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unsaturated

aqueous_equation.cpp
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			/*-------------------------------------------------------------------------------

			Copyright (c) 2015 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
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			(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 "aqueous_equation.hpp"
			#include "variables_box.hpp"
			#include "transport_constraints.hpp"

			#include "../../../dfpm/meshes/mesh1d.hpp"
			#include "../../../utils/compat.hpp"
			#include "../../../physics/constants.hpp"

			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 AqueousTransportEquation::AqueousTransportEquationImpl
			{
			mesh::Mesh1DPtr m_mesh;
			LiquidAqueousComponentVariableBox m_vars;
			std::vector<index_t> m_ideq;
			scalar_t m_scaling {1.0};

			mesh::Mesh1D* mesh() {return m_mesh.get();}
			LiquidAqueousComponentVariableBox& vars() {return m_vars;}

			bool node_has_equation(index_t node) {
			return m_ideq[node] > no_equation;
			}

			bool node_can_flux(index_t node) {
			return m_ideq[node] > no_eq_no_var;
			}

			index_t id_equation(index_t node) {
			return m_ideq[node];
			}

			void fix_node(index_t node) {
			m_ideq[node] = no_equation;
			}

			void gas_node(index_t node) {
			m_ideq[node] = no_eq_no_var;
			}

			AqueousTransportEquationImpl(
			mesh::Mesh1DPtr the_mesh,
			LiquidAqueousComponentVariableBox the_vars
			):
			m_mesh(the_mesh),
			m_vars(the_vars),
			m_ideq(the_mesh->nb_nodes(), not_initialized)
			{}

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

			AqueousTransportEquation::AqueousTransportEquation(
			mesh::Mesh1DPtr the_mesh,
			LiquidAqueousComponentVariableBox& variables,
			const TransportConstraints& constraints):
			m_tot_ndf(the_mesh->nb_nodes()),
			m_impl(make_unique<AqueousTransportEquationImpl>(the_mesh, variables))
			{
			number_equations(constraints);
			}

			AqueousTransportEquation::~AqueousTransportEquation() = default;

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

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

			//! \brief Compute the residuals inside 'element'
			void AqueousTransportEquation::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();
			LiquidAqueousComponentVariableBox& 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))
			{
			// 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 diff_aq = (displacement(node_1)
			- displacement(node_0)
			);
			const scalar_t diff_flux = coeff_diff * diff_aq/ m_mesh->get_dx(element);

			// advection
			if (vars.advection_flux(element) < 0)
			{
			flux_0 = -vars.advection_flux(element)*diff_aq;
			}
			else
			{
			flux_1 = -vars.advection_flux(element)*diff_aq;
			}
			flux_0 += diff_flux;
			flux_0 *= m_mesh->get_face_area(element);
			flux_1 -= diff_flux;
			flux_1 *= m_mesh->get_face_area(element);
			}


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

			scalar_t transient_0 = porosity_0aq_tot_conc_0vars.saturation.velocity(node_0)
			+ saturation_0aq_tot_conc_0vars.porosity.velocity(node_0)
			+ porosity_0saturation_0velocity(node_0);

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

			}

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

			scalar_t transient_1 = porosity_1aq_tot_conc_1vars.saturation.velocity(node_1)
			+ saturation_1aq_tot_conc_1vars.porosity.velocity(node_1)
			+ porosity_1saturation_1velocity(node_1);

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

			//! \brief Compute the residuals
			void AqueousTransportEquation::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());
			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_equation(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_equation(node_1))
			{
			residuals(m_impl->id_equation(node_1)) += element_residual(1);
			}
			}
			}

			//! \brief Compute the jacobian
			void AqueousTransportEquation::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_equation(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;

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

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

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

			//! \brief Update the solution
			void AqueousTransportEquation::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_equation(node))
			{
			velocity(node) += lambda*update(m_impl->id_equation(node));
			}
			}
			displacement = predictor + alpha_dt*velocity;
			m_impl->compute_transport_rate(alpha_dt, displacement);
			}

			void AqueousTransportEquation::number_equations(const TransportConstraints& constraints)
			{
			for (int fixed_node: constraints.fixed_nodes())
			{
			m_impl->fix_node(fixed_node);
			}
			for (int gas_node: constraints.gas_nodes())
			{
			m_impl->gas_node(gas_node);
			}
			index_t neq = 0;
			for (index_t node: m_impl->mesh()->range_nodes())
			{
			if (m_impl->m_ideq[node] == not_initialized)
			{
			m_impl->m_ideq[node] = neq;
			++neq;
			}
			}
			m_neq = neq;
			}

			void AqueousTransportEquation::AqueousTransportEquationImpl::compute_transport_rate(
			scalar_t dt,
			const Vector& displacement)
			{
			MainVariable& aqueous_concentration = m_vars.aqueous_concentration;
			const MainVariable& saturation = m_vars.saturation;
			const MainVariable& solid_conc = m_vars.solid_concentration;
			const MainVariable& pressure = m_vars.partial_pressure;
			const SecondaryTransientVariable& porosity = m_vars.porosity;

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

			const scalar_t transient = (
			(porosity(node)saturation(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)
			);

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


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

specmicp/src/reactmicp/systems/unsaturated/aqueous_equation.cpp008df9c9036ereactmicp/unsaturated

aqueous_equation.cppView Options

specmicp/src/reactmicp/systems/unsaturated/aqueous_equation.cpp
008df9c9036ereactmicp/unsaturated

aqueous_equation.cpp
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