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unsaturated

saturation_equation.cpp
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			/*-------------------------------------------------------------------------------

			Copyright (c) 2014,2015 F. Georget <fabieng@princeton.edu>, Princeton University
			All rights reserved.

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			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
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			-----------------------------------------------------------------------------*/

			#include "saturation_equation.hpp"

			#include "variables_box.hpp"
			#include "transport_constraints.hpp"

			#include "../../../dfpm/meshes/mesh1d.hpp"
			#include "../../../dfpmsolver/parabolic_driver.hpp"

			#include "../../../utils/compat.hpp"


			#include <vector>

			namespace specmicp {
			namespace dfpmsolver {

			// explicit template instanciation
			template class dfpmsolver::ParabolicDriver<reactmicp::systems::unsaturated::SaturationEquation>;

			} //end namespace dfpmsolver
			} //end namespace specmicp

			namespace specmicp {
			namespace reactmicp {
			namespace systems {
			namespace unsaturated {

			static constexpr index_t no_equation {-1};
			static constexpr index_t no_eq_no_var {-2};
			static constexpr index_t not_initialized {-5};

			struct SPECMICP_DLL_LOCAL SaturationEquation::SaturationEquationImpl
			{

			mesh::Mesh1DPtr m_mesh;
			SaturationVariableBox m_vars;
			std::vector<index_t> m_ideq;
			bool m_store_residual_info;
			scalar_t m_scaling {1.0};


			SaturationEquationImpl(
			mesh::Mesh1DPtr the_mesh,
			SaturationVariableBox vars):
			m_mesh(the_mesh),
			m_vars(vars),
			m_ideq(the_mesh->nb_nodes(), not_initialized)
			{}

			index_t& id_equation(index_t node) {return m_ideq[node];}
			bool node_can_flux(index_t node) {return m_ideq[node] != no_eq_no_var;}
			bool node_has_eq(index_t node) {return m_ideq[node] > no_equation;}

			void set_store_residual_info() {
			m_store_residual_info = true;
			}
			void reset_store_residual_info() {
			m_store_residual_info = false;
			}

			bool store_residual_info() {
			return m_store_residual_info;
			}

			//! \brief Return a pointer to the mesh
			mesh::Mesh1D* mesh() {return m_mesh.get();}
			range_t range_nodes() {return m_mesh->range_nodes();}

			void set_relative_variables(const Vector& displacement);
			void set_relative_variables(index_t node, const Vector& displacement);

			void compute_transport_rate(scalar_t dt, const Vector& displacement);
			};



			SaturationEquation::~SaturationEquation() = default;

			SaturationEquation::SaturationEquation(mesh::Mesh1DPtr the_mesh,
			SaturationVariableBox &variables,
			const TransportConstraints& constraints
			):
			m_neq(-1),
			m_tot_ndf(the_mesh->nb_nodes()),
			m_impl(make_unique<SaturationEquationImpl>(the_mesh, variables))
			{
			number_equations(constraints);
			}

			void SaturationEquation::number_equations(const TransportConstraints& constraints)
			{

			for (index_t node: constraints.fixed_nodes())
			{
			m_impl->id_equation(node) = no_equation;
			}
			for (index_t node: constraints.gas_nodes())
			{
			m_impl->id_equation(node) = no_eq_no_var;
			}
			index_t neq = 0;
			for (index_t node: m_impl->range_nodes()) {
			if (m_impl->id_equation(node) == not_initialized)
			{
			m_impl->id_equation(node) = neq;
			++neq;
			}
			}
			m_neq = neq;
			}

			index_t SaturationEquation::id_equation(index_t id_dof)
			{
			return m_impl->id_equation(id_dof)<0?no_equation:m_impl->id_equation(id_dof);
			}

			void SaturationEquation::set_scaling(scalar_t value)
			{
			m_impl->m_scaling = value;
			}

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

			void SaturationEquation::residuals_element(
			index_t element,
			const Vector& displacement,
			const Vector& velocity,
			Eigen::Vector2d& element_residual,
			bool use_chemistry_rate
			)
			{
			element_residual.setZero();

			mesh::Mesh1D* m_mesh = m_impl->mesh();
			SaturationVariableBox& vars = m_impl->m_vars;

			const scalar_t mass_coeff_0 = m_mesh->get_volume_cell_element(element, 0);
			const scalar_t mass_coeff_1 = m_mesh->get_volume_cell_element(element, 1);

			const index_t node_0 = m_mesh->get_node(element, 0);
			const index_t node_1 = m_mesh->get_node(element, 1);


			scalar_t flux_0 = 0.0;
			scalar_t flux_1 = 0.0;

			if (m_impl->node_can_flux(node_0) and m_impl->node_can_flux(node_1))
			{
			// Cap pressure gradient
			const scalar_t perm_0 = vars.liquid_permeability(node_0)
			* vars.relative_liquid_permeability(node_0);
			const scalar_t perm_1 = vars.liquid_permeability(node_1)
			* vars.relative_liquid_permeability(node_1);
			const scalar_t perm = 2.0/(1.0/perm_0 + 1.0/perm_1);


			const scalar_t aq_coefficient = (vars.aqueous_concentration(node_0)
			+ vars.aqueous_concentration(node_1)
			) / 2.0;
			const scalar_t cap_pressure_gradient = ( vars.capillary_pressure(node_1)
			- vars.capillary_pressure(node_0)
			) / m_mesh->get_dx(element);
			const scalar_t advection_flux = (perm/vars.constants.viscosity_liquid_water)*cap_pressure_gradient;
			const scalar_t cappres_flux = -aq_coefficient*advection_flux;

			// Diffusion Cw
			const scalar_t coeff_diff_0 = vars.liquid_diffusivity(node_0)
			* vars.relative_liquid_diffusivity(node_0);
			const scalar_t coeff_diff_1 = vars.liquid_diffusivity(node_1)
			* vars.relative_liquid_diffusivity(node_1);

			const scalar_t coeff_diff = 2.0/(1.0/coeff_diff_0 + 1.0/coeff_diff_1);

			const scalar_t aq_flux = coeff_diff*(vars.aqueous_concentration(node_1)
			- vars.aqueous_concentration(node_0)
			) / m_mesh->get_dx(element);
			// Tot flux
			const scalar_t tot_flux = m_mesh->get_face_area(element)*(cappres_flux + aq_flux);
			flux_0 = tot_flux;
			flux_1 = -tot_flux;

			// Storage
			if (m_impl->store_residual_info())
			{
			// advective flux stored by element
			vars.advection_flux(element) = advection_flux;

			// fluxes to compute exchange term
			vars.liquid_saturation.transport_fluxes(node_0) += flux_0;
			vars.liquid_saturation.transport_fluxes(node_1) += flux_1;
			}
			}


			// transient
			if (m_impl->node_has_eq(node_0))
			{
			const scalar_t porosity_0 = vars.porosity(node_0);
			const scalar_t aq_tot_conc_0 = vars.aqueous_concentration(node_0);
			const scalar_t saturation_0 = displacement(node_0);

			scalar_t transient_0 = (
			porosity_0 * aq_tot_conc_0 * velocity(node_0)
			+ saturation_0 * aq_tot_conc_0 * vars.porosity.velocity(node_0)
			+ porosity_0 * saturation_0 * vars.aqueous_concentration.velocity(node_0)
			);

			auto res = mass_coeff_0*transient_0 - flux_0;
			if (use_chemistry_rate)
			{
			const scalar_t chemistry_0 = vars.liquid_saturation.chemistry_rate(node_0)
			+ vars.solid_concentration.chemistry_rate(node_0)
			+ vars.vapor_pressure.chemistry_rate(node_0)
			;
			res -= mass_coeff_0*chemistry_0;
			}
			element_residual(0) = res / m_impl->m_scaling;
			}

			if (m_impl->node_has_eq(node_1))
			{
			const scalar_t porosity_1 = vars.porosity(node_1);
			const scalar_t aq_tot_conc_1 = vars.aqueous_concentration(node_1);
			const scalar_t saturation_1 = displacement(node_1);

			scalar_t transient_1 = (
			porosity_1 * aq_tot_conc_1 * velocity(node_1)
			+ saturation_1 * aq_tot_conc_1 * vars.porosity.velocity(node_1)
			+ porosity_1 * saturation_1 * vars.aqueous_concentration.velocity(node_1)
			);

			auto res = mass_coeff_1*transient_1 - flux_1;
			if (use_chemistry_rate)
			{
			const scalar_t chemistry_1 = vars.liquid_saturation.chemistry_rate(node_1)
			+ vars.solid_concentration.chemistry_rate(node_1)
			+ vars.vapor_pressure.chemistry_rate(node_1)
			;
			res -= mass_coeff_1*chemistry_1;
			}
			element_residual(1) = res / m_impl->m_scaling;
			}
			}

			//! \brief Compute the residuals
			void SaturationEquation::compute_residuals(
			const Vector& displacement,
			const Vector& velocity,
			Vector& residuals,
			bool use_chemistry_rate
			)
			{
			mesh::Mesh1D* m_mesh = m_impl->mesh();
			residuals.setZero(get_neq());
			m_impl->set_store_residual_info();
			set_relative_variables(displacement);
			Eigen::Vector2d element_residual;
			for (index_t element: m_mesh->range_elements())
			{
			residuals_element(element, displacement, velocity, element_residual, use_chemistry_rate);

			const index_t node_0 = m_mesh->get_node(element, 0);
			if (m_impl->node_has_eq(node_0))
			{
			residuals(m_impl->id_equation(node_0)) += element_residual(0);
			}
			const index_t node_1 = m_mesh->get_node(element, 1);
			if (m_impl->node_has_eq(node_1))
			{
			residuals(m_impl->id_equation(node_1)) += element_residual(1);
			}

			}

			m_impl->reset_store_residual_info();
			}

			void SaturationEquation::compute_jacobian(
			Vector& displacement,
			Vector& velocity,
			Eigen::SparseMatrix<scalar_t>& jacobian,
			scalar_t alphadt
			)
			{
			mesh::Mesh1D* m_mesh = m_impl->mesh();
			dfpm::list_triplet_t jacob;
			const index_t estimation = 3*get_neq();
			jacob.reserve(estimation);
			// assume relative variables are set
			for (index_t element: m_mesh->range_elements())
			{
			Eigen::Vector2d element_residual_orig;
			residuals_element(element, displacement, velocity, element_residual_orig, false);

			for (index_t enodec=0; enodec<2; ++enodec)
			{
			const index_t nodec = m_mesh->get_node(element, enodec);
			if (not m_impl->node_has_eq(nodec)) continue;

			const scalar_t tmp_d = displacement(nodec);
			const scalar_t tmp_v = velocity(nodec);

			scalar_t h = eps_jacobian*std::abs(tmp_v);
			if (h<1e-4*eps_jacobian) h = eps_jacobian;
			velocity(nodec) = tmp_v + h;
			h = velocity(nodec) - tmp_v;

			displacement(nodec) = tmp_d + alphadt*h;

			m_impl->set_relative_variables(nodec, displacement);

			Eigen::Vector2d element_residual;
			residuals_element(element, displacement, velocity, element_residual, false);

			displacement(nodec) = tmp_d;
			velocity(nodec) = tmp_v;
			m_impl->set_relative_variables(nodec, displacement);

			for (index_t enoder=0; enoder<2; ++enoder)
			{
			const index_t noder = m_mesh->get_node(element, enoder);
			if (not m_impl->node_has_eq(noder)) continue;

			jacob.push_back(dfpm::triplet_t(
			m_impl->id_equation(noder),
			m_impl->id_equation(nodec),
			(element_residual(enoder) - element_residual_orig(enoder))/h
			));
			}
			}
			}
			jacobian = Eigen::SparseMatrix<scalar_t>(get_neq(), get_neq());
			jacobian.setFromTriplets(jacob.begin(), jacob.end());
			}


			void SaturationEquation::update_solution(
			const Vector& update,
			scalar_t lambda,
			scalar_t alpha_dt,
			Vector& predictor,
			Vector& displacement,
			Vector& velocity
			)
			{
			for (index_t node: m_impl->mesh()->range_nodes())
			{
			if (m_impl->node_has_eq(node))
			{
			velocity(node) += lambda*update(m_impl->id_equation(node));
			}
			}
			displacement = predictor + alpha_dt*velocity;
			m_impl->compute_transport_rate(alpha_dt, displacement);


			}

			void SaturationEquation::set_relative_variables(const Vector& displacement)
			{
			return m_impl->set_relative_variables(displacement);
			}

			void SaturationEquation::SaturationEquationImpl::set_relative_variables(
			index_t node,
			const Vector& displacement
			)
			{
			if (not node_can_flux(node)) return;

			const scalar_t saturation = displacement(node);
			m_vars.relative_liquid_diffusivity(node) = m_vars.relative_liquid_diffusivity_f(node, saturation);
			m_vars.relative_liquid_permeability(node) = m_vars.relative_liquid_permeability_f(node, saturation);
			m_vars.capillary_pressure(node) = m_vars.capillary_pressure_f(node, saturation);

			}

			void SaturationEquation::SaturationEquationImpl::set_relative_variables(const Vector& displacement)
			{
			for (index_t node: m_mesh->range_nodes())
			{
			set_relative_variables(node, displacement);
			}
			}


			void SaturationEquation::SaturationEquationImpl::compute_transport_rate(
			scalar_t dt,
			const Vector& displacement)
			{
			MainVariable& saturation = m_vars.liquid_saturation;
			const MainVariable& solid_conc = m_vars.solid_concentration;
			const MainVariable& pressure = m_vars.vapor_pressure;
			const SecondaryTransientVariable& porosity = m_vars.porosity;
			const SecondaryTransientVariable& aqueous_concentration = m_vars.aqueous_concentration;

			for (index_t node: m_mesh->range_nodes())
			{
			if (! node_has_eq(node)) continue;

			const scalar_t transient = (
			(porosity(node)aqueous_concentration(node)displacement(node))
			- (porosity.predictor(node)aqueous_concentration.predictor(node)saturation.predictor(node))
			) / dt;

			const scalar_t chem_rates = (
			saturation.chemistry_rate(node)
			+ solid_conc.chemistry_rate(node)
			+ pressure.chemistry_rate(node)
			);

			saturation.transport_fluxes(node) = transient - chem_rates;
			}
			}


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

specmicp/src/reactmicp/systems/unsaturated/saturation_equation.cppc4d70155decareactmicp/unsaturated

saturation_equation.cppView Options

specmicp/src/reactmicp/systems/unsaturated/saturation_equation.cpp
c4d70155decareactmicp/unsaturated

saturation_equation.cpp
View Options