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transport_program.cpp
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/*-------------------------------------------------------------------------------
Copyright (c) 2014,2015 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
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_program.hpp"
#include "../../../dfpm/meshes/mesh1d.hpp"
#include "variables.hpp"
namespace specmicp {
namespace reactmicp {
namespace systems {
namespace satdiff {
//class SaturatedDiffusion::
SaturatedDiffusion::SaturatedDiffusion(SaturatedVariablesPtr variables,
std::vector<index_t> list_fixed_nodes):
m_ndf(2*variables->nb_component()),
m_tot_ndf(2*variables->nb_component()*variables->get_mesh()->nb_nodes()),
m_mesh(variables->get_mesh()),
m_variables(variables),
m_is_in_residual_computation(false)
{
number_equations(list_fixed_nodes, {}, {0, 1});
}
SaturatedDiffusion::SaturatedDiffusion(SaturatedVariablesPtr variables,
std::vector<index_t> list_fixed_nodes,
std::map<index_t, index_t> list_slave_nodes,
std::vector<index_t> list_immobile_components):
m_ndf(2*variables->nb_component()),
m_tot_ndf(2*variables->nb_component()*variables->get_mesh()->nb_nodes()),
m_mesh(variables->get_mesh()),
m_variables(variables),
m_is_in_residual_computation(false)
{
number_equations(list_fixed_nodes, list_slave_nodes, list_immobile_components);
}
void SaturatedDiffusion::number_equations(std::vector<index_t> list_fixed_nodes,
std::map<index_t, index_t> list_slave_nodes,
std::vector<index_t> list_immobile_components)
{
m_ideq.resizeLike(m_variables->displacement());
m_ideq.setZero();
// flag fixed nodes
for (index_t node: list_fixed_nodes)
{
for (index_t component=2; component<m_variables->nb_component(); ++component)
{
m_ideq(m_variables->dof_aqueous_concentration(node, component)) = no_equation;
}
}
// flag slaves nodes
// we flag them by making their ideq more negative than no_equation
for (auto slave_pair: list_slave_nodes)
{
for (index_t component=2; component<m_variables->nb_component(); ++component)
{
m_ideq(m_variables->dof_aqueous_concentration(slave_pair.first, component)) = no_equation-1;
}
}
// set equation numbers
index_t neq = 0;
for (index_t node=0; node<m_mesh->nb_nodes(); ++node)
{
for (index_t component: list_immobile_components)
{
m_ideq(m_variables->dof_aqueous_concentration(node, component)) = no_equation;
m_ideq(m_variables->dof_aqueous_concentration(node, component)) = no_equation;
}
for (index_t component=0; component<m_variables->nb_component(); ++component)
{
index_t dof = m_variables->dof_aqueous_concentration(node, component);
if (m_ideq(dof) > no_equation) // attribute an equation number if it is NOT a slave nor a fixed node
{
m_ideq(dof) = neq;
++neq;
}
dof = m_variables->dof_solid_concentration(node, component);
m_ideq(dof) = no_equation;
}
}
// slave nodes
// attribute the correct equation number
for (auto slave_pair: list_slave_nodes)
{
for (index_t component=1; component<m_variables->nb_component(); ++component)
{
m_ideq(m_variables->dof_aqueous_concentration(slave_pair.first, component)) =
m_ideq(m_variables->dof_aqueous_concentration(slave_pair.second, component));
}
}
m_neq = neq;
}
void SaturatedDiffusion::compute_residuals(
const Vector& displacement,
const Vector& velocity,
Vector& residual)
{
residual = Vector::Zero(get_neq());
m_is_in_residual_computation = true;
for (index_t element: m_mesh->range_elements())
{
for (index_t component=2; component<m_variables->nb_component(); ++component)
{
Eigen::Vector2d element_residual;
element_residual.setZero();
residuals_element_component(element, component, displacement, velocity, element_residual);
for (index_t en=0; en<2; ++en)
{
const index_t node = m_mesh->get_node(element, en);
const index_t id = m_ideq(m_variables->dof_aqueous_concentration(node, component));
if (id != no_equation) {residual(id) += element_residual(en);}
}
}
}
m_is_in_residual_computation = false;
}
void SaturatedDiffusion::residuals_element_component(
index_t element,
index_t component,
const Vector& displacement,
const Vector& velocity,
Eigen::Vector2d& element_residual
)
{
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);
const scalar_t diff_coeff = 1.0/(0.5/m_variables->diffusion_coefficient(node_0) +
0.5/m_variables->diffusion_coefficient(node_1));
scalar_t flux_coeff = -( m_mesh->get_face_area(element) / m_mesh->get_dx(element)
* diff_coeff
) ;
const index_t dof_0 = m_variables->dof_aqueous_concentration(node_0, component);
const index_t dof_1 = m_variables->dof_aqueous_concentration(node_1, component);
// diffusion
scalar_t flux_diffusion = flux_coeff*(displacement(dof_0) - displacement(dof_1));
element_residual(0) = flux_diffusion;
element_residual(1) = - flux_diffusion;
// advection
if (m_variables->fluid_velocity(element) != 0.0)
{
scalar_t flux_advection = (m_mesh->get_face_area(element))
*m_variables->fluid_velocity(element);
if (m_variables->fluid_velocity(element) > 0)
{
flux_advection *= (displacement(dof_0) - displacement(dof_1));
element_residual(1) += flux_advection;
}
else
{
flux_advection *= (displacement(dof_1) - displacement(dof_0));
element_residual(0) -= flux_advection;
}
}
if (m_is_in_residual_computation)
{
m_variables->aqueous_concentration(node_0, component,
m_variables->transport_rate()) += element_residual(0);
m_variables->aqueous_concentration(node_1, component,
m_variables->transport_rate()) += element_residual(1);
}
// velocity
element_residual(0) += mass_coeff_0*(velocity(dof_0)*m_variables->porosity(node_0)
+m_variables->vel_porosity(node_0)*displacement(dof_0));
element_residual(1) += mass_coeff_1*(velocity(dof_1)*m_variables->porosity(node_1)
+ m_variables->vel_porosity(node_1)*displacement(dof_1));
// external rate
element_residual(0) += mass_coeff_0*m_variables->solid_concentration(node_0, component,
m_variables->chemistry_rate());
element_residual(1) += mass_coeff_1*m_variables->solid_concentration(node_1, component,
m_variables->chemistry_rate());
}
void SaturatedDiffusion::compute_jacobian(
Vector& displacement,
Vector& velocity,
Eigen::SparseMatrix<scalar_t>& jacobian,
scalar_t alphadt
)
{
dfpm::list_triplet_t jacob;
const index_t ncomp = m_variables->nb_component();
const index_t estimation = m_mesh->nb_nodes()*(ncomp*m_mesh->nen);
jacob.reserve(estimation);
for (index_t element: m_mesh->range_elements())
{
jacobian_element(element, displacement, velocity, jacob, alphadt);
}
jacobian = Eigen::SparseMatrix<scalar_t>(get_neq(), get_neq());
jacobian.setFromTriplets(jacob.begin(), jacob.end());
}
void SaturatedDiffusion::jacobian_element(
index_t element,
Vector& displacement,
Vector& velocity,
dfpm::list_triplet_t& jacobian,
scalar_t alphadt)
{
for (index_t component=1; component<m_variables->nb_component(); ++component)
{
Eigen::Vector2d element_residual_orig(Eigen::Vector2d::Zero());
residuals_element_component(element, component, displacement, velocity, element_residual_orig);
for (index_t en=0; en<2; ++en)
{
Eigen::Vector2d element_residual(Eigen::Vector2d::Zero());
const index_t node = m_mesh->get_node(element, en);
const index_t dof = m_variables->dof_aqueous_concentration(node, component);
const index_t idc = m_ideq(dof);
if (idc == no_equation) continue;
const scalar_t tmp_v = velocity(dof);
const scalar_t tmp_d = displacement(dof);
scalar_t h = eps_jacobian*std::abs(tmp_v);
if (h < 1e-4*eps_jacobian) h = eps_jacobian;
velocity(dof) = tmp_v + h;
h = velocity(dof) - tmp_v;
displacement(dof) = tmp_d + alphadt*h;
residuals_element_component(element, component, displacement, velocity, element_residual);
velocity(dof) = tmp_v;
displacement(dof) = tmp_d;
for (index_t enr=0; enr<2; ++enr)
{
const index_t noder = m_mesh->get_node(element, enr);
const index_t idr = m_ideq(m_variables->dof_aqueous_concentration(noder, component));
if (idr == no_equation) continue;
jacobian.push_back(dfpm::triplet_t(
idr,
idc,
(element_residual(enr) - element_residual_orig(enr))/h
));
}
}
}
}
//! \brief Update the solutions
void SaturatedDiffusion::update_solution(const Vector& update,
scalar_t lambda,
scalar_t alpha_dt,
Vector& predictor,
Vector& displacement,
Vector& velocity)
{
for (index_t node: m_mesh->range_nodes())
{
for (index_t component=1; component< m_variables->nb_component(); ++component)
{
const index_t dof = m_variables->dof_aqueous_concentration(node, component);
const index_t id = m_ideq(dof);
if (id == no_equation) continue;
velocity(dof) += lambda*update(id);
}
}
//displacement = m_variables->predictor() + alpha_dt*velocity;
displacement = predictor + alpha_dt*velocity;
}
} // end namespace satdiff
} // end namespace systems
} // end namespace reactmicp
} // end namespace specmicp

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