transport_stagger.cpp
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Created: Mon, May 20, 05:59

transport_stagger.cpp
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	/* =============================================================================

	Copyright (c) 2014 - 2016
	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 "transport_stagger.hpp"
	#include "reactmicp/solver/staggers_base/stagger_structs.hpp"
	#include "variables.hpp"
	#include "variables_box.hpp"

	#include "boundary_conditions.hpp"

	#include "saturation_equation.hpp"
	#include "saturation_pressure_equation.hpp"
	#include "pressure_equation.hpp"
	#include "aqueous_equation.hpp"
	#include "aqueous_pressure_equation.hpp"

	#include "specmicp_database/database_holder.hpp"

	#include "dfpm/solver/parabolic_driver.hpp"

	#include "specmicp_common/log.hpp"
	#include "specmicp_common/config.h"

	#include <memory>
	#include <iostream>

	namespace specmicp {

	namespace dfpmsolver {
	extern template class ParabolicDriver<specmicp::reactmicp::systems::unsaturated::SaturationEquation>;
	extern template class ParabolicDriver<specmicp::reactmicp::systems::unsaturated::PressureEquation>;
	extern template class ParabolicDriver<specmicp::reactmicp::systems::unsaturated::AqueousTransportEquation>;
	extern template class ParabolicDriver<specmicp::reactmicp::systems::unsaturated::AqueousGasTransportEquation>;
	extern template class ParabolicDriver<specmicp::reactmicp::systems::unsaturated::SaturationPressureEquation>;
	} //end namespace dfpmsolver

	namespace reactmicp {
	namespace systems {
	namespace unsaturated {


	//! \brief Type of the equation
	//! \internal
	enum class EquationType {
	Saturation,
	LiquidAqueous,
	Pressure
	};

	//! \brief Format type to a string (for message error)
	//! \internal
	static std::string to_string(EquationType eq_type);

	//! \brief Format DFPM solver retcode to a string
	static std::string to_string(dfpmsolver::ParabolicDriverReturnCode retcode);

	// forward declaration of wrapper classes
	// They are defined at the bootom of this file
	class TaskBase;
	class SaturationTask;

	using VariablesBase = solver::VariablesBase;


	// =================================== //
	// //
	// Declaration of the implementation //
	// //
	// =================================== //

	//! \brief Implementation class for the Unsaturated transport stagger
	//! \internal
	//!
	//! This class does all the work
	//! It was designed to be OpenMP compatible
	class UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl
	{
	public:
	// Constructor
	// -----------
	UnsaturatedTransportStaggerImpl(
	UnsaturatedVariablesPtr variables,
	std::shared_ptr<BoundaryConditions> boundary_conditions,
	bool merge_saturation_pressure,
	bool merge_aqueous_pressure
	);

	// Main functions
	// --------------

	//! \brief Return the residual
	scalar_t get_residual(UnsaturatedVariables * const vars);
	//! \brief Return the first residual (start of timestep)
	scalar_t get_residual_0(UnsaturatedVariables * const vars);
	//! \brief Return the update (norm of velocity vector)
	scalar_t get_update(UnsaturatedVariables * const vars);

	//! \brief Initialize timestep
	void initialize_timestep(
	scalar_t dt,
	UnsaturatedVariables * const vars);
	//! \brief Restart the timestep
	solver::StaggerReturnCode restart_timestep(UnsaturatedVariables* vars);

	// Timestep management
	// -------------------

	//! \brief Save the timestep
	void save_dt(scalar_t dt) {m_dt = dt;}
	//! \brief Return the timestep
	scalar_t get_dt() {return m_dt;}

	// Task index
	// ----------
	index_t& id_aqueous_task(index_t component) {
	return m_aq_equation_task[static_cast<std::size_t>(component)];
	}
	index_t id_aqueous_task(index_t component) const {
	return m_aq_equation_task[static_cast<std::size_t>(component)];
	}
	index_t& id_gas_task(index_t component) {
	return m_aq_equation_task[static_cast<std::size_t>(component)];
	}
	index_t id_gas_task(index_t component) const {
	return m_aq_equation_task[static_cast<std::size_t>(component)];
	}

	//! \brief Return the options of the saturation equation
	dfpmsolver::ParabolicDriverOptions* get_saturation_options();
	//! \brief Return the options of aqueous equation of component
	dfpmsolver::ParabolicDriverOptions* get_aqueous_options(index_t component);
	//! \brief Return the options of gas equation of component
	dfpmsolver::ParabolicDriverOptions* get_gas_options(index_t component);

	private:

	scalar_t m_norm_0 {1.0};
	// timestep management
	scalar_t m_dt {-1.0};

	//! \brief The saturation equations
	std::unique_ptr<TaskBase> m_saturation_equation;
	// Equation and solver
	std::vector<std::unique_ptr<TaskBase>> m_equation_list;

	std::vector<index_t> m_aq_equation_task;
	std::vector<index_t> m_gas_equation_task;

	std::vector<bool> m_merged_gas;


	};

	// Main functions
	// ===============

	// call of the implementation

	UnsaturatedTransportStagger::UnsaturatedTransportStagger(
	std::shared_ptr<UnsaturatedVariables> variables,
	std::shared_ptr<BoundaryConditions> boundary_conditions,
	bool merge_saturation_pressure,
	bool merge_aqueous_pressure
	):
	m_impl(utils::make_pimpl<UnsaturatedTransportStaggerImpl>(
	variables, boundary_conditions,
	merge_saturation_pressure, merge_aqueous_pressure
	))
	{
	}

	UnsaturatedTransportStagger::~UnsaturatedTransportStagger() = default;


	static UnsaturatedVariables * const get_var(VariablesBase * const var) {
	return static_cast<UnsaturatedVariables * const >(var);
	}

	void
	UnsaturatedTransportStagger::initialize_timestep(
	scalar_t dt,
	VariablesBase* var
	)
	{
	m_impl->initialize_timestep(dt, get_var(var));
	}

	solver::StaggerReturnCode
	UnsaturatedTransportStagger::restart_timestep(VariablesBase * const var)
	{
	return m_impl->restart_timestep(get_var(var));
	}

	scalar_t
	UnsaturatedTransportStagger::get_residual(VariablesBase * const var)
	{
	return m_impl->get_residual(get_var(var));
	}

	scalar_t
	UnsaturatedTransportStagger::get_residual_0(VariablesBase * const var)
	{
	return m_impl->get_residual_0(get_var(var));
	}

	scalar_t
	UnsaturatedTransportStagger::get_update(VariablesBase * const var)
	{
	return m_impl->get_update(get_var(var));
	}


	dfpmsolver::ParabolicDriverOptions*
	UnsaturatedTransportStagger::get_saturation_options()
	{
	return m_impl->get_saturation_options();
	}

	dfpmsolver::ParabolicDriverOptions*
	UnsaturatedTransportStagger::get_aqueous_options(index_t component)
	{
	return m_impl->get_aqueous_options(component);
	}

	dfpmsolver::ParabolicDriverOptions*
	UnsaturatedTransportStagger::get_gas_options(index_t component)
	{
	return m_impl->get_gas_options(component);
	}

	// =============================== //
	// =============================== //
	// //
	// Implementation details //
	// ---------------------- //
	// //
	// =============================== //
	// =============================== //

	// 2 main sections
	// - Solver wrappers : wrapper around 1 couple equation/solver
	// - UnsaturatedTransportStaggerImpl : call the wrappers

	// =============================== //
	// //
	// Solver wrappers //
	// //
	// =============================== //

	// This wrappers are used to abstract the residual computation
	// and the methods to solve every equations


	//! \brief Base class for a task
	//!
	//! A task is how we solve governing equations,
	//! and obtain residuals and update
	//!
	//! \internal
	class SPECMICP_DLL_LOCAL TaskBase
	{
	public:
	TaskBase(index_t component, EquationType eq_type):
	m_type(eq_type),
	m_component(component)
	{}

	virtual ~TaskBase() {}

	//! \brief Compute the squared residuals
	virtual scalar_t compute_squared_residual(
	UnsaturatedVariables * const vars
	) = 0;
	//! \brief Compute the squared residuals at the beginning of the timestep
	virtual scalar_t compute_squared_residual_0(
	UnsaturatedVariables * const vars
	) = 0;
	//! \brief Compute the squared update of the variables
	virtual scalar_t compute_squared_update(
	UnsaturatedVariables * const vars
	) = 0;

	//! \brief Initialize the timestep
	virtual void initialize_timestep(
	scalar_t dt, UnsaturatedVariables * const vars
	) = 0;

	//! \brief Solve the governing equation
	virtual dfpmsolver::ParabolicDriverReturnCode restart_timestep(
	UnsaturatedVariables * const vars
	) = 0;

	//! \brief Return the component index (in the db)
	index_t component() {return m_component;}

	//! \brief The equation type
	EquationType equation_type() {return m_type;}

	private:
	EquationType m_type;
	index_t m_component;
	};


	//! \brief Base class for a equation solver
	//!
	//! \internal
	template <typename Derived, typename traits>
	class SPECMICP_DLL_LOCAL EquationTask: public TaskBase
	{
	public:
	using EqT = typename traits::EqT;
	using SolverT = typename traits::SolverT;

	EquationTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	typename traits::VariableBoxT& variables,
	std::shared_ptr<BoundaryConditions> bcs
	):
	TaskBase(component, traits::equation_type),
	m_equation(component, the_mesh, variables, bcs),
	m_solver(m_equation)
	{}

	EquationTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	typename traits::VariableBoxT& variables,
	std::shared_ptr<BoundaryConditions> bcs,
	scalar_t scaling
	):
	TaskBase(component, traits::equation_type),
	m_equation(component, the_mesh, variables, bcs),
	m_solver(m_equation)
	{
	m_equation.set_scaling(scaling);
	}

	Derived* derived() {return static_cast<Derived*>(this);}

	// This function must be implemented by subclass
	MainVariable& get_var(UnsaturatedVariables * const vars) {
	return derived()->get_var(vars);
	}

	scalar_t compute_squared_residual(
	UnsaturatedVariables * const vars
	) override {
	Vector residuals;
	const MainVariable& main = get_var(vars);
	m_equation.compute_residuals(main.variable, main.velocity, residuals, true);
	return residuals.squaredNorm()/m_norm_square_0;
	}
	scalar_t compute_squared_residual_0(
	UnsaturatedVariables * const vars
	) override {
	Vector residuals;
	const MainVariable& main = get_var(vars);
	m_equation.compute_residuals(main.variable, main.velocity, residuals, false);
	m_norm_square_0 = residuals.squaredNorm();
	if (m_norm_square_0 < 1e-8) m_norm_square_0 = 1.0;
	return 1.0;
	}
	scalar_t compute_squared_update(
	UnsaturatedVariables * const vars
	) override {
	const MainVariable& main = get_var(vars);
	return main.velocity.squaredNorm();
	}

	void initialize_timestep(
	scalar_t dt,
	UnsaturatedVariables * const vars
	) override {
	m_dt = dt;
	MainVariable& main = get_var(vars);
	main.predictor = main.variable;
	main.transport_fluxes.setZero();
	main.velocity.setZero();
	m_solver.initialize_timestep(dt, get_var(vars).variable);
	}

	dfpmsolver::ParabolicDriverReturnCode restart_timestep(
	UnsaturatedVariables * const vars
	) override {
	MainVariable& main = get_var(vars);
	m_solver.velocity() = main.velocity;
	auto retcode = m_solver.restart_timestep(main.variable);
	if (retcode > dfpmsolver::ParabolicDriverReturnCode::NotConvergedYet)
	{
	main.velocity = m_solver.velocity();
	}
	return retcode;
	}

	dfpmsolver::ParabolicDriverOptions& get_options() {
	return m_solver.get_options();
	}

	const dfpmsolver::ParabolicDriverOptions& get_options() const {
	return m_solver.get_options();
	}

	scalar_t get_dt() {return m_dt;}

	protected:
	scalar_t m_norm_square_0 {-1};
	scalar_t m_dt {-1};
	EqT m_equation;
	SolverT m_solver;
	};

	//! \brief Traits struct for the SaturationTask class
	//!
	//! \internal
	struct SPECMICP_DLL_LOCAL SaturationTaskTraits {
	using EqT = SaturationEquation;
	using SolverT = dfpmsolver::ParabolicDriver<EqT>;
	using VariableBoxT = SaturationVariableBox;
	static constexpr EquationType equation_type {EquationType::Saturation};
	};

	//! \brief Wrapper for the saturation equation solver
	//!
	//! \internal
	class SPECMICP_DLL_LOCAL SaturationTask:
	public EquationTask<SaturationTask, SaturationTaskTraits>
	{
	using base = EquationTask<SaturationTask, SaturationTaskTraits>;
	public:

	SaturationTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	SaturationTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs
	):
	EquationTask<SaturationTask, SaturationTaskTraits>(
	component, the_mesh, variables, bcs)
	{}
	SaturationTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	SaturationTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs,
	scalar_t scaling
	):
	EquationTask<SaturationTask, SaturationTaskTraits>(
	component, the_mesh, variables, bcs, scaling)
	{}

	MainVariable& get_var(UnsaturatedVariables * const vars) {
	return vars->get_liquid_saturation();
	}

	// Also take into account the solid total concentration
	scalar_t compute_squared_update(
	UnsaturatedVariables * const vars
	) override {
	scalar_t solid_update = vars->get_solid_concentration(component()).velocity.squaredNorm();
	return solid_update + base::compute_squared_update(vars);
	}
	};

	//! \brief Traits struct for the SaturationPressureTask class
	//!
	//! \internal
	struct SPECMICP_DLL_LOCAL SaturationPressureTaskTraits {
	using EqT = SaturationPressureEquation;
	using SolverT = dfpmsolver::ParabolicDriver<EqT>;
	using VariableBoxT = SaturationPressureVariableBox;
	static constexpr EquationType equation_type {EquationType::Saturation};
	};

	//! \brief Wrapper for the saturation equation solver
	//!
	//! \internal
	class SPECMICP_DLL_LOCAL SaturationPressureTask:
	public EquationTask<SaturationPressureTask, SaturationPressureTaskTraits>
	{
	using base = EquationTask<SaturationPressureTask, SaturationPressureTaskTraits>;
	public:

	SaturationPressureTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	SaturationPressureTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs
	):
	EquationTask<SaturationPressureTask, SaturationPressureTaskTraits>(
	component, the_mesh, variables, bcs)
	{}
	SaturationPressureTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	SaturationPressureTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs,
	scalar_t scaling
	):
	EquationTask<SaturationPressureTask, SaturationPressureTaskTraits>(
	component, the_mesh, variables, bcs, scaling)
	{}

	MainVariable& get_var(UnsaturatedVariables * const vars) {
	return vars->get_liquid_saturation();
	}

	// Also take into account the solid total concentration
	scalar_t compute_squared_update(
	UnsaturatedVariables * const vars
	) override {
	scalar_t solid_update = vars->get_solid_concentration(component()).velocity.squaredNorm();
	return solid_update + base::compute_squared_update(vars);
	}
	};

	//! \brief Traits struct for the LiquidAqueousTask class
	//!
	//! \internal
	struct SPECMICP_DLL_LOCAL LiquidAqueousTaskTraits {
	using EqT = AqueousTransportEquation;
	using SolverT = dfpmsolver::ParabolicDriver<EqT>;
	using VariableBoxT = LiquidAqueousComponentVariableBox;
	static constexpr EquationType equation_type {EquationType::LiquidAqueous};
	};

	//! \brief Wrapper for the liquid transport of aqueous component equation
	//!
	//! \internal
	class SPECMICP_DLL_LOCAL LiquidAqueousTask:
	public EquationTask<LiquidAqueousTask, LiquidAqueousTaskTraits>
	{
	using base = EquationTask<LiquidAqueousTask, LiquidAqueousTaskTraits>;

	public:
	LiquidAqueousTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	LiquidAqueousTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs
	):
	EquationTask<LiquidAqueousTask, LiquidAqueousTaskTraits>(
	component, the_mesh, variables, bcs)
	{}
	LiquidAqueousTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	LiquidAqueousTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs,
	scalar_t scaling
	):
	EquationTask<LiquidAqueousTask, LiquidAqueousTaskTraits>(
	component, the_mesh, variables, bcs, scaling)
	{}

	MainVariable& get_var(UnsaturatedVariables * const vars) {
	return vars->get_aqueous_concentration(component());
	}

	// Also take into account the solid total concentration
	scalar_t compute_squared_update(
	UnsaturatedVariables * const vars
	) override {
	scalar_t solid_update = vars->get_solid_concentration(component()).velocity.squaredNorm();
	return solid_update + base::compute_squared_update(vars);
	}
	};


	//! \brief Traits struct for the LiquidGasAqueousTask class
	//!
	//! \internal
	struct SPECMICP_DLL_LOCAL LiquidGasAqueousTaskTraits {
	using EqT = AqueousGasTransportEquation;
	using SolverT = dfpmsolver::ParabolicDriver<EqT>;
	using VariableBoxT = LiquidGasAqueousVariableBox;
	static constexpr EquationType equation_type {EquationType::LiquidAqueous};
	};

	//! \brief Wrapper for the liquid transport of aqueous component equation
	//!
	//! \internal
	class SPECMICP_DLL_LOCAL LiquidGasAqueousTask:
	public EquationTask<LiquidGasAqueousTask, LiquidGasAqueousTaskTraits>
	{
	using base = EquationTask<LiquidGasAqueousTask, LiquidGasAqueousTaskTraits>;

	public:
	LiquidGasAqueousTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	LiquidGasAqueousTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs
	):
	base(component, the_mesh, variables, bcs)
	{}
	LiquidGasAqueousTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	LiquidGasAqueousTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs,
	scalar_t scaling
	):
	base(component, the_mesh, variables, bcs, scaling)
	{}

	MainVariable& get_var(UnsaturatedVariables * const vars) {
	return vars->get_aqueous_concentration(component());
	}

	// Also take into account the solid total concentration
	scalar_t compute_squared_update(
	UnsaturatedVariables * const vars
	) override {
	scalar_t solid_update = vars->get_solid_concentration(component()).velocity.squaredNorm();
	return solid_update + base::compute_squared_update(vars);
	}
	};


	//! \brief Traits struct for the Pressure Task traits
	//!
	//! \internal
	struct SPECMICP_DLL_LOCAL PressureTaskTraits {
	using EqT = PressureEquation;
	using SolverT = dfpmsolver::ParabolicDriver<EqT>;
	using VariableBoxT = PressureVariableBox;
	static constexpr EquationType equation_type {EquationType::Pressure};
	};

	//! \brief Wrapper for the pressure equation solver
	//!
	//! \internal
	class SPECMICP_DLL_LOCAL PressureTask:
	public EquationTask<PressureTask, PressureTaskTraits>
	{
	using base = EquationTask<PressureTask, PressureTaskTraits>;

	public:
	PressureTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	PressureTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs
	):
	EquationTask<PressureTask, PressureTaskTraits>(
	component, the_mesh, variables, bcs)
	{}
	PressureTask(
	index_t component,
	mesh::Mesh1DPtr the_mesh,
	PressureTaskTraits::VariableBoxT&& variables,
	std::shared_ptr<BoundaryConditions> bcs,
	scalar_t scaling
	):
	EquationTask<PressureTask, PressureTaskTraits>(
	component, the_mesh, variables, bcs, scaling)
	{}

	MainVariable& get_var(UnsaturatedVariables * const vars) {
	return vars->get_pressure_main_variables(component());
	}
	};

	// ================================== //
	// //
	// UnsaturatedTransportStaggerImpl //
	// //
	// ================================== //

	// constructor
	// ===========

	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::UnsaturatedTransportStaggerImpl(
	UnsaturatedVariablesPtr variables,
	std::shared_ptr<BoundaryConditions> bcs,
	bool merge_saturation_pressure,
	bool merge_aqueous_pressure
	):
	m_merged_gas(variables->get_database()->nb_component(), false)
	{
	database::RawDatabasePtr raw_db = variables->get_database();
	mesh::Mesh1DPtr the_mesh = variables->get_mesh();

	m_aq_equation_task = std::vector<index_t>(
	raw_db->nb_component(), no_equation);
	m_gas_equation_task = std::vector<index_t>(
	raw_db->nb_component(), no_equation);

	dfpmsolver::ParabolicDriverOptions* opts = nullptr;
	// Saturation equations
	// ====================
	//
	// There is 2 choices for the saturation equation
	// Either SaturationPressureEquation or SaturationPressure
	if (merge_saturation_pressure and variables->component_has_gas(0))
	{
	m_saturation_equation = make_unique<SaturationPressureTask>(
	0, the_mesh,
	variables->get_saturation_pressure_variables(),
	bcs,
	variables->get_aqueous_scaling(0)
	);
	m_merged_gas[0] = true;
	opts = &(static_cast<SaturationPressureTask*>(
	m_saturation_equation.get())->get_options());

	}
	else
	{
	m_saturation_equation = make_unique<SaturationTask>(
	0, the_mesh,
	variables->get_saturation_variables(),
	bcs,
	variables->get_aqueous_scaling(0)
	);
	opts = &(static_cast<SaturationTask*>(
	m_saturation_equation.get())->get_options());
	}
	opts->residuals_tolerance = 1e-8;
	opts->absolute_tolerance = 1e-12;
	opts->step_tolerance = 1e-12;
	opts->threshold_stationary_point = 1e-12;
	opts->maximum_iterations = 500;
	opts->sparse_solver = sparse_solvers::SparseSolver::SparseLU;
	opts->quasi_newton = 3;
	opts->maximum_step_length = 0.1;
	opts->max_iterations_at_max_length = 5000;

	const index_t size = raw_db->nb_aqueous_components() + variables->nb_gas();
	m_equation_list.reserve(size);

	// Liquid aqueous diffusion-advection
	// ==================================
	for (index_t id: raw_db->range_aqueous_component())
	{
	if (merge_aqueous_pressure and variables->component_has_gas(id))
	{
	m_equation_list.emplace_back(
	make_unique<LiquidGasAqueousTask>(
	id, the_mesh,
	variables->get_liquid_gas_aqueous_variables(id),
	bcs,
	variables->get_aqueous_scaling(id))
	);
	m_merged_gas[id] = true;
	} else {
	m_equation_list.emplace_back(
	make_unique<LiquidAqueousTask>(
	id, the_mesh,
	variables->get_liquid_aqueous_component_variables(id),
	bcs,
	variables->get_aqueous_scaling(id))
	);
	}
	id_aqueous_task(id) = m_equation_list.size()-1;
	dfpmsolver::ParabolicDriverOptions& opts = *get_aqueous_options(id);
	opts.maximum_iterations = 500;
	opts.residuals_tolerance = 1e-8;
	opts.absolute_tolerance = 1e-12;
	opts.step_tolerance = 1e-12;
	opts.threshold_stationary_point = 1e-12;
	opts.sparse_solver = sparse_solvers::SparseSolver::SparseLU;
	opts.maximum_step_length= 1e6;
	}

	// Water partial pressure
	// ======================
	//
	// Depending on the saturation equation chosen we may or may not include
	// this equations
	if (variables->component_has_gas(0) and (not m_merged_gas[0]))
	{
	m_equation_list.emplace_back(
	make_unique<PressureTask>(0, the_mesh,
	variables->get_pressure_variables(0),
	bcs,
	variables->get_gaseous_scaling(0)
	));
	id_gas_task(0) = m_equation_list.size()-1;
	dfpmsolver::ParabolicDriverOptions& opts = *get_gas_options(0);
	opts.maximum_iterations = 500;
	opts.residuals_tolerance = 1e-8;
	opts.absolute_tolerance = 1e-12;
	opts.step_tolerance = 1e-12;
	opts.threshold_stationary_point = 1e-12;
	opts.sparse_solver = sparse_solvers::SparseSolver::SparseLU;
	opts.maximum_step_length= 1e6;
	}
	// Gaseous diffusion
	for (index_t id: raw_db->range_aqueous_component())
	{
	if (variables->component_has_gas(id) and (not m_merged_gas[id])) {
	m_equation_list.emplace_back(
	make_unique<PressureTask>(id, the_mesh,
	variables->get_pressure_variables(id),
	bcs,
	variables->get_gaseous_scaling(id)
	));
	id_gas_task(id) = m_equation_list.size()-1;
	dfpmsolver::ParabolicDriverOptions& opts = *get_gas_options(id);
	opts.maximum_iterations = 500;
	opts.residuals_tolerance = 1e-8;
	opts.absolute_tolerance = 1e-12;
	opts.step_tolerance = 1e-12;
	opts.threshold_stationary_point = 1e-12;
	opts.sparse_solver = sparse_solvers::SparseSolver::SparseLU;
	opts.maximum_step_length= 1e6;
	}
	}
	}


	dfpmsolver::ParabolicDriverOptions*
	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::get_saturation_options()
	{
	dfpmsolver::ParabolicDriverOptions* opts = nullptr;
	if (m_merged_gas[0]) {
	opts = &static_cast<SaturationPressureTask*>(
	m_saturation_equation.get())->get_options();
	} else {
	opts = &static_cast<SaturationTask*>(
	m_saturation_equation.get())->get_options();
	}

	return opts;
	}

	dfpmsolver::ParabolicDriverOptions*
	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::get_aqueous_options(
	index_t component)
	{
	dfpmsolver::ParabolicDriverOptions* opts = nullptr;
	auto id = id_aqueous_task(component);

	if (id != no_equation) {
	if (m_merged_gas[component]) {
	opts = &static_cast<LiquidGasAqueousTask*>(
	m_equation_list[id].get())->get_options();
	} else {
	opts = &static_cast<LiquidAqueousTask*>(
	m_equation_list[id].get())->get_options();
	}
	}
	return opts;
	}

	dfpmsolver::ParabolicDriverOptions*
	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::get_gas_options(
	index_t component)
	{

	dfpmsolver::ParabolicDriverOptions* opts = nullptr;
	auto id = id_gas_task(component);

	if (id != no_equation) {
	opts = &static_cast<PressureTask*>(
	m_equation_list[id].get())->get_options();
	}
	return opts;
	}

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

	scalar_t
	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::get_residual(
	UnsaturatedVariables * const vars
	)
	{
	auto sum = m_saturation_equation->compute_squared_residual(vars);
	#ifdef SPECMICP_HAVE_OPENMP
	#pragma omp parallel for \
	reduction(+: sum)
	#endif
	for (std::size_t ideq=0; ideq<m_equation_list.size(); ++ideq) {
	auto& task = m_equation_list[ideq];
	sum += task->compute_squared_residual(vars);
	}
	auto norm = std::sqrt(sum);
	//std::cout << "; " << norm << std::endl;
	return norm;
	}

	scalar_t
	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::get_residual_0(
	UnsaturatedVariables * const vars
	)
	{
	return m_norm_0;
	}

	scalar_t
	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::get_update(
	UnsaturatedVariables * const vars
	)
	{
	scalar_t sum = m_saturation_equation->compute_squared_update(vars);

	#ifdef SPECMICP_HAVE_OPENMP
	#pragma omp parallel for \
	reduction(+: sum)
	#endif
	for (std::size_t ideq=0; ideq<m_equation_list.size(); ++ideq) {
	auto& task = m_equation_list[ideq];
	sum += task->compute_squared_update(vars);
	}
	return std::sqrt(sum);
	}

	// Solving the equations
	// =====================

	void
	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::initialize_timestep(
	scalar_t dt,
	UnsaturatedVariables * const vars
	)
	{
	save_dt(dt);

	vars->get_advection_flux().set_zero();

	m_saturation_equation->initialize_timestep(dt, vars);
	scalar_t sum = m_saturation_equation->compute_squared_residual_0(vars);

	#ifdef SPECMICP_HAVE_OPENMP
	#pragma omp parallel for \
	reduction(+: sum)
	#endif
	for (std::size_t ideq=0; ideq<m_equation_list.size(); ++ideq) {
	auto& task = m_equation_list[ideq];
	task->initialize_timestep(dt, vars);
	sum += task->compute_squared_residual_0(vars);
	}
	m_norm_0 = 1.0;//std::sqrt(sum);
	}

	solver::StaggerReturnCode
	UnsaturatedTransportStagger::UnsaturatedTransportStaggerImpl::restart_timestep(
	UnsaturatedVariables * const vars
	)
	{
	dfpmsolver::ParabolicDriverReturnCode retcode;

	bool flag_fail = false;
	bool flag_error_minimized = false;

	// Saturation equation
	retcode = m_saturation_equation->restart_timestep(vars);
	if (dfpmsolver::has_failed(retcode)) {
	WARNING << "Failed to solve saturation equation, return code :"
	<< to_string(retcode);
	flag_fail = true;
	}
	if (retcode == dfpmsolver::ParabolicDriverReturnCode::ErrorMinimized)
	flag_error_minimized = true;

	// Other equation
	if (not flag_fail)
	{
	vars->set_relative_variables();
	#ifdef SPECMICP_HAVE_OPENMP
	#pragma omp parallel for \
	reduction(or: flag_fail) \
	reduction(and: flag_error_minimized)
	#endif
	for (std::size_t ideq=0; ideq<m_equation_list.size(); ++ideq) {
	auto& task = m_equation_list[ideq];
	retcode = task->restart_timestep(vars);
	if (dfpmsolver::has_failed(retcode)) {
	WARNING << "Equation of type '" << to_string(task->equation_type())
	<< "' for component " << task->component()
	<< " has failed with return code : "
	<< to_string(retcode);
	flag_fail = true;
	}
	flag_error_minimized = flag_error_minimized and
	(retcode == dfpmsolver::ParabolicDriverReturnCode::ErrorMinimized);
	}
	}

	// Return code
	solver::StaggerReturnCode return_code = solver::StaggerReturnCode::ResidualMinimized;
	if (flag_error_minimized)
	{
	return_code = solver::StaggerReturnCode::ErrorMinimized;
	}
	if (flag_fail)
	return_code = solver::StaggerReturnCode::UnknownError;

	return return_code;

	}

	// ================================ //
	// //
	// Helper functions //
	// //
	// ================================ //

	static std::string to_string(EquationType eq_type)
	{
	std::string str;
	switch (eq_type) {
	case EquationType::LiquidAqueous:
	str = "Liquid advection-diffusion";
	break;
	case EquationType::Pressure:
	str = "Gaseous diffusion";
	break;
	case EquationType::Saturation:
	str = "Saturation equation";
	break;
	default:
	str = "Unknown equation";
	break;
	}
	return str;
	}

	std::string to_string(dfpmsolver::ParabolicDriverReturnCode retcode)
	{
	using RetCode = dfpmsolver::ParabolicDriverReturnCode;
	std::string str;
	switch (retcode) {
	case RetCode::ResidualMinimized:
	str = "ResidualMinimized";
	break;
	case RetCode::ErrorMinimized:
	str = "ErrorMinimized";
	break;
	case RetCode::NotConvergedYet:
	str = "NotConvergedYet";
	break;
	case RetCode::StationaryPoint:
	str = "StationaryPoint";
	break;
	case RetCode::ErrorLinearSystem:
	str = "ErrorLinearSystem";
	break;
	case RetCode::MaxStepTakenTooManyTimes:
	str = "MaxStepTakenTooManyTimes";
	break;
	case RetCode::MaxIterations:
	str = "MaxIterations";
	break;
	case RetCode::LinesearchFailed:
	str = "LinesearchFailed";
	default:
	str = "Unknown return code";
	break;
	}
	return str;
	}

	} //end namespace unsaturated
	} //end namespace systems
	} //end namespace reactmicp
	} //end namespace specmicp

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