fluid_diffusion_model.cc
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fluid_diffusion_model.cc
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	/**
	* @file fluid_diffusion_model.hh
	*
	* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
	*
	* @date creation: Aug 2019
	*
	* @brief Implementation of Transient fluid diffusion model
	*
	* @section LICENSE
	*
	* Copyright (©) 2010-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
	* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
	*
	* Akantu is free software: you can redistribute it and/or modify it under the
	* terms of the GNU Lesser General Public License as published by the Free
	* Software Foundation, either version 3 of the License, or (at your option) any
	* later version.
	*
	* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
	* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
	* details.
	*
	* You should have received a copy of the GNU Lesser General Public License
	* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
	*
	*/

	/* -------------------------------------------------------------------------- */
	#include "fluid_diffusion_model.hh"
	#include "dumpable_inline_impl.hh"
	#include "element_synchronizer.hh"
	#include "fe_engine_template.hh"
	#include "generalized_trapezoidal.hh"
	#include "group_manager_inline_impl.hh"
	#include "integrator_gauss.hh"
	#include "mesh.hh"
	#include "parser.hh"
	#include "shape_lagrange.hh"

	#ifdef AKANTU_USE_IOHELPER
	#include "dumper_element_partition.hh"
	#include "dumper_elemental_field.hh"
	#include "dumper_internal_material_field.hh"
	#include "dumper_iohelper_paraview.hh"
	#endif

	/* -------------------------------------------------------------------------- */
	namespace akantu {

	namespace fluid_diffusion {
	namespace details {
	class ComputeRhoFunctor {
	public:
	ComputeRhoFunctor(const FluidDiffusionModel & model) : model(model){};

	void operator()(Matrix<Real> & rho, const Element & element) const {
	const auto & type = element.type;
	const auto & gt = element.ghost_type;
	const auto & aperture = model.getApertureOnQpoints(type, gt);
	auto nb_quad_points = aperture.getNbComponent();
	Real aperture_av = 0.;
	for (auto q : arange(nb_quad_points)) {
	aperture_av += aperture(element.element, q);
	}
	aperture_av /= nb_quad_points;
	if (model.isModelVelocityDependent()) {
	rho.set(model.getCompressibility() * aperture_av);
	} else {
	rho.set((model.getCompressibility() + model.getPushability()) *
	aperture_av);
	}
	}

	private:
	const FluidDiffusionModel & model;
	};
	} // namespace details
	} // namespace fluid_diffusion

	/* -------------------------------------------------------------------------- */
	FluidDiffusionModel::FluidDiffusionModel(Mesh & mesh, UInt dim, const ID & id)
	: Model(mesh, ModelType::_fluid_diffusion_model, dim, id),
	pressure_gradient("pressure_gradient", id),
	pressure_on_qpoints("pressure_on_qpoints", id),
	delta_pres_on_qpoints("delta_pres_on_qpoints", id),
	permeability_on_qpoints("permeability_on_qpoints", id),
	aperture_on_qpoints("aperture_on_qpoints", id),
	prev_aperture_on_qpoints("prev_aperture_on_qpoints", id),
	k_gradp_on_qpoints("k_gradp_on_qpoints", id) {
	AKANTU_DEBUG_IN();

	// mesh.registerEventHandler(*this, akantu::_ehp_lowest);

	this->spatial_dimension = std::max(1, int(mesh.getSpatialDimension()) - 1);

	this->initDOFManager();

	this->registerDataAccessor(*this);

	if (this->mesh.isDistributed()) {
	auto & synchronizer = this->mesh.getElementSynchronizer();
	this->registerSynchronizer(synchronizer, SynchronizationTag::_fdm_pressure);
	this->registerSynchronizer(synchronizer,
	SynchronizationTag::_fdm_gradient_pressure);
	}

	registerFEEngineObject<FEEngineType>(id + ":fem", mesh, spatial_dimension);

	#ifdef AKANTU_USE_IOHELPER
	this->mesh.registerDumper<DumperParaview>("fluid_diffusion", id, true);
	this->mesh.addDumpMesh(mesh, spatial_dimension, _not_ghost, _ek_regular);
	#endif

	this->registerParam("viscosity", viscosity, 1., _pat_parsmod);
	this->registerParam("compressibility", compressibility, 1., _pat_parsmod);
	this->registerParam("default_aperture", default_aperture, 1.e-5,
	_pat_parsmod);
	this->registerParam("use_aperture_speed", use_aperture_speed, _pat_parsmod);
	this->registerParam("pushability", pushability, 1., _pat_parsmod);
	this->registerParam("insertion_damage", insertion_damage, 0., _pat_parsmod);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::initModel() {
	auto & fem = this->getFEEngine();
	fem.initShapeFunctions(_not_ghost);
	fem.initShapeFunctions(_ghost);

	pressure_on_qpoints.initialize(fem, _nb_component = 1);
	delta_pres_on_qpoints.initialize(fem, _nb_component = 1);
	pressure_gradient.initialize(fem, _nb_component = 1);
	permeability_on_qpoints.initialize(fem, _nb_component = 1);
	aperture_on_qpoints.initialize(fem, _nb_component = 1);
	if (use_aperture_speed) {
	prev_aperture_on_qpoints.initialize(fem, _nb_component = 1);
	}
	k_gradp_on_qpoints.initialize(fem, _nb_component = 1);

	this->initBC(this, pressure, *external_flux);
	}

	/* -------------------------------------------------------------------------- */
	FEEngine & FluidDiffusionModel::getFEEngineBoundary(const ID & name) {
	return aka::as_type<FEEngine>(getFEEngineClassBoundary<FEEngineType>(name));
	}
	/* -------------------------------------------------------------------------- */
	FluidDiffusionModel::~FluidDiffusionModel() = default;

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assembleCapacityLumped(const GhostType & ghost_type) {
	AKANTU_DEBUG_IN();

	auto & fem = getFEEngineClass<FEEngineType>();
	fluid_diffusion::details::ComputeRhoFunctor compute_rho(*this);

	for (const auto & type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	fem.assembleFieldLumped(compute_rho, "M", "pressure", this->getDOFManager(),
	type, ghost_type);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	MatrixType FluidDiffusionModel::getMatrixType(const ID & matrix_id) const {
	if (matrix_id == "K" or matrix_id == "M") {
	return _symmetric;
	}

	return _mt_not_defined;
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assembleMatrix(const ID & matrix_id) {
	if (matrix_id == "K") {
	this->assemblePermeabilityMatrix();
	} else if (matrix_id == "M" and need_to_reassemble_capacity) {
	this->assembleCapacity();
	}
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assembleLumpedMatrix(const ID & matrix_id) {
	if (matrix_id == "M" and need_to_reassemble_capacity) {
	this->assembleCapacityLumped();
	}
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assembleResidual() {
	AKANTU_DEBUG_IN();

	this->assembleInternalFlux();

	this->getDOFManager().assembleToResidual("pressure", *this->external_flux, 1);
	this->getDOFManager().assembleToResidual("pressure", *this->internal_flux, 1);

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::predictor() { ++pressure_release; }

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::afterSolveStep(bool converged) {
	AKANTU_DEBUG_IN();

	if (not converged) {
	return;
	}

	++solution_release;
	need_to_reassemble_capacity_lumped = true;
	need_to_reassemble_capacity = true;

	/// interpolating pressures on integration points for further use by BC
	const GhostType gt = _not_ghost;
	for (auto && type : mesh.elementTypes(spatial_dimension, gt, _ek_regular)) {
	Array<Real> tmp(pressure_on_qpoints(type, gt));
	this->getFEEngine().interpolateOnIntegrationPoints(
	*pressure, pressure_on_qpoints(type, gt), 1, type, gt);
	delta_pres_on_qpoints(type, gt) = pressure_on_qpoints(type, gt);
	delta_pres_on_qpoints(type, gt) -= tmp;
	}
	AKANTU_DEBUG_OUT();
	}
	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assembleCapacityLumped() {
	AKANTU_DEBUG_IN();

	if (!this->getDOFManager().hasLumpedMatrix("M")) {
	this->getDOFManager().getNewLumpedMatrix("M");
	}

	this->getDOFManager().getLumpedMatrix("M").zero();

	assembleCapacityLumped(_not_ghost);
	assembleCapacityLumped(_ghost);

	need_to_reassemble_capacity_lumped = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::initSolver(
	TimeStepSolverType time_step_solver_type,
	NonLinearSolverType /non_linear_solver_type/) {
	DOFManager & dof_manager = this->getDOFManager();

	this->allocNodalField(this->pressure, 1, "pressure");
	this->allocNodalField(this->external_flux, 1, "external_flux");
	this->allocNodalField(this->internal_flux, 1, "internal_flux");
	this->allocNodalField(this->blocked_dofs, 1, "blocked_dofs");
	// this->allocNodalField(this->aperture, "aperture");

	if (!dof_manager.hasDOFs("pressure")) {
	dof_manager.registerDOFs("pressure", *this->pressure, _dst_nodal);
	dof_manager.registerBlockedDOFs("pressure", *this->blocked_dofs);
	}

	if (time_step_solver_type == TimeStepSolverType::_dynamic \|\|
	time_step_solver_type == TimeStepSolverType::_dynamic_lumped) {
	this->allocNodalField(this->pressure_rate, 1, "pressure_rate");

	if (!dof_manager.hasDOFsDerivatives("pressure", 1)) {
	dof_manager.registerDOFsDerivative("pressure", 1, *this->pressure_rate);
	}
	}
	}
	/* -------------------------------------------------------------------------- */
	std::tuple<ID, TimeStepSolverType>
	FluidDiffusionModel::getDefaultSolverID(const AnalysisMethod & method) {
	switch (method) {
	case _explicit_lumped_mass: {
	return std::make_tuple("explicit_lumped",
	TimeStepSolverType::_dynamic_lumped);
	}
	case _static: {
	return std::make_tuple("static", TimeStepSolverType::_static);
	}
	case _implicit_dynamic: {
	return std::make_tuple("implicit", TimeStepSolverType::_dynamic);
	}
	default:
	return std::make_tuple("unknown", TimeStepSolverType::_not_defined);
	}
	}

	/* -------------------------------------------------------------------------- */
	ModelSolverOptions FluidDiffusionModel::getDefaultSolverOptions(
	const TimeStepSolverType & type) const {
	ModelSolverOptions options;

	switch (type) {
	case TimeStepSolverType::_dynamic_lumped: {
	options.non_linear_solver_type = NonLinearSolverType::_lumped;
	options.integration_scheme_type["pressure"] =
	IntegrationSchemeType::_forward_euler;
	options.solution_type["pressure"] = IntegrationScheme::_pressure_rate;
	break;
	}
	case TimeStepSolverType::_static: {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["pressure"] =
	IntegrationSchemeType::_pseudo_time;
	options.solution_type["pressure"] = IntegrationScheme::_not_defined;
	break;
	}
	case TimeStepSolverType::_dynamic: {
	if (this->method == _explicit_consistent_mass) {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["pressure"] =
	IntegrationSchemeType::_forward_euler;
	options.solution_type["pressure"] = IntegrationScheme::_pressure_rate;
	} else {
	options.non_linear_solver_type = NonLinearSolverType::_newton_raphson;
	options.integration_scheme_type["pressure"] =
	IntegrationSchemeType::_backward_euler;
	options.solution_type["pressure"] = IntegrationScheme::_pressure;
	}
	break;
	}
	default:
	AKANTU_EXCEPTION(type << " is not a valid time step solver type");
	}

	return options;
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assemblePermeabilityMatrix() {
	AKANTU_DEBUG_IN();

	this->computePermeabilityOnQuadPoints(_not_ghost);
	if (permeability_release[_not_ghost] == permeability_matrix_release) {
	return;
	}

	if (!this->getDOFManager().hasMatrix("K")) {
	this->getDOFManager().getNewMatrix("K", getMatrixType("K"));
	}
	this->getDOFManager().getMatrix("K").zero();

	this->assemblePermeabilityMatrix(_not_ghost);
	// switch (mesh.getSpatialDimension()) {
	// case 1:
	// this->assemblePermeabilityMatrix<1>(_not_ghost);
	// break;
	// case 2:
	// this->assemblePermeabilityMatrix<2>(_not_ghost);
	// break;
	// case 3:
	// this->assemblePermeabilityMatrix<3>(_not_ghost);
	// break;
	// }

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assemblePermeabilityMatrix(
	const GhostType & ghost_type) {
	AKANTU_DEBUG_IN();

	auto & fem = this->getFEEngine();

	for (auto && type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	auto nb_element = mesh.getNbElement(type, ghost_type);
	auto nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
	auto nb_quadrature_points = fem.getNbIntegrationPoints(type, ghost_type);

	auto bt_d_b = std::make_unique<Array<Real>>(
	nb_element * nb_quadrature_points,
	nb_nodes_per_element * nb_nodes_per_element, "B^tDB");

	fem.computeBtDB(permeability_on_qpoints(type, ghost_type), *bt_d_b, 2, type,
	ghost_type);

	/// compute @f$ k_e = \int_e \mathbf{B}^t * \mathbf{D} * \mathbf{B}@f$
	auto K_e = std::make_unique<Array<Real>>(
	nb_element, nb_nodes_per_element * nb_nodes_per_element, "K_e");

	fem.integrate(bt_d_b, K_e, nb_nodes_per_element * nb_nodes_per_element,
	type, ghost_type);

	this->getDOFManager().assembleElementalMatricesToMatrix(
	"K", "pressure", *K_e, type, ghost_type, _symmetric);
	}

	permeability_matrix_release = permeability_release[ghost_type];

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::computePermeabilityOnQuadPoints(
	const GhostType & ghost_type) {

	// if already computed once check if need to compute
	if (not initial_permeability[ghost_type]) {
	// if aperture did not change, permeability will not vary
	if (solution_release == permeability_release[ghost_type]) {
	return;
	}
	}

	for (const auto & type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {

	// auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	// auto nb_element = mesh.getNbElement(type);
	// Array<Real> aperture_interpolated(nb_element * nb_nodes_per_element,
	// 1);

	// // compute the pressure on quadrature points
	// this->getFEEngine().interpolateOnIntegrationPoints(
	// *aperture, aperture_interpolated, 1, type, ghost_type);

	auto & perm = permeability_on_qpoints(type, ghost_type);
	auto & aperture = aperture_on_qpoints(type, ghost_type);
	for (auto && tuple : zip(perm, aperture)) {
	auto & k = std::get<0>(tuple);
	auto & aper = std::get<1>(tuple);
	k = aper * aper * aper / (12 * this->viscosity);
	}
	}

	permeability_release[ghost_type] = solution_release;
	initial_permeability[ghost_type] = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::computeKgradP(const GhostType & ghost_type) {
	computePermeabilityOnQuadPoints(ghost_type);

	for (const auto & type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	auto & gradient = pressure_gradient(type, ghost_type);
	this->getFEEngine().gradientOnIntegrationPoints(*pressure, gradient, 1,
	type, ghost_type);

	for (auto && values : zip(permeability_on_qpoints(type, ghost_type),
	gradient, k_gradp_on_qpoints(type, ghost_type))) {
	const auto & k = std::get<0>(values);
	const auto & BP = std::get<1>(values);
	auto & k_BP = std::get<2>(values);

	k_BP = k * BP;
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assembleInternalFlux() {
	AKANTU_DEBUG_IN();

	this->internal_flux->clear();

	this->synchronize(SynchronizationTag::_fdm_pressure);
	auto & fem = this->getFEEngine();

	for (auto ghost_type : ghost_types) {
	// compute k \grad P
	computeKgradP(ghost_type);

	for (auto type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);

	auto & k_gradp_on_qpoints_vect = k_gradp_on_qpoints(type, ghost_type);

	UInt nb_quad_points = k_gradp_on_qpoints_vect.size();
	Array<Real> bt_k_gP(nb_quad_points, nb_nodes_per_element);
	fem.computeBtD(k_gradp_on_qpoints_vect, bt_k_gP, type, ghost_type);

	if (this->use_aperture_speed) {
	auto aper_speed = aperture_on_qpoints(type, ghost_type);
	aper_speed -= prev_aperture_on_qpoints(type, ghost_type);
	aper_speed *= 1 / this->time_step;
	Array<Real> aper_speed_by_shapes(nb_quad_points, nb_nodes_per_element);

	fem.computeNtb(aper_speed, aper_speed_by_shapes, type, ghost_type);
	bt_k_gP += aper_speed_by_shapes;
	}
	UInt nb_elements = mesh.getNbElement(type, ghost_type);
	Array<Real> int_bt_k_gP(nb_elements, nb_nodes_per_element);

	fem.integrate(bt_k_gP, int_bt_k_gP, nb_nodes_per_element, type,
	ghost_type);

	this->getDOFManager().assembleElementalArrayLocalArray(
	int_bt_k_gP, *this->internal_flux, type, ghost_type, -1);
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Real FluidDiffusionModel::getStableTimeStep() {
	AKANTU_DEBUG_IN();

	Real el_size;
	Real min_el_size = std::numeric_limits<Real>::max();
	Real max_aper_on_qpoint = std::numeric_limits<Real>::min();

	for (const auto & type :
	mesh.elementTypes(spatial_dimension, _not_ghost, _ek_regular)) {

	auto nb_nodes_per_element = mesh.getNbNodesPerElement(type);
	auto & aper = aperture_on_qpoints(type, _not_ghost);
	auto nb_quad_per_element = aper.getNbComponent();
	auto mesh_dim = this->mesh.getSpatialDimension();
	Array<Real> coord(0, nb_nodes_per_element * mesh_dim);
	FEEngine::extractNodalToElementField(mesh, mesh.getNodes(), coord, type,
	_not_ghost);

	for (auto && data : zip(make_view(coord, mesh_dim, nb_nodes_per_element),
	make_view(aper, nb_quad_per_element))) {
	Matrix<Real> & el_coord = std::get<0>(data);
	Vector<Real> & el_aper = std::get<1>(data);
	el_size = getFEEngine().getElementInradius(el_coord, type);
	min_el_size = std::min(min_el_size, el_size);
	max_aper_on_qpoint = std::max(max_aper_on_qpoint, el_aper.norm<L_inf>());
	}

	AKANTU_DEBUG_INFO("The minimum element size : "
	<< min_el_size
	<< " and the max aperture is : " << max_aper_on_qpoint);
	}

	Real min_dt = 2. * min_el_size * min_el_size / 4 * this->compressibility /
	max_aper_on_qpoint / max_aper_on_qpoint;

	mesh.getCommunicator().allReduce(min_dt, SynchronizerOperation::_min);

	AKANTU_DEBUG_OUT();

	return min_dt;
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::setTimeStep(Real dt, const ID & solver_id) {
	Model::setTimeStep(time_step, solver_id);
	this->time_step = dt;
	#if defined(AKANTU_USE_IOHELPER)
	// this->mesh.getDumper("fluid_diffusion").setTimeStep(time_step);
	#endif
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::readMaterials() {
	auto sect = this->getParserSection();

	if (not std::get<1>(sect)) {
	const auto & section = std::get<0>(sect);
	this->parseSection(section);
	}
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::initFullImpl(const ModelOptions & options) {
	readMaterials();
	Model::initFullImpl(options);
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::assembleCapacity() {
	AKANTU_DEBUG_IN();
	auto ghost_type = _not_ghost;

	this->getDOFManager().getMatrix("M").zero();

	auto & fem = getFEEngineClass<FEEngineType>();

	fluid_diffusion::details::ComputeRhoFunctor rho_functor(*this);

	for (auto && type :
	mesh.elementTypes(spatial_dimension, ghost_type, _ek_regular)) {
	fem.assembleFieldMatrix(rho_functor, "M", "pressure", this->getDOFManager(),
	type, ghost_type);
	}

	need_to_reassemble_capacity = false;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::computeRho(Array<Real> & rho, ElementType type,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	rho.copy(aperture_on_qpoints(type, ghost_type));
	if (this->use_aperture_speed) {
	rho *= this->compressibility;
	} else {
	rho *= (this->compressibility + this->pushability);
	}

	AKANTU_DEBUG_OUT();
	} // namespace akantu

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::onElementsAdded(const Array<Element> & element_list,
	const NewElementsEvent & /event/) {
	AKANTU_DEBUG_IN();
	if (element_list.empty()) {
	return;
	}
	/// TODO had to do this ugly way because the meeting is in 3 days
	// removing it will make the assemble mass matrix fail. jacobians are not
	// updated
	auto & fem = this->getFEEngine();
	fem.initShapeFunctions(_not_ghost);
	fem.initShapeFunctions(_ghost);

	this->resizeFields();

	auto type_fluid =
	*mesh.elementTypes(spatial_dimension, _not_ghost, _ek_regular).begin();
	const auto nb_quad_elem =
	getFEEngine().getNbIntegrationPoints(type_fluid, _not_ghost);
	auto aperture_it =
	make_view(getApertureOnQpoints(type_fluid), nb_quad_elem).begin();

	/// assign default aperture to newly added nodes
	for (auto && element : element_list) {
	auto elem_id = element.element;
	for (auto ip : arange(nb_quad_elem)) {
	aperture_it[elem_id](ip) = this->default_aperture;
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::resizeFields() {

	AKANTU_DEBUG_IN();

	/// elemental fields
	auto & fem = this->getFEEngine();
	pressure_on_qpoints.initialize(fem, _nb_component = 1);
	delta_pres_on_qpoints.initialize(fem, _nb_component = 1);
	pressure_gradient.initialize(fem, _nb_component = 1);
	permeability_on_qpoints.initialize(fem, _nb_component = 1);
	aperture_on_qpoints.initialize(fem, _nb_component = 1);
	if (use_aperture_speed) {
	prev_aperture_on_qpoints.initialize(fem, _nb_component = 1);
	}
	k_gradp_on_qpoints.initialize(fem, _nb_component = 1);

	/// nodal fields
	UInt nb_nodes = mesh.getNbNodes();

	if (pressure != nullptr) {
	pressure->resize(nb_nodes, 0.);
	++solution_release;
	}
	if (external_flux != nullptr) {
	external_flux->resize(nb_nodes, 0.);
	}
	if (internal_flux != nullptr) {
	internal_flux->resize(nb_nodes, 0.);
	}
	if (blocked_dofs != nullptr) {
	blocked_dofs->resize(nb_nodes, false);
	}
	if (pressure_rate != nullptr) {
	pressure_rate->resize(nb_nodes, 0.);
	}
	need_to_reassemble_capacity_lumped = true;
	need_to_reassemble_capacity = true;

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	#if defined(AKANTU_COHESIVE_ELEMENT)
	void FluidDiffusionModel::getApertureOnQpointsFromCohesive(
	const SolidMechanicsModelCohesive & coh_model, bool first_time) {
	AKANTU_DEBUG_IN();

	// get element types
	auto & coh_mesh = coh_model.getMesh();
	const auto dim = coh_mesh.getSpatialDimension();
	const GhostType gt = _not_ghost;
	auto type = *coh_mesh.elementTypes(dim, gt, _ek_regular).begin();
	const ElementType type_facets = Mesh::getFacetType(type);
	const ElementType typecoh = FEEngine::getCohesiveElementType(type_facets);
	// const auto nb_coh_elem = coh_mesh.getNbElement(typecoh);
	const auto nb_quad_coh_elem = coh_model.getFEEngine("CohesiveFEEngine")
	.getNbIntegrationPoints(typecoh, gt);

	auto type_fluid =
	*mesh.elementTypes(spatial_dimension, gt, _ek_regular).begin();
	const auto nb_fluid_elem = mesh.getNbElement(type_fluid);
	const auto nb_quad_elem =
	getFEEngine().getNbIntegrationPoints(type_fluid, gt);
	// AKANTU_DEBUG_ASSERT(nb_quad_coh_elem == nb_quad_elem,
	// "Different number of integration points per cohesive "
	// "and fluid elements");

	// save previous aperture
	if (not first_time and use_aperture_speed) {
	prev_aperture_on_qpoints.copy(aperture_on_qpoints);
	}

	// AKANTU_DEBUG_ASSERT(nb_coh_elem == nb_fluid_elem,
	// "Different number of cohesive and fluid elements");

	auto aperture_it =
	make_view(getApertureOnQpoints(type_fluid), nb_quad_elem).begin();

	/// loop on each segment element
	for (auto && element_nb : arange(nb_fluid_elem)) {
	Element element{type_fluid, element_nb, gt};
	auto global_coh_elem =
	mesh.getElementalData<akantu::Element>("cohesive_elements")(element);
	auto ge = global_coh_elem.element;
	auto le = coh_model.getMaterialLocalNumbering(
	global_coh_elem.type, global_coh_elem.ghost_type)(ge);
	auto model_mat_index = coh_model.getMaterialByElement(
	global_coh_elem.type, global_coh_elem.ghost_type)(ge);
	const auto & material = coh_model.getMaterial(model_mat_index);

	// /// access cohesive material
	// const auto & mat = dynamic_cast<const MaterialCohesive &>(material);
	// const auto & normal_open_norm = mat.getNormalOpeningNorm(typecoh, gt);
	const auto normal_open_norm_it =
	make_view(material.getArray<Real>("normal_opening_norm", typecoh),
	nb_quad_coh_elem)
	.begin();
	if (nb_quad_elem == 1) {
	/// coh el quad points are averaged to assign single opening to flow el
	Real aperture_av = 0.;
	for (UInt ip : arange(nb_quad_coh_elem)) {
	auto normal_open_norm_ip = normal_open_norm_it[le](ip);
	aperture_av += normal_open_norm_ip;
	}
	aperture_av /= nb_quad_coh_elem;
	auto & aperture_ip = aperture_it[ge](0);
	if (aperture_av < this->default_aperture) {
	aperture_ip = this->default_aperture;
	} else {
	aperture_ip = aperture_av;
	}
	} else {
	/// each flow el quad point gets aperture from corresponding coh el qp
	for (UInt ip : arange(nb_quad_coh_elem)) {
	auto normal_open_norm_ip = normal_open_norm_it[le](ip);
	auto & aperture_ip = aperture_it[ge](ip);
	if (normal_open_norm_ip < this->default_aperture) {
	aperture_ip = this->default_aperture;
	} else {
	aperture_ip = normal_open_norm_ip;
	}
	}
	}
	}

	// save previous aperture
	if (first_time && use_aperture_speed) {
	prev_aperture_on_qpoints.copy(aperture_on_qpoints);
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::updateFluidElementsFromCohesive(
	const SolidMechanicsModelCohesive & coh_model) {
	AKANTU_DEBUG_IN();

	// get element types
	auto & coh_mesh = coh_model.getMesh();
	const auto dim = coh_mesh.getSpatialDimension();
	const GhostType gt = _not_ghost;
	auto type = *coh_mesh.elementTypes(dim, gt, _ek_regular).begin();
	const ElementType type_facets = Mesh::getFacetType(type);
	const ElementType typecoh = FEEngine::getCohesiveElementType(type_facets);
	const auto nb_coh_elem = coh_mesh.getNbElement(typecoh);
	const auto nb_quad_coh_elem = coh_model.getFEEngine("CohesiveFEEngine")
	.getNbIntegrationPoints(typecoh, gt);

	auto type_fluid =
	*mesh.elementTypes(spatial_dimension, gt, _ek_regular).begin();
	const auto nb_fluid_elem = mesh.getNbElement(type_fluid);

	// check if there is need to add more fluid elements
	if (nb_coh_elem == nb_fluid_elem) {
	return;
	}

	NewElementsEvent new_facets;
	NewNodesEvent new_nodes;
	NewElementsEvent new_fluid_facets;

	/// loop on each cohesive element and check its damage
	for (auto && coh_el : arange(nb_coh_elem)) {

	// check if this cohesive element is present in fluid mesh
	auto & existing_coh_elements =
	mesh.getData<Element>("cohesive_elements", type_facets, gt);
	Element coh_element = {typecoh, coh_el, gt};
	auto it = existing_coh_elements.find(coh_element);
	if (it != UInt(-1)) {
	continue;
	}

	// check damage at the cohesive element
	// Element element{type_fluid, element_nb, gt};
	auto le = coh_model.getMaterialLocalNumbering(typecoh, gt)(coh_el);
	auto model_mat_index = coh_model.getMaterialByElement(typecoh, gt)(coh_el);
	const auto & material = coh_model.getMaterial(model_mat_index);
	const auto damage_it =
	make_view(material.getArray<Real>("damage", typecoh), nb_quad_coh_elem)
	.begin();
	Real damage_av = 0.;
	for (auto ip : arange(nb_quad_coh_elem)) {
	auto damage_ip = damage_it[le](ip);
	damage_av += damage_ip;
	}
	damage_av /= nb_quad_coh_elem;

	if (damage_av < this->insertion_damage) {
	continue;
	}

	// add fluid element to connectivity and corresponding nodes
	Array<UInt> & nodes_added = new_nodes.getList();
	auto & crack_facets = coh_mesh.getElementGroup("crack_facets");
	auto & nodes = mesh.getNodes();
	auto && coh_nodes = coh_mesh.getNodes();
	auto && coh_conn = coh_mesh.getConnectivity(typecoh, gt);
	Vector<UInt> conn(coh_conn.getNbComponent() / 2);
	auto coh_facet_conn_it = make_view(coh_mesh.getConnectivity(typecoh, gt),
	coh_conn.getNbComponent() / 2)
	.begin();
	auto cohesive_nodes_first_half = coh_facet_conn_it[2 * coh_el];
	for (auto c : akantu::arange(conn.size())) {
	auto coh_node = cohesive_nodes_first_half(c);
	Vector<Real> pos(mesh.getSpatialDimension());
	for (auto && data : enumerate(pos)) {
	std::get<1>(data) = coh_nodes(coh_node, std::get<0>(data));
	}
	auto idx = nodes.find(pos);
	if (idx == UInt(-1)) {
	nodes.push_back(pos);
	conn(c) = nodes.size() - 1;
	nodes_added.push_back(nodes.size() - 1);
	} else {
	conn(c) = idx;
	}
	}
	mesh.getData<Element>("cohesive_elements", type_facets, gt)
	.push_back(coh_element);
	mesh.getConnectivity(type_facets, gt).push_back(conn);
	Element fluid_facet{type_facets,
	mesh.getConnectivity(type_facets, gt).size() - 1, gt};
	new_fluid_facets.getList().push_back(fluid_facet);

	// instantiate connectivity type for this facet type if not yet done
	if (not coh_mesh.getConnectivities().exists(type_facets, gt)) {
	coh_mesh.addConnectivityType(type_facets, gt);
	}

	// add two facets per cohesive element into cohesive mesh
	auto & facet_conn_mesh = coh_mesh.getConnectivity(type_facets, gt);
	for (auto f : akantu::arange(2)) {
	Vector<UInt> coh_nodes_one_side = coh_facet_conn_it[2 * coh_el + f];
	facet_conn_mesh.push_back(coh_nodes_one_side);
	Element new_facet{type_facets, facet_conn_mesh.size() - 1, gt};
	crack_facets.add(new_facet);
	new_facets.getList().push_back(new_facet);
	}
	}
	mesh.sendEvent(new_nodes);
	mesh.sendEvent(new_fluid_facets);
	MeshUtils::fillElementToSubElementsData(coh_mesh);
	coh_mesh.sendEvent(new_facets);

	AKANTU_DEBUG_OUT();
	}

	#endif

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::applyExternalFluxAtElementGroup(
	const Real & rate, const ElementGroup & source_facets,
	GhostType ghost_type) {
	AKANTU_DEBUG_IN();

	for (auto && type :
	source_facets.elementTypes(spatial_dimension, ghost_type)) {
	const auto & element_ids = source_facets.getElements(type, ghost_type);

	const auto nb_fluid_elem = mesh.getNbElement(type);
	const auto type_size = element_ids.size();
	AKANTU_DEBUG_ASSERT(type_size <= nb_fluid_elem,
	"Number of provided source facets exceeds total number "
	"of flow elements");
	const auto fluid_conn_it =
	make_view(mesh.getConnectivity(type, ghost_type),
	mesh.getConnectivity(type, ghost_type).getNbComponent())
	.begin();
	auto & source = getExternalFlux();
	source.clear();

	/// loop on each element of the group
	for (auto el : element_ids) {
	AKANTU_DEBUG_ASSERT(el <= nb_fluid_elem,
	"Element number in the source facets group exceeds "
	"maximum number of flow elements");

	const Vector<UInt> fluid_conn = fluid_conn_it[el];
	for (const auto & node : fluid_conn) {
	source(node) += rate / (fluid_conn.size() * element_ids.size());
	}
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	Array<Real> FluidDiffusionModel::getQpointsCoord() {
	AKANTU_DEBUG_IN();

	const auto & nodes_coords = mesh.getNodes();
	const GhostType gt = _not_ghost;
	auto type_fluid =
	*mesh.elementTypes(spatial_dimension, gt, _ek_regular).begin();
	const auto nb_fluid_elem = mesh.getNbElement(type_fluid);
	auto & fem = this->getFEEngine();
	const auto nb_quad_points = fem.getNbIntegrationPoints(type_fluid, gt);

	Array<Real> quad_coords(nb_fluid_elem * nb_quad_points,
	spatial_dimension + 1);
	fem.interpolateOnIntegrationPoints(nodes_coords, quad_coords,
	spatial_dimension + 1, type_fluid, gt);
	AKANTU_DEBUG_OUT();
	return quad_coords;
	}

	/* -------------------------------------------------------------------------- */
	/* -------------------------------------------------------------------------- */
	#ifdef AKANTU_USE_IOHELPER

	std::shared_ptr<dumpers::Field> FluidDiffusionModel::createNodalFieldBool(
	const std::string & field_name, const std::string & group_name,
	__attribute__((unused)) bool padding_flag) {

	std::map<std::string, Array<bool> *> uint_nodal_fields;
	uint_nodal_fields["blocked_dofs"] = blocked_dofs.get();

	auto field = mesh.createNodalField(uint_nodal_fields[field_name], group_name);
	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> FluidDiffusionModel::createNodalFieldReal(
	const std::string & field_name, const std::string & group_name,
	__attribute__((unused)) bool padding_flag) {

	if (field_name == "capacity_lumped") {
	AKANTU_EXCEPTION(
	"Capacity lumped is a nodal field now stored in the DOF manager."
	"Therefore it cannot be used by a dumper anymore");
	}

	std::map<std::string, Array<Real> *> real_nodal_fields;
	real_nodal_fields["pressure"] = pressure.get();
	real_nodal_fields["pressure_rate"] = pressure_rate.get();
	real_nodal_fields["external_flux"] = external_flux.get();
	real_nodal_fields["internal_flux"] = internal_flux.get();
	// real_nodal_fields["increment"] = increment.get();

	std::shared_ptr<dumpers::Field> field =
	mesh.createNodalField(real_nodal_fields[field_name], group_name);

	return field;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> FluidDiffusionModel::createElementalField(
	const std::string & field_name, const std::string & group_name,
	bool /padding_flag/, UInt /spatial_dimension/,
	ElementKind element_kind) {

	std::shared_ptr<dumpers::Field> field;

	if (field_name == "partitions") {
	field = mesh.createElementalField<UInt, dumpers::ElementPartitionField>(
	mesh.getConnectivities(), group_name, this->spatial_dimension,
	element_kind);
	} else if (field_name == "pressure_gradient") {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->mesh.getNbDataPerElem(pressure_gradient);

	field = mesh.createElementalField<Real, dumpers::InternalMaterialField>(
	pressure_gradient, group_name, this->spatial_dimension, element_kind,
	nb_data_per_elem);
	} else if (field_name == "permeability") {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->mesh.getNbDataPerElem(permeability_on_qpoints);

	field = mesh.createElementalField<Real, dumpers::InternalMaterialField>(
	permeability_on_qpoints, group_name, this->spatial_dimension,
	element_kind, nb_data_per_elem);
	} else if (field_name == "aperture") {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->mesh.getNbDataPerElem(aperture_on_qpoints);

	field = mesh.createElementalField<Real, dumpers::InternalMaterialField>(
	aperture_on_qpoints, group_name, this->spatial_dimension, element_kind,
	nb_data_per_elem);
	} else if (field_name == "pressure_on_qpoints") {
	ElementTypeMap<UInt> nb_data_per_elem =
	this->mesh.getNbDataPerElem(pressure_on_qpoints);

	field = mesh.createElementalField<Real, dumpers::InternalMaterialField>(
	pressure_on_qpoints, group_name, this->spatial_dimension, element_kind,
	nb_data_per_elem);
	}

	return field;
	}

	/* -------------------------------------------------------------------------- */
	#else
	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> FluidDiffusionModel::createElementalField(
	__attribute__((unused)) const std::string & field_name,
	__attribute__((unused)) const std::string & group_name,
	__attribute__((unused)) bool padding_flag,
	__attribute__((unused)) UInt spatial_dimension,
	__attribute__((unused)) ElementKind element_kind) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> FluidDiffusionModel::createNodalFieldBool(
	__attribute__((unused)) const std::string & field_name,
	__attribute__((unused)) const std::string & group_name,
	__attribute__((unused)) bool padding_flag) {
	return nullptr;
	}

	/* -------------------------------------------------------------------------- */
	std::shared_ptr<dumpers::Field> FluidDiffusionModel::createNodalFieldReal(
	__attribute__((unused)) const std::string & field_name,
	__attribute__((unused)) const std::string & group_name,
	__attribute__((unused)) bool padding_flag) {
	return nullptr;
	}
	#endif

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::dump(const std::string & dumper_name) {
	mesh.dump(dumper_name);
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::dump(const std::string & dumper_name, UInt step) {
	mesh.dump(dumper_name, step);
	}

	/* -------------------------------------------------------------------------
	*/
	void FluidDiffusionModel::dump(const std::string & dumper_name, Real time,
	UInt step) {
	mesh.dump(dumper_name, time, step);
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::dump() { mesh.dump(); }

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::dump(UInt step) { mesh.dump(step); }

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::dump(Real time, UInt step) { mesh.dump(time, step); }

	/* -------------------------------------------------------------------------- */
	inline UInt
	FluidDiffusionModel::getNbData(const Array<UInt> & indexes,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt nb_nodes = indexes.size();

	switch (tag) {
	case SynchronizationTag::_fdm_pressure: {
	size += nb_nodes * sizeof(Real);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	inline void
	FluidDiffusionModel::packData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	for (auto index : indexes) {
	switch (tag) {
	case SynchronizationTag::_fdm_pressure: {
	buffer << (*pressure)(index);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	inline void FluidDiffusionModel::unpackData(CommunicationBuffer & buffer,
	const Array<UInt> & indexes,
	const SynchronizationTag & tag) {
	AKANTU_DEBUG_IN();

	for (auto index : indexes) {
	switch (tag) {
	case SynchronizationTag::_fdm_pressure: {
	buffer >> (*pressure)(index);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}

	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	inline UInt
	FluidDiffusionModel::getNbData(const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	AKANTU_DEBUG_IN();

	UInt size = 0;
	UInt nb_nodes_per_element = 0;
	Array<Element>::const_iterator<Element> it = elements.begin();
	Array<Element>::const_iterator<Element> end = elements.end();
	for (; it != end; ++it) {
	const Element & el = *it;
	nb_nodes_per_element += Mesh::getNbNodesPerElement(el.type);
	}

	switch (tag) {
	case SynchronizationTag::_fdm_pressure: {
	size += nb_nodes_per_element * sizeof(Real); // pressure
	break;
	}
	case SynchronizationTag::_fdm_gradient_pressure: {
	// pressure gradient
	size += getNbIntegrationPoints(elements) * sizeof(Real);
	size += nb_nodes_per_element * sizeof(Real); // nodal pressures
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}

	AKANTU_DEBUG_OUT();
	return size;
	}

	/* -------------------------------------------------------------------------- */
	inline void
	FluidDiffusionModel::packData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) const {
	switch (tag) {
	case SynchronizationTag::_fdm_pressure: {
	packNodalDataHelper(*pressure, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_fdm_gradient_pressure: {
	packElementalDataHelper(pressure_gradient, buffer, elements, true,
	getFEEngine());
	packNodalDataHelper(*pressure, buffer, elements, mesh);
	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	inline void FluidDiffusionModel::unpackData(CommunicationBuffer & buffer,
	const Array<Element> & elements,
	const SynchronizationTag & tag) {
	switch (tag) {
	case SynchronizationTag::_fdm_pressure: {
	unpackNodalDataHelper(*pressure, buffer, elements, mesh);
	break;
	}
	case SynchronizationTag::_fdm_gradient_pressure: {
	unpackElementalDataHelper(pressure_gradient, buffer, elements, true,
	getFEEngine());
	unpackNodalDataHelper(*pressure, buffer, elements, mesh);

	break;
	}
	default: {
	AKANTU_ERROR("Unknown ghost synchronization tag : " << tag);
	}
	}
	}

	/* -------------------------------------------------------------------------- */
	void FluidDiffusionModel::injectIntoFacetsByCoord(const Vector<Real> & position,
	const Real & injection_rate) {
	AKANTU_DEBUG_IN();

	auto dim = mesh.getSpatialDimension();
	const auto gt = _not_ghost;
	const auto & pos = mesh.getNodes();
	const auto pos_it = make_view(pos, dim).begin();
	auto & source = *external_flux;

	Vector<Real> bary_facet(dim);

	Real min_dist = std::numeric_limits<Real>::max();
	Element inj_facet;
	for_each_element(
	mesh,
	[&](auto && facet) {
	mesh.getBarycenter(facet, bary_facet);
	auto dist = std::abs(bary_facet.distance(position));
	if (dist < min_dist) {
	min_dist = dist;
	inj_facet = facet;
	}
	},
	_spatial_dimension = dim - 1);

	auto & facet_conn = mesh.getConnectivity(inj_facet.type, gt);
	auto nb_nodes_per_elem = facet_conn.getNbComponent();
	for (auto node : arange(nb_nodes_per_elem)) {
	source(facet_conn(inj_facet.element, node)) =
	injection_rate / nb_nodes_per_elem;
	}
	AKANTU_DEBUG_OUT();
	}

	/* -------------------------------------------------------------------------- */
	} // namespace akantu

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