leaching_kinetic.cpp
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Created: Tue, Nov 5, 10:18

leaching_kinetic.cpp
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	// ============================================

	// Leaching of a cement paste
	// with kinetic dissolution of C3S

	// =============================================

	// This file can be used to learn how to use ReactMiCP


	// Include ReactMiCP
	#include "reactmicp.hpp"

	#include "specmicp/adimensional/adimensional_system_solution_saver.hpp"
	#include "reactmicp/systems/saturated_react/diffusive_upscaling_stagger.hpp"
	#include "reactmicp/systems/saturated_react/kinetic_stagger.hpp"

	// Other includes that would be needed later :
	#include <Eigen/QR>

	#include "physics/laws.hpp"
	#include "utils/timer.hpp"
	#include <functional>
	#include <iostream>
	#include <fstream>


	// we use the following namespaces
	using namespace specmicp;
	using namespace reactmicp;
	using namespace reactmicp::systems;

	using namespace specmicp::reactmicp::systems::satdiff;
	using namespace reactmicp::solver;

	// We declare some functions that we will be using :

	// Database
	// ========

	// Parse and Prepare the database
	RawDatabasePtr get_database(const std::string& path_to_database);

	// Boundary and initial conditions
	// ===============================

	// Return the chemistry constraints for the inital condition
	AdimensionalSystemConstraints get_cement_initial_constraints(
	RawDatabasePtr the_database,
	const units::UnitsSet& units_set);
	// return the chemistry constraints for the boundary condition
	AdimensionalSystemConstraints get_bc_initial_constraints(
	RawDatabasePtr the_database,
	const units::UnitsSet& units_set);


	Vector initial_compo(const Vector& publi);

	void compo_from_oxyde(Vector& compo_oxyde, Vector& compo_species);

	// The mesh
	// ========

	// There is two version
	// a uniform mesh
	mesh::Mesh1DPtr get_mesh(scalar_t dx);
	// and a non uniform mesh
	mesh::Mesh1DPtr get_mesh();

	// Options
	// =======

	// Speciation solver options
	AdimensionalSystemSolverOptions get_specmicp_options();
	// Transport options
	void set_transport_options(dfpmsolver::ParabolicDriverOptions& transport_options);
	// Reactive Solver options
	void set_reactive_solver_options(reactmicp::solver::ReactiveTransportOptions& reactive_options);


	// Kinetic model and variables
	// ===========================

	// Kinetic variables
	class C3SKineticVariables : public KineticSaturatedVariablesBase
	{
	public:

	Vector amount_minerals; // concentration of C3S
	Vector predictor; // Initial amount
	Vector velocity; // dC_c3s/dt
	Vector volume_fractions;
	};

	using C3SKineticVariablesPtr = std::shared_ptr<C3SKineticVariables>;

	// The dissolution model
	class C3SDissolutionModel : public KineticModelBase
	{
	public:
	C3SDissolutionModel(RawDatabasePtr the_database, const units::UnitsSet the_units):
	m_database(the_database),
	m_units(the_units),
	id_c3s(the_database->get_id_mineral_kinetic("C3S"))
	{
	if (id_c3s == no_species)
	throw database::invalid_database("The database do not contain C3S !");

	}

	KineticSaturatedVariablesBasePtr initialize_variables(mesh::Mesh1DPtr the_mesh, scalar_t init_vol_fraction);

	//! \brief Initialize a timestep
	void initialize_timestep(scalar_t dt, KineticSaturatedVariablesBasePtr kinetic_variables) override;
	//! \brief Restart a timestep
	void restart_timestep(
	index_t node,
	const AdimensionalSystemSolution& eq_solution,
	KineticSaturatedVariablesBasePtr kinetic_variables) override;
	//! \brief Return the volume fraction of kinetic (or inert) phases
	scalar_t get_volume_fraction_kinetic(index_t node, KineticSaturatedVariablesBasePtr kinetic_variables) override;
	//! \brief Return the velocity of the total immobile kinetic concentration for component
	scalar_t get_velocity_kinetic(index_t node, index_t component, KineticSaturatedVariablesBasePtr kinetic_variables) override;

	private:
	scalar_t volume_fraction(scalar_t concentration);
	scalar_t dy_dt(scalar_t log_IAP, scalar_t Aeff);

	scalar_t m_dt {-1.0};

	RawDatabasePtr m_database;
	units::UnitsSet m_units;

	index_t id_c3s;
	};

	KineticSaturatedVariablesBasePtr C3SDissolutionModel::initialize_variables(mesh::Mesh1DPtr the_mesh, scalar_t init_vol_fraction)
	{
	C3SKineticVariablesPtr var = std::make_shared<C3SKineticVariables>();

	var->predictor.setZero(the_mesh->nb_nodes());
	var->velocity.setZero(the_mesh->nb_nodes());

	var->volume_fractions.setConstant(the_mesh->nb_nodes(), init_vol_fraction);
	var->amount_minerals.setConstant(the_mesh->nb_nodes(),
	init_vol_fraction/m_database->molar_volume_mineral_kinetic(id_c3s, m_units.length));

	var->volume_fractions(0) = 0.0;
	var->amount_minerals(0) = 0.0;

	return std::static_pointer_cast<KineticSaturatedVariablesBase>(var);
	}

	void C3SDissolutionModel::initialize_timestep(scalar_t dt, KineticSaturatedVariablesBasePtr kinetic_variables)
	{
	m_dt = dt;
	C3SKineticVariablesPtr true_kin_var = std::static_pointer_cast<C3SKineticVariables>(kinetic_variables);

	true_kin_var->predictor = true_kin_var->amount_minerals;
	true_kin_var->velocity.setZero();
	}

	void C3SDissolutionModel::restart_timestep(
	index_t node,
	const AdimensionalSystemSolution &eq_solution,
	KineticSaturatedVariablesBasePtr kinetic_variables
	)
	{
	C3SKineticVariablesPtr true_kin_var = std::static_pointer_cast<C3SKineticVariables>(kinetic_variables);

	AdimensionalSystemSolutionExtractor extr(eq_solution, m_database, m_units);
	scalar_t log_IAP = 0;
	for (index_t component: m_database->range_component())
	{
	if (m_database->nu_mineral_kinetic(id_c3s, component) == 0.0) continue;
	log_IAP += m_database->nu_mineral_kinetic(id_c3s, component)*extr.log_molality_component(component);
	}
	scalar_t tmp = 0;

	scalar_t Aeff = 0;
	scalar_t porosity = extr.porosity();
	if (porosity > 0.6)
	{
	Aeff= 14001e-4/1e-3m_database->molar_mass_mineral_kinetic(id_c3s)/m_database->molar_volume_mineral_kinetic(id_c3s)*true_kin_var->volume_fractions(node);
	tmp = 1e-6*dy_dt(log_IAP, Aeff);
	}
	true_kin_var->velocity(node) = tmp;

	tmp = true_kin_var->predictor(node) + m_dt*true_kin_var->velocity(node);
	if (tmp < 1e-20) {

	tmp =0.0;
	true_kin_var->velocity(node) = - true_kin_var->predictor(node) / m_dt;
	}

	true_kin_var->amount_minerals(node) = tmp;

	true_kin_var->volume_fractions(node) = tmp*m_database->molar_volume_mineral_kinetic(id_c3s, m_units.length);
	}

	scalar_t C3SDissolutionModel::dy_dt(scalar_t log_IAP, scalar_t Aeff)
	{
	scalar_t res = (-57.0 -std::log(10)*log_IAP)/21.5;
	scalar_t tmp_2 = std::pow(res, 3.73);
	res = - 125.3e-6Aeff(1.0 - std::exp(-tmp_2));
	return res;

	}

	scalar_t C3SDissolutionModel::get_volume_fraction_kinetic(index_t node, KineticSaturatedVariablesBasePtr kinetic_variables)
	{
	C3SKineticVariablesPtr true_kin_var = std::static_pointer_cast<C3SKineticVariables>(kinetic_variables);
	return true_kin_var->volume_fractions(node);
	}

	scalar_t C3SDissolutionModel::get_velocity_kinetic(index_t node, index_t component, KineticSaturatedVariablesBasePtr kinetic_variables)
	{
	C3SKineticVariablesPtr true_kin_var = std::static_pointer_cast<C3SKineticVariables>(kinetic_variables);
	return m_database->nu_mineral_kinetic(id_c3s, component)*true_kin_var->velocity(node);
	}

	// ==============
	// Output
	// ==============

	// Many information is generated throughout a computation and we can't save everything
	// The reactmicp runner can call a function to output the desired information
	// Here the output function is a member function for convenience
	class OutputPolicy
	{
	public:
	// Initialise the output
	// SimulationInformation contain basic information from the simulation
	OutputPolicy(const SimulationInformation& simul_info,
	mesh::Mesh1DPtr the_mesh,
	RawDatabasePtr the_database,
	units::UnitsSet the_units):
	m_mesh(the_mesh),
	m_database(the_database),
	m_units(the_units)

	{
	// Open the files
	// Save the pH
	out_c_ph.open(simul_info.complete_filepath("ph", suffix));
	// Save the total aqueous concentration of HCO3[-]
	out_c_hco3.open(simul_info.complete_filepath("c_hco3", suffix));
	// save the total solid concentration of s_ca
	out_s_ca.open(simul_info.complete_filepath("s_ca", suffix));
	// Save the volume fraction of calcite
	out_calcite.open(simul_info.complete_filepath("calcite", suffix));
	// Save the porosity
	out_poro.open(simul_info.complete_filepath("poro", suffix));
	out_kin_vol_frac.open(simul_info.complete_filepath("kin_vol_frac", suffix));
	// save useful indices from the database
	m_id_hco3 = m_database->get_id_component("HCO3[-]");
	m_id_ca = m_database->get_id_component("Ca[2+]");
	m_id_calcite = m_database->get_id_mineral("Calcite");
	}


	void output(scalar_t time, VariablesBasePtr variables)
	{
	SaturatedVariablesPtr true_var = cast_var_from_base(variables);

	out_c_ph << time;
	out_c_hco3 << time;
	out_s_ca << time;
	out_calcite << time;
	out_poro << time;
	out_kin_vol_frac << time;

	for (index_t node: m_mesh->range_nodes())
	{
	// Again AdimensionalSystemSolutionExtractor is used to obtain information about the speciation system
	AdimensionalSystemSolutionExtractor extractor(true_var ->equilibrium_solution(node), m_database, m_units);
	out_c_ph << "\t" << extractor.pH();
	out_c_hco3 << "\t" << true_var->aqueous_concentration(node, m_id_hco3);
	out_s_ca << "\t" << true_var->solid_concentration(node, m_id_ca);
	out_calcite << "\t" << extractor.volume_fraction_mineral(m_id_calcite);
	out_poro << "\t" << extractor.porosity();
	out_kin_vol_frac << "\t" << std::static_pointer_cast<C3SKineticVariables>(true_var->kinetic_variables())->volume_fractions(node);
	}
	out_c_hco3 << std::endl;
	out_c_ph << std::endl;
	out_s_ca << std::endl;
	out_calcite << std::endl;
	out_poro << std::endl;
	out_kin_vol_frac << std::endl;

	}

	private:
	mesh::Mesh1DPtr m_mesh;
	RawDatabasePtr m_database;
	units::UnitsSet m_units;

	std::string suffix { "dat" };

	std::ofstream out_c_ph;
	std::ofstream out_c_hco3;
	std::ofstream out_s_ca;
	std::ofstream out_calcite;
	std::ofstream out_poro;
	std::ofstream out_kin_vol_frac;

	index_t m_id_hco3;
	index_t m_id_ca;
	index_t m_id_calcite;
	};

	// ===================
	// MAIN
	// ===================

	int main()
	{
	// initialize eigen
	// This is needed if OpenMP is used
	Eigen::initParallel();

	// Setup the log
	// The output will be on cerr
	specmicp::logger::ErrFile::stream() = &std::cerr;
	// And only Warning and error messages will be printed
	specmicp::stdlog::ReportLevel() = specmicp::logger::Warning;

	// The database
	// -------------

	// Obtain the database
	RawDatabasePtr the_database = get_database("../data/cemdata.js");

	// SpecMiCP options
	// ----------------

	// Set the options
	AdimensionalSystemSolverOptions specmicp_options = get_specmicp_options();
	units::UnitsSet units_set = specmicp_options.units_set;


	// The mesh
	// --------

	// Obtain the mesh
	mesh::Mesh1DPtr the_mesh = get_mesh(0.0050); // uniform
	//mesh::Mesh1DPtr the_mesh = get_mesh(); // non uniform
	index_t nb_nodes = the_mesh->nb_nodes(); // just boilerplate to make things easier


	// Print the mesh
	io::print_mesh("out_carbo_mesh.dat", the_mesh, units::LengthUnit::centimeter);


	// Initial and boundary conditions
	// --------------------------------

	// Obtain the initial constraints
	// Note : the database is modified at this point
	// Only the relevant components are kept at this point
	AdimensionalSystemConstraints cement_constraints = get_cement_initial_constraints(the_database, units_set);

	// Freeze the database
	the_database->freeze_db();


	// Obtain the initial condition
	AdimensionalSystemSolution cement_solution = solve_equilibrium(
	the_database,
	cement_constraints,
	specmicp_options);

	if(not the_database->is_valid())
	throw std::runtime_error("The database has been changed during the initial condition computation");


	// Just to check that everything is ok !
	AdimensionalSystemSolutionExtractor extractor(cement_solution, the_database, units_set);
	std::cout << "Porosity : " << extractor.porosity() << std::endl;
	std::cout << "Water volume fraction " << extractor.volume_fraction_water() << std::endl;



	//return EXIT_SUCCESS;

	// Obtain the boundary conditions
	AdimensionalSystemConstraints bc_constraints = get_bc_initial_constraints(
	the_database,
	specmicp_options.units_set
	);
	AdimensionalSystemSolution bc_solution = solve_equilibrium(
	the_database,
	bc_constraints,
	specmicp_options
	);

	if(not the_database->is_valid())
	throw std::runtime_error("The database has been changed during the boundary conditions computation");


	// The constraints
	// --------------

	// Boundary condition
	// 'list_fixed_nodes' lists the node with fixed composition
	std::vector<index_t> list_fixed_nodes = {0};


	// list_constraints lists the different speciation constraints in the system
	// Note : the total concentrations are computed from the initial solution,
	// and thus different total concentrations do not constitute a reason to create different constraints
	std::vector<specmicp::AdimensionalSystemConstraints> list_constraints = {cement_constraints,
	bc_constraints};

	// index_constraints links a node to the set of constraints that will be used
	std::vector<int> index_constraints(nb_nodes, 0);
	index_constraints[0] = 1; // Boundary conditions

	// This is the list of initial composition
	std::vector<specmicp::AdimensionalSystemSolution> list_initial_composition = {cement_solution, bc_solution};
	// This list links a node to its initial conditions
	std::vector<int> index_initial_state(nb_nodes, 0);
	index_initial_state[0] = 1; // boundary condition

	// Variables
	// -----------

	// Create the main set of variables
	// They will be initialized using the list of initial composition
	satdiff::SaturatedVariablesPtr variables =
	satdiff::init_variables(the_mesh, the_database, units_set,
	list_fixed_nodes,
	list_initial_composition,
	index_initial_state);

	std::shared_ptr<C3SDissolutionModel> kinetic_model = std::make_shared<C3SDissolutionModel>(the_database, units_set);
	variables->kinetic_variables() = kinetic_model->initialize_variables(the_mesh, 0.2);

	// Staggers
	// ---------

	// This section initialize the staggers

	// The equilibrium stagger
	// - - - - - - - - - - - -

	std::shared_ptr<KineticStagger> kinetic_stagger =
	std::make_shared<satdiff::KineticStagger>(kinetic_model, list_constraints, index_constraints, specmicp_options);

	// The transport stagger
	// - - - - - - - - - - -

	std::shared_ptr<SaturatedTransportStagger> transport_stagger =
	std::make_shared<satdiff::SaturatedTransportStagger>(variables, list_fixed_nodes);
	set_transport_options(transport_stagger->options_solver());

	// The upscaling stagger
	// - - - - - - - - - - -

	CappedPowerLawParameters upscaling_param;
	upscaling_param.d_eff_0 = 2.726e-12*1e4;
	upscaling_param.cap = 1e10*1e6;
	upscaling_param.exponent = 3.32;
	upscaling_param.porosity_0 = 0.25;
	upscaling_param.porosity_res = 0.02;

	CappedPowerLaw upscaling_law(upscaling_param);

	UpscalingStaggerPtr upscaling_stagger =
	std::make_shared<DiffusiveUpscalingStagger>(upscaling_law.get_law(),the_database, units_set);

	// Solver
	// ------

	// This section initialize the reactive transport solver

	ReactiveTransportSolver solver(transport_stagger, kinetic_stagger, upscaling_stagger);
	set_reactive_solver_options(solver.get_options());
	transport_stagger->initialize(variables);
	kinetic_stagger->initialize(variables);
	upscaling_stagger->initialize(variables);


	// Some basic information about the simulation
	// First argument : the name of the simulation
	// Second argument : the output function will be called every 3600s
	SimulationInformation simul_info("kincarbo", 1800);
	simul_info.output_prefix = "out_kincarbo_";

	// Runner
	// -------

	// Create the runner : loop through the timestep
	ReactiveTransportRunner runner(solver, 0.1, 100.0, simul_info);


	// Create the output class
	OutputPolicy output_policy(simul_info, the_mesh, the_database, specmicp_options.units_set);
	// and bind it to the runner
	runner.set_output_policy(std::bind(&OutputPolicy::output, &output_policy, std::placeholders::_1, std::placeholders::_2));

	// Solve the problem
	runner.run_until(10243600, cast_var_to_base(variables));


	if(not the_database->is_valid())
	throw std::runtime_error("The database has been changed during the computation");

	AdimensionalSystemSolutionSaver saver(the_database);
	saver.save_solutions(simul_info.complete_filepath("solutions", "dat"), variables->equilibrium_solutions());

	// output information at the end of the timestep

	io::print_minerals_profile(the_database, variables, the_mesh, specmicp_options.units_set,
	simul_info.complete_filepath("profiles_end", "dat"));
	io::print_components_total_aqueous_concentration(the_database, variables,
	the_mesh, specmicp_options.units_set,
	simul_info.complete_filepath("c_profiles_end", "dat"));
	io::print_components_total_solid_concentration(the_database, variables,
	the_mesh, specmicp_options.units_set,
	simul_info.complete_filepath("s_profiles_end", "dat"));
	}


	AdimensionalSystemSolverOptions get_specmicp_options()
	{
	AdimensionalSystemSolverOptions options;


	options.solver_options.maxiter_maxstep = 100;
	options.solver_options.maxstep = 20.0;
	options.solver_options.threshold_cycling_linesearch = 1e-6;

	options.solver_options.set_tolerance(1e-8, 1e-14);
	options.solver_options.disable_condition_check();
	options.solver_options.disable_descent_direction();
	options.solver_options.enable_non_monotone_linesearch();
	options.solver_options.enable_scaling();


	options.system_options.non_ideality_tolerance = 1e-14;
	options.system_options.cutoff_total_concentration = 1e-10;

	options.units_set.length = units::LengthUnit::centimeter;

	return options;
	}

	void set_transport_options(dfpmsolver::ParabolicDriverOptions& transport_options)
	{
	transport_options.maximum_iterations = 450;
	transport_options.quasi_newton = 3;
	transport_options.residuals_tolerance = 1e-8;
	transport_options.step_tolerance = 1e-14;
	transport_options.absolute_tolerance = 1e-18;

	transport_options.alpha = 1.0;
	//transport_options.linesearch = dfpmsolver::ParabolicLinesearch::Strang;
	transport_options.sparse_solver = SparseSolver::SparseLU;
	//transport_options.sparse_solver = SparseSolver::GMRES;
	transport_options.threshold_stationary_point = 1e-4;
	}

	void set_reactive_solver_options(reactmicp::solver::ReactiveTransportOptions& reactive_options)
	{
	reactive_options.maximum_iterations = 100; //500;
	reactive_options.residuals_tolerance = 1e-2;
	reactive_options.good_enough_tolerance = 1.0;

	reactive_options.absolute_residuals_tolerance = 1e-14;
	reactive_options.implicit_upscaling = true;
	}

	RawDatabasePtr get_database(const std::string& path_to_database) {
	database::Database the_database(path_to_database);
	std::map<std::string, std::string> swapping({
	{"H[+]","HO[-]"},
	{"Si(OH)4", "SiO(OH)3[-]"},
	{"Al[3+]","Al(OH)4[-]"}
	});
	the_database.swap_components(swapping);
	the_database.remove_gas_phases();
	return the_database.get_database();

	}



	AdimensionalSystemConstraints get_cement_initial_constraints(
	RawDatabasePtr the_database,
	const units::UnitsSet& units_set)
	{

	Vector oxyde_compo(4);
	oxyde_compo << 66.98, 21.66, 7.19, 2.96;
	Vector species_compo;
	compo_from_oxyde(oxyde_compo, species_compo);

	scalar_t mult = 1e-6;
	species_compo *= 0.85e-2;
	Formulation formulation;
	formulation.mass_solution = 1.0;
	formulation.amount_minerals = {
	{"C3S", species_compo(0)},
	{"C2S", species_compo(1)},
	{"C3A", species_compo(2)},
	{"Gypsum", species_compo(3)},
	{"Calcite", species_compo(0)*1e-3}

	};
	formulation.extra_components_to_keep = {"HCO3[-]"};
	formulation.concentration_aqueous =
	{
	{"Na[+]", mult*1.0298},
	{"K[+]", mult*0.0801},
	{"Cl[-]", mult*0.0001},
	{"HO[-]", mult*1.8298}
	},
	formulation.minerals_to_keep = {
	"Portlandite",
	"CSH,jennite",
	"CSH,tobermorite",
	"SiO2(am)",
	"Calcite",
	"Al(OH)3(mic)",
	"C3AH6",
	"C3ASO_41H5_18",
	"C3ASO_84H4_32",
	"C4AH19",
	"C4AH13",
	"C2AH7_5",
	"CAH10",
	"Monosulfoaluminate",
	"Tricarboaluminate",
	"Monocarboaluminate",
	"Hemicarboaluminate",
	"Straetlingite",
	"Gypsum",
	"Ettringite",
	//"Thaumasite"
	};
	Dissolver dissolver(the_database);
	dissolver.set_units(units_set);

	AdimensionalSystemConstraints constraints;
	constraints.set_charge_keeper(1);

	constraints.total_concentrations = dissolver.dissolve(formulation);

	std::cout << constraints.total_concentrations << std::endl;

	constraints.set_saturated_system();
	constraints.set_inert_volume_fraction(0.2);

	return constraints;
	}

	AdimensionalSystemConstraints get_bc_initial_constraints(
	RawDatabasePtr the_database,
	const units::UnitsSet& units_set)
	{
	const scalar_t rho_w = laws::density_water(units::celsius(25.0), units_set.length, units_set.mass);
	const scalar_t nacl = 0.3*rho_w;
	const scalar_t kcl = 0.28*rho_w;

	Vector total_concentrations;
	total_concentrations.setZero(the_database->nb_component());
	total_concentrations(the_database->get_id_component("K[+]")) = kcl;
	total_concentrations(the_database->get_id_component("Cl[-]")) = nacl + kcl;
	total_concentrations(the_database->get_id_component("Na[+]")) = nacl;
	total_concentrations(the_database->get_id_component("SiO(OH)3[-]")) = 0.0001*rho_w;

	AdimensionalSystemConstraints constraints;
	constraints.add_fixed_activity_component(the_database->get_id_component("HO[-]"), -10.3);
	constraints.set_charge_keeper(the_database->get_id_component("HCO3[-]"));
	constraints.total_concentrations = total_concentrations;

	constraints.set_saturated_system();
	constraints.disable_surface_model();
	constraints.fixed_fugacity_cs ={};

	return constraints;
	}

	AdimensionalSystemSolution get_bc_initial_compo(
	RawDatabasePtr the_database,
	const AdimensionalSystemConstraints& constraints,
	const AdimensionalSystemSolverOptions& options
	)
	{
	Vector variables;
	AdimensionalSystemSolver solver(the_database,
	constraints,
	options);

	micpsolver::MiCPPerformance perf = solver.solve(variables, true);

	if (perf.return_code <= micpsolver::MiCPSolverReturnCode::NotConvergedYet)
	throw std::runtime_error("Failed to solve initial composition");

	std::cout << variables << std::endl;

	return solver.get_raw_solution(variables);
	}

	void compo_from_oxyde(Vector& compo_oxyde, Vector& compo_species)
	{
	constexpr double M_CaO = 56.08;
	constexpr double M_SiO2 = 60.09;
	constexpr double M_Al2O3 = 101.96;
	constexpr double M_SO3 = 80.06;

	Eigen::MatrixXd compo_in_oxyde(4, 4);
	Vector molar_mass(4);
	molar_mass << 1.0/M_CaO, 1.0/M_SiO2, 1.0/M_Al2O3, 1.0/M_SO3;
	compo_oxyde = compo_oxyde.cwiseProduct(molar_mass);
	//C3S C2S C3A Gypsum
	compo_in_oxyde << 3, 2, 3, 1, // CaO
	1, 1, 0, 0, // SiO2
	0, 0, 1, 0, // Al2O3
	0, 0, 0, 1; // SO3
	Eigen::ColPivHouseholderQR<Eigen::MatrixXd> solver(compo_in_oxyde);
	compo_species = solver.solve(compo_oxyde);

	}


	Vector initial_compo(const Vector& publi)
	{
	Matrix publi_stochio(5,5);
	publi_stochio << 1, 0, 0, 0, 0,
	9, 6, 0, 0, 0,
	3, 0, 1, 1, 0,
	3, 0, 1, 3, 0,
	0, 0, 0, 0, 1;

	Matrix cemdata_stochio(5, 5);
	cemdata_stochio << 1, 0, 0, 0, 0,
	1.0/0.6, 1.0, 0, 0, 0,
	3, 0, 1, 1, 0,
	3, 0, 1, 3, 0,
	0, 0, 0, 0, 1;

	Vector oxyde;
	Eigen::ColPivHouseholderQR<Matrix> solver(publi_stochio);
	oxyde = solver.solve(publi);

	Vector for_cemdata = cemdata_stochio*oxyde;
	return for_cemdata;
	}


	mesh::Mesh1DPtr get_mesh(scalar_t dx)
	{
	const scalar_t total_length = 0.75/2.0 + dx; //cm
	const scalar_t height = 20.0;

	index_t nb_nodes = total_length/dx + 1;

	return mesh::uniform_axisymmetric_mesh1d(nb_nodes, total_length, dx, height);
	}

	mesh::Mesh1DPtr get_mesh()
	{
	Vector radius(71);

	const scalar_t height = 20;

	radius <<
	3.751,
	3.750,
	3.745,
	3.740,
	3.735,
	3.730,
	3.720,
	3.710,
	3.700,
	3.690,
	3.680,
	3.670,
	3.660,
	3.645,
	3.630,
	3.615,
	3.600,
	3.580,
	3.560,
	3.540,
	3.520,
	3.500,
	3.475,
	3.450,
	3.425,
	3.400,
	3.375,
	3.350,
	3.325,
	3.300,
	3.275,
	3.250,
	3.225,
	3.200,
	3.175,
	3.150,
	3.125,
	3.100,
	3.050,
	3.025,
	3.000,
	2.950,
	2.900,
	2.850,
	2.800,
	2.750,
	2.700,
	2.650,
	2.600,
	2.550,
	2.500,
	2.450,
	2.400,
	2.350,
	2.300,
	2.250,
	2.200,
	2.150,
	2.100,
	2.050,
	2.000,
	1.950,
	1.900,
	1.850,
	1.800,
	1.750,
	1.700,
	1.650,
	1.600,
	1.550,
	1.500
	;
	radius = radius/10;
	return mesh::axisymmetric_mesh1d(radius, height);
	}

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