacity(const Vector& x, index_t component) const
			{
			specmicp_assert(aqueous_component_equation_type(component)
			== AqueousComponentEquationType::FixedFugacity);
			index_t id_g = m_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)
			res -= m_data->nu_mineral(m, i)*(log_component_molality(x, i) + log_gamma_component(i));
			}
			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_wm_data->nb_surface_sites(s)sorbed_species_concentration(s);
			}
			return res/surface_total_concentration();
			}

			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
			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:
			continue;
			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;
			}
			}
			// 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);
			}
			// 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);
			}

			void AdimensionalSystem::jacobian_water(Vector& x, Matrix& jacobian)
			{
			if (water_equation_type() == WaterEquationType::MassConservation)
			{
			const scalar_t rho_w = density_water();
			scalar_t tmp = -1.0/m_data->molar_mass_basis_si(0);
			const scalar_t factor = total_concentration_bc(0);
			for (index_t j: m_data->range_aqueous())
			{
			if ( m_data->nu_aqueous(j, 0) == 0 and not is_aqueous_active(j)) continue;
			tmp -= m_data->nu_aqueous(j, 0)*secondary_molality(j);
			}
			tmp *= rho_w;
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_aqueous_active(s)) continue;
			tmp -= m_data->nu_sorbed(s, 0)*secondary_molality(s);
			}
			jacobian(0, 0) = 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;
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j)) continue;
			tmp -= m_data->nu_aqueous(j,0)m_data->nu_aqueous(j,k)secondary_molality(j);
			}
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp -= m_data->nu_sorbed(s, 0)m_data->nu_sorbed(s, k)sorbed_species_concentration(s);
			}
			tmp *= conc_w;
			jacobian(0, ideq_paq(k)) = log10 * tmp/factor;

			}
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation) continue;
			jacobian(0, ideq_min(m)) = -m_data->nu_mineral(m, 0)/molar_volume_mineral(m)/factor;
			}
			}
			else if (water_equation_type() == WaterEquationType::SaturatedSystem)
			{
			jacobian(0, 0) = -1;
			for (index_t m: m_data->range_mineral())
			{
			if (ideq_min(m) == no_equation) continue;
			jacobian(0, 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;
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j)) continue;
			tmp_iip -= log10m_data->nu_aqueous(j, i)m_data->nu_aqueous(j, k)*secondary_molality(j);
			}
			if (ideq_surf() != no_equation)
			{
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp_iip -= log10m_data->nu_sorbed(s, i)m_data->nu_sorbed(s, k)*sorbed_species_concentration(s);
			}
			}
			tmp_iip *= conc_w;
			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);
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j) or m_data->nu_aqueous(j, i) == 0 ) continue;
			tmp_iw -= m_data->nu_aqueous(j, i)*secondary_molality(j);
			}
			if (ideq_surf() != no_equation)
			{
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp_iw -= m_data->nu_sorbed(s, i)*sorbed_species_concentration(s);
			}
			}
			tmp_iw *= density_water();
			jacobian(idp, ideq_w()) = tmp_iw/factor;
			}
			// Surface
			if (ideq_surf() != no_equation)
			{
			scalar_t tmp_s = 0.0;
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp_s -= conc_wm_data->nu_sorbed(s, i)m_data->nb_surface_sites(s)*sorbed_species_concentration(s);
			}
			jacobian(idp, ideq_surf()) = log10*tmp_s/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)log10tmp_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_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
			} // 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);
			}
			}
			}

			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 = - conc_w*free_sorption_site_concentration(x);
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp_s -= conc_wm_data->nb_surface_sites(s) m_data->nb_surface_sites(s)*sorbed_species_concentration(s);
			}
			jacobian(ids, ids) = 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 = - rho_w*free_sorption_site_concentration(x);
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp_w -= rho_wm_data->nb_surface_sites(s)sorbed_species_concentration(s);
			}
			jacobian(ids, idw) = 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 = 0.0;
			for (index_t s: m_data->range_sorbed())
			{
			if (not is_active_sorbed(s)) continue;
			tmp_k -= conc_w*m_data->nb_surface_sites(s)
			* m_data->nu_sorbed(s, k)
			* sorbed_species_concentration(s);
			}
			jacobian(ids, idk) = log10*tmp_k/factor;
			}

			// water
			}

			// ========================== //
			// //
			// Secondary variables //
			// //
			// ========================== //

			void AdimensionalSystem::set_secondary_variables(const Vector& x)
			{
			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_saturation_gas = 1 - saturation_water(x) - sum_saturation_minerals(x) - m_inert_volume_fraction;
			}

			void AdimensionalSystem::set_pressure_fugacity(const Vector& x)
			{
			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;
			logp += m_data->nu_gas(k, i) * (log_component_molality(x, i) + log_gamma_component(i));
			}
			m_gas_fugacity(k) = pow10(logp);
			}
			}

			void AdimensionalSystem::set_secondary_concentration(const Vector& x)
			{
			for (index_t j: m_data->range_aqueous())
			{
			if (not is_aqueous_active(j))
			{
			m_secondary_conc(j) = 0.0;
			continue;
			}
			scalar_t logconc = -m_data->logk_aqueous(j) - m_loggamma(j+m_data->nb_component);
			for (index_t k: m_data->range_aqueous_component())
			{
			if (m_data->nu_aqueous(j, k) == 0) continue;
			logconc += m_data->nu_aqueous(j, k)*(log_component_molality(x, k) + m_loggamma(k));
			}
			m_secondary_conc(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_sorbed_concentrations(s) = 0.0;
			continue;
			}
			scalar_t logconc = -m_data->logk_sorbed(s) +
			m_data->nb_surface_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;
			logconc += m_data->nu_sorbed(s, k)*(log_component_molality(x, k) + m_loggamma(k));
			}
			m_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_loggamma.norm();
			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_loggamma.norm())/previous_norm <
			get_options().non_ideality_tolerance) {
			may_have_converged = true;
			break;
			}
			previous_norm = m_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_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_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_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_secondary_conc, m_loggamma, m_ionic_strength,
			m_gas_fugacity,
			m_sorbed_concentrations,
			m_inert_volume_fraction);
			}

			// Water, saturation and density
			// ==============================

			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;
			}

			scalar_t AdimensionalSystem::density_water() const
			{
			return laws::density_water(units::celsius(25.0), length_unit(), mass_unit());
			}

			scalar_t AdimensionalSystem::molar_volume_mineral(index_t mineral) const
			{
			return m_data->molar_volume_mineral(mineral, length_unit());
			}

			// 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()) = 0.0;
			xtot.block(offset_minerals(), 0, m_data->nb_mineral, 1).setZero();

			m_loggamma.setZero();
			m_secondary_conc.setZero();
			m_sorbed_concentrations.setZero();
			}

			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()) = 0.0;
			xtot.segment(offset_minerals(), m_data->nb_mineral).setZero();
			m_loggamma.setZero();
			m_secondary_conc.setZero();
			m_sorbed_concentrations.setZero();
			}

			} // end namespace specmicp

specmicp/src/specmicp/adimensional/adimensional_system.cpp9cf41f6dfb45reactmicp/unsaturated

adimensional_system.cppView Options

specmicp/src/specmicp/adimensional/adimensional_system.cpp
9cf41f6dfb45reactmicp/unsaturated

adimensional_system.cpp
View Options