/
melt.cc
1905 lines (1576 loc) · 91 KB
/
melt.cc
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/*
Copyright (C) 2016 by the authors of the ASPECT code.
This file is part of ASPECT.
ASPECT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
ASPECT 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with ASPECT; see the file LICENSE. If not see
<http://www.gnu.org/licenses/>.
*/
#include <aspect/melt.h>
#include <aspect/simulator.h>
#include <aspect/utilities.h>
#include <deal.II/base/signaling_nan.h>
#include <deal.II/dofs/dof_tools.h>
#include <deal.II/lac/sparsity_tools.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/fe/fe_dgq.h>
#include <deal.II/fe/fe_dgp.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/work_stream.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/grid/filtered_iterator.h>
#include <deal.II/grid/grid_tools.h>
namespace aspect
{
namespace MaterialModel
{
template <int dim>
void MeltOutputs<dim>::average (const MaterialAveraging::AveragingOperation operation,
const FullMatrix<double> &projection_matrix,
const FullMatrix<double> &expansion_matrix)
{
average_property (operation, projection_matrix, expansion_matrix,
compaction_viscosities);
average_property (operation, projection_matrix, expansion_matrix,
fluid_viscosities);
average_property (operation, projection_matrix, expansion_matrix,
permeabilities);
average_property (operation, projection_matrix, expansion_matrix,
fluid_densities);
// The fluid density gradients are unfortunately stored in reverse
// indexing and averaging is not implemented for tensors (only for
// doubles). It's also not quite clear whether these should
// really be averaged, so avoid this for now
}
template <int dim>
double
MeltInterface<dim>::p_c_scale (const MaterialModel::MaterialModelInputs<dim> &inputs,
const MaterialModel::MaterialModelOutputs<dim> &outputs,
const MeltHandler<dim> &handler,
bool consider_is_melt_cell) const
{
Assert(inputs.current_cell.state() == IteratorState::valid, ExcMessage("sorry, I need a cell."));
if (consider_is_melt_cell && !handler.is_melt_cell(inputs.current_cell))
return 0.0;
const MaterialModel::MeltOutputs<dim> *melt_outputs = outputs.template get_additional_output<MaterialModel::MeltOutputs<dim> >();
const double ref_K_D = this->reference_darcy_coefficient();
double K_D = 1.0;
double max_K_D = 0.0;
const unsigned int N = melt_outputs->permeabilities.size();
for (unsigned int q=0; q<N; ++q)
{
K_D *= std::pow (std::max(melt_outputs->permeabilities[q], 0.0) / melt_outputs->fluid_viscosities[q], 1./N);
max_K_D = std::max(max_K_D, melt_outputs->permeabilities[q] / melt_outputs->fluid_viscosities[q]);
}
// For melt cells, we return the average Darcy coefficient of the cell,
// but always a value larger than a threshold depending on the reference Darcy coefficient,
// so that K_D can never be zero (or close to zero) in melt cells.
// The same threshold is used when computing which cells are melt cells (the else branch),
// with the difference that we return a p_c_scale of zero to indicate that the cell is not
// a melt cell if the maximum Darcy coefficient of the cell is below the threshold.
if (consider_is_melt_cell)
K_D = std::max(K_D, 1e-3 * ref_K_D);
else
K_D = (max_K_D < 1e-3 * ref_K_D) ? 0.0 : K_D;
// If the reference permeability is set to zero, there is no melt transport in the whole model and we return zero.
return (ref_K_D > 0 ? std::sqrt(K_D / ref_K_D) : 0.0);
}
}
namespace Assemblers
{
namespace
{
template <int dim>
bool
is_velocity_or_pressures (const Introspection<dim> &introspection,
const unsigned int p_c_component_index,
const unsigned int p_f_component_index,
const unsigned int component_index)
{
if (component_index == p_c_component_index)
return true;
if (component_index == p_f_component_index)
return true;
for (unsigned int i=0; i<dim; ++i)
if (component_index == introspection.component_indices.velocities[i])
return true;
return false;
}
}
template <int dim>
void
MeltInterface<dim>::create_additional_material_model_outputs(MaterialModel::MaterialModelOutputs<dim> &outputs) const
{
MeltHandler<dim>::create_material_model_outputs(outputs);
const unsigned int n_points = outputs.viscosities.size();
if (this->get_parameters().enable_additional_stokes_rhs
&& outputs.template get_additional_output<MaterialModel::AdditionalMaterialOutputsStokesRHS<dim> >() == NULL)
{
outputs.additional_outputs.push_back(
std_cxx11::shared_ptr<MaterialModel::AdditionalMaterialOutputsStokesRHS<dim> >
(new MaterialModel::AdditionalMaterialOutputsStokesRHS<dim> (n_points)));
}
Assert(!this->get_parameters().enable_additional_stokes_rhs
||
outputs.template get_additional_output<MaterialModel::AdditionalMaterialOutputsStokesRHS<dim> >()->rhs_u.size()
== n_points, ExcInternalError());
}
template <int dim>
void
MeltStokesPreconditioner<dim>::
execute (internal::Assembly::Scratch::ScratchBase<dim> &scratch_base,
internal::Assembly::CopyData::CopyDataBase<dim> &data_base) const
{
internal::Assembly::Scratch::StokesPreconditioner<dim> &scratch = dynamic_cast<internal::Assembly::Scratch::StokesPreconditioner<dim>& > (scratch_base);
internal::Assembly::CopyData::StokesPreconditioner<dim> &data = dynamic_cast<internal::Assembly::CopyData::StokesPreconditioner<dim>& > (data_base);
const Introspection<dim> &introspection = this->introspection();
const FiniteElement<dim> &fe = this->get_fe();
const unsigned int stokes_dofs_per_cell = data.local_dof_indices.size();
const unsigned int n_q_points = scratch.finite_element_values.n_quadrature_points;
const double pressure_scaling = this->get_pressure_scaling();
const double p_c_scale = dynamic_cast<const MaterialModel::MeltInterface<dim>*>(&this->get_material_model())->p_c_scale(scratch.material_model_inputs, scratch.material_model_outputs, this->get_melt_handler(), true);
MaterialModel::MeltOutputs<dim> *melt_outputs = scratch.material_model_outputs.template get_additional_output<MaterialModel::MeltOutputs<dim> >();
Assert(dynamic_cast<const MaterialModel::MeltInterface<dim>*>(&this->get_material_model()) !=
NULL, ExcMessage("Error: The current material model needs to be derived from MeltInterface to use melt transport."));
const FEValuesExtractors::Scalar ex_p_f = introspection.variable("fluid pressure").extractor_scalar();
const FEValuesExtractors::Scalar ex_p_c = introspection.variable("compaction pressure").extractor_scalar();
const unsigned int p_f_component_index = introspection.variable("fluid pressure").first_component_index;
const unsigned int p_c_component_index = introspection.variable("compaction pressure").first_component_index;
for (unsigned int i=0, i_stokes=0; i_stokes<stokes_dofs_per_cell; /*increment at end of loop*/)
{
const unsigned int component_index_i = fe.system_to_component_index(i).first;
if (is_velocity_or_pressures(introspection,p_c_component_index,p_f_component_index,component_index_i))
{
data.local_dof_indices[i_stokes] = scratch.local_dof_indices[i];
scratch.dof_component_indices[i_stokes] = fe.system_to_component_index(i).first;
++i_stokes;
}
++i;
}
for (unsigned int q=0; q<n_q_points; ++q)
{
for (unsigned int i=0, i_stokes=0; i_stokes<stokes_dofs_per_cell; /*increment at end of loop*/)
{
const unsigned int component_index_i = fe.system_to_component_index(i).first;
if (is_velocity_or_pressures(introspection,p_c_component_index,p_f_component_index,component_index_i))
{
scratch.grads_phi_u[i_stokes] = scratch.finite_element_values[introspection.extractors.velocities].symmetric_gradient(i,q);
scratch.div_phi_u[i_stokes] = scratch.finite_element_values[introspection.extractors.velocities].divergence (i, q);
scratch.phi_p[i_stokes] = scratch.finite_element_values[ex_p_f].value (i, q);
scratch.phi_p_c[i_stokes] = scratch.finite_element_values[ex_p_c].value (i, q);
scratch.grad_phi_p[i_stokes] = scratch.finite_element_values[ex_p_f].gradient (i, q);
++i_stokes;
}
++i;
}
const double eta = scratch.material_model_outputs.viscosities[q];
const double one_over_eta = 1. / eta;
const double eta_two_thirds = scratch.material_model_outputs.viscosities[q] * 2.0 / 3.0;
const double K_D = this->get_melt_handler().limited_darcy_coefficient(melt_outputs->permeabilities[q] / melt_outputs->fluid_viscosities[q], p_c_scale > 0);
/*
- R = 1/eta M_p + K_D L_p for p
S = - (1/eta + 1/viscosity_c) M_p for p_c
*/
const double viscosity_c = melt_outputs->compaction_viscosities[q];
const SymmetricTensor<4,dim> &stress_strain_director =
scratch.material_model_outputs.stress_strain_directors[q];
const bool use_tensor = (stress_strain_director != dealii::identity_tensor<dim> ());
const double JxW = scratch.finite_element_values.JxW(q);
for (unsigned int i=0; i<stokes_dofs_per_cell; ++i)
for (unsigned int j=0; j<stokes_dofs_per_cell; ++j)
{
if (scratch.dof_component_indices[i] == scratch.dof_component_indices[j])
data.local_matrix(i,j) += ((use_tensor ?
2.0 * eta * (scratch.grads_phi_u[i] * stress_strain_director * scratch.grads_phi_u[j])
:
2.0 * eta * (scratch.grads_phi_u[i] * scratch.grads_phi_u[j]))
-
(use_tensor ?
eta_two_thirds * (scratch.div_phi_u[i] * trace(stress_strain_director * scratch.grads_phi_u[j]))
:
eta_two_thirds * (scratch.div_phi_u[i] * scratch.div_phi_u[j]))
+
(one_over_eta *
pressure_scaling *
pressure_scaling)
* scratch.phi_p[i] * scratch.phi_p[j]
+
(K_D *
pressure_scaling *
pressure_scaling) *
scratch.grad_phi_p[i] *
scratch.grad_phi_p[j]
+
(1./eta + 1./viscosity_c) * p_c_scale * p_c_scale *
pressure_scaling *
pressure_scaling *
(scratch.phi_p_c[i] * scratch.phi_p_c[j])
)
* JxW;
// add S between p_c and p_f
if (true)
data.local_matrix(i,j) +=
(
(p_c_scale * one_over_eta *
pressure_scaling *
pressure_scaling)
* scratch.phi_p[i] * scratch.phi_p_c[j]
+
(p_c_scale * one_over_eta *
pressure_scaling *
pressure_scaling)
* scratch.phi_p_c[i] * scratch.phi_p[j]
)
* JxW;
}
}
}
namespace
{
/**
* Compute the right-hand side of the fluid pressure equation of the Stokes
* system in case the simulation uses melt transport. This includes a term
* derived from Darcy's law, a term including the melting rate and a term dependent
* on the densities and velocities of fluid and solid.
*/
template <int dim>
double
compute_fluid_pressure_rhs(const SimulatorAccess<dim> *simulator_access,
const internal::Assembly::Scratch::StokesSystem<dim> &scratch,
const unsigned int q_point,
const double K_D)
{
if (!simulator_access->get_parameters().include_melt_transport)
return 0.0;
const Introspection<dim> &introspection = simulator_access->introspection();
const MaterialModel::MeltOutputs<dim> *melt_out = scratch.material_model_outputs.template get_additional_output<MaterialModel::MeltOutputs<dim> >();
Assert(melt_out != NULL, ExcInternalError());
const unsigned int porosity_index = introspection.compositional_index_for_name("porosity");
const unsigned int is_compressible = simulator_access->get_material_model().is_compressible();
const double melting_rate = scratch.material_model_outputs.reaction_terms[q_point][porosity_index];
const double solid_density = scratch.material_model_outputs.densities[q_point];
const double fluid_density = melt_out->fluid_densities[q_point];
const double solid_compressibility = scratch.material_model_outputs.compressibilities[q_point];
const Tensor<1,dim> fluid_density_gradient = melt_out->fluid_density_gradients[q_point];
const Tensor<1,dim> current_u = scratch.velocity_values[q_point];
const double porosity = std::max(scratch.material_model_inputs.composition[q_point][porosity_index],0.0);
const Tensor<1,dim>
gravity = simulator_access->get_gravity_model().gravity_vector (scratch.finite_element_values.quadrature_point(q_point));
double fluid_pressure_RHS = 0.0;
// melting term
fluid_pressure_RHS -= melting_rate * (1.0/fluid_density - 1.0/solid_density);
// compression term
// The whole expression for the first term on the RHS would be
// (u_s \cdot g) (\phi \rho_f \kappa_f + (1 - \phi) \rho_s \kappa_s).
// However, we already have the term (u_s \cdot g) \rho_s \kappa_s in the
// assembly of the stokes system without melt. Because of that, we only
// need to have -\phi \rho_s \kappa_s here.
fluid_pressure_RHS += is_compressible
?
(current_u * fluid_density_gradient) * porosity / fluid_density
- (current_u * gravity) * porosity * solid_density * solid_compressibility
+ K_D * (fluid_density_gradient * gravity)
:
0.0;
return fluid_pressure_RHS;
}
}
template <int dim>
void
MeltStokesSystem<dim>::
execute (internal::Assembly::Scratch::ScratchBase<dim> &scratch_base,
internal::Assembly::CopyData::CopyDataBase<dim> &data_base) const
{
internal::Assembly::Scratch::StokesSystem<dim> &scratch = dynamic_cast<internal::Assembly::Scratch::StokesSystem<dim>& > (scratch_base);
internal::Assembly::CopyData::StokesSystem<dim> &data = dynamic_cast<internal::Assembly::CopyData::StokesSystem<dim>& > (data_base);
const Introspection<dim> &introspection = this->introspection();
const FiniteElement<dim> &fe = this->get_fe();
const unsigned int stokes_dofs_per_cell = data.local_dof_indices.size();
const unsigned int n_q_points = scratch.finite_element_values.n_quadrature_points;
Assert(dynamic_cast<const MaterialModel::MeltInterface<dim>*>(&this->get_material_model()) !=
NULL, ExcMessage("Error: The current material model needs to be derived from MeltInterface to use melt transport."));
const double p_c_scale = dynamic_cast<const MaterialModel::MeltInterface<dim>*>(&this->get_material_model())->p_c_scale(scratch.material_model_inputs, scratch.material_model_outputs, this->get_melt_handler(), true);
const FEValuesExtractors::Scalar extractor_pressure = introspection.variable("fluid pressure").extractor_scalar();
const FEValuesExtractors::Scalar ex_p_c = introspection.variable("compaction pressure").extractor_scalar();
const unsigned int p_f_component_index = introspection.variable("fluid pressure").first_component_index;
const unsigned int p_c_component_index = introspection.variable("compaction pressure").first_component_index;
MaterialModel::MeltOutputs<dim> *melt_outputs = scratch.material_model_outputs.template get_additional_output<MaterialModel::MeltOutputs<dim> >();
const MaterialModel::AdditionalMaterialOutputsStokesRHS<dim>
*force = scratch.material_model_outputs.template get_additional_output<MaterialModel::AdditionalMaterialOutputsStokesRHS<dim> >();
const double pressure_scaling = this->get_pressure_scaling();
for (unsigned int i=0, i_stokes=0; i_stokes<stokes_dofs_per_cell; /*increment at end of loop*/)
{
const unsigned int component_index_i = fe.system_to_component_index(i).first;
if (is_velocity_or_pressures(introspection,p_c_component_index,p_f_component_index,component_index_i))
{
data.local_dof_indices[i_stokes] = scratch.local_dof_indices[i];
++i_stokes;
}
++i;
}
for (unsigned int q=0; q<n_q_points; ++q)
{
for (unsigned int i=0, i_stokes=0; i_stokes<stokes_dofs_per_cell; /*increment at end of loop*/)
{
const unsigned int component_index_i = fe.system_to_component_index(i).first;
if (is_velocity_or_pressures(introspection,p_c_component_index,p_f_component_index,component_index_i))
{
scratch.phi_u[i_stokes] = scratch.finite_element_values[introspection.extractors.velocities].value (i,q);
scratch.phi_p[i_stokes] = scratch.finite_element_values[extractor_pressure].value (i, q);
scratch.phi_p_c[i_stokes] = scratch.finite_element_values[ex_p_c].value (i, q);
scratch.grad_phi_p[i_stokes] = scratch.finite_element_values[extractor_pressure].gradient (i, q);
if (scratch.rebuild_stokes_matrix)
{
scratch.grads_phi_u[i_stokes] = scratch.finite_element_values[introspection.extractors.velocities].symmetric_gradient(i,q);
scratch.div_phi_u[i_stokes] = scratch.finite_element_values[introspection.extractors.velocities].divergence (i, q);
}
++i_stokes;
}
++i;
}
// Viscosity scalar
const double eta = (scratch.rebuild_stokes_matrix
?
scratch.material_model_outputs.viscosities[q]
:
numbers::signaling_nan<double>());
const double eta_two_thirds = (scratch.rebuild_stokes_matrix
?
scratch.material_model_outputs.viscosities[q] * 2.0 / 3.0
:
numbers::signaling_nan<double>());
const Tensor<1,dim>
gravity = this->get_gravity_model().gravity_vector (scratch.finite_element_values.quadrature_point(q));
const SymmetricTensor<4,dim> &stress_strain_director =
scratch.material_model_outputs.stress_strain_directors[q];
const bool use_tensor = (stress_strain_director != dealii::identity_tensor<dim> ());
const double compressibility
= (this->get_material_model().is_compressible()
?
scratch.material_model_outputs.compressibilities[q]
:
numbers::signaling_nan<double>() );
const double density_s = scratch.material_model_outputs.densities[q]; // density of the solid
const unsigned int porosity_index = introspection.compositional_index_for_name("porosity");
const double porosity = std::max(scratch.material_model_inputs.composition[q][porosity_index],0.000);
const double K_D = this->get_melt_handler().limited_darcy_coefficient(melt_outputs->permeabilities[q] / melt_outputs->fluid_viscosities[q], p_c_scale > 0);
const double viscosity_c = melt_outputs->compaction_viscosities[q];
const Tensor<1,dim> density_gradient_f = melt_outputs->fluid_density_gradients[q];
const double density_f = melt_outputs->fluid_densities[q];
const double p_f_RHS = compute_fluid_pressure_rhs(this,
scratch,
q,
K_D);
const double bulk_density = (1.0 - porosity) * density_s + porosity * density_f;
const double JxW = scratch.finite_element_values.JxW(q);
for (unsigned int i=0; i<stokes_dofs_per_cell; ++i)
{
data.local_rhs(i) += (
(bulk_density * gravity * scratch.phi_u[i])
+
// add a force to the RHS if present
(force!=NULL ?
(force->rhs_u[q] * scratch.phi_u[i]
+ pressure_scaling * force->rhs_p[q] * scratch.phi_p[i]
+ pressure_scaling * force->rhs_melt_pc[q] * p_c_scale * scratch.phi_p_c[i])
: 0.0)
+
// add the term that results from the compressibility. compared
// to the manual, this term seems to have the wrong sign, but this
// is because we negate the entire equation to make sure we get
// -div(u) as the adjoint operator of grad(p) (see above where
// we assemble the matrix)
(this->get_material_model().is_compressible()
?
(pressure_scaling *
compressibility * density_s *
(scratch.velocity_values[q] * gravity) *
scratch.phi_p[i])
:
0)
+ pressure_scaling *
p_f_RHS * scratch.phi_p[i]
- pressure_scaling *
K_D * density_f *
(scratch.grad_phi_p[i] * gravity)
)
* JxW;
if (scratch.rebuild_stokes_matrix)
for (unsigned int j=0; j<stokes_dofs_per_cell; ++j)
{
data.local_matrix(i,j) += ( (use_tensor ?
eta * 2.0 * (scratch.grads_phi_u[i] * stress_strain_director * scratch.grads_phi_u[j])
:
eta * 2.0 * (scratch.grads_phi_u[i] * scratch.grads_phi_u[j]))
- (use_tensor ?
eta_two_thirds * (scratch.div_phi_u[i] * trace(stress_strain_director * scratch.grads_phi_u[j]))
:
eta_two_thirds * (scratch.div_phi_u[i] * scratch.div_phi_u[j])
)
- (pressure_scaling *
scratch.div_phi_u[i] * scratch.phi_p[j])
// finally the term -div(u). note the negative sign to make this
// operator adjoint to the grad(p) term
- (pressure_scaling *
scratch.phi_p[i] * scratch.div_phi_u[j])
+
(- pressure_scaling * pressure_scaling / viscosity_c * p_c_scale * p_c_scale
* scratch.phi_p_c[i] * scratch.phi_p_c[j])
- pressure_scaling * scratch.div_phi_u[i] * scratch.phi_p_c[j] * p_c_scale
- pressure_scaling * scratch.phi_p_c[i] * scratch.div_phi_u[j] * p_c_scale
- K_D * pressure_scaling * pressure_scaling *
(scratch.grad_phi_p[i] * scratch.grad_phi_p[j])
+ (this->get_material_model().is_compressible()
?
K_D * pressure_scaling * pressure_scaling / density_f
* scratch.phi_p[i] * (scratch.grad_phi_p[j] * density_gradient_f)
:
0.0))
* JxW;
}
}
}
}
template <int dim>
void
MeltStokesSystemBoundary<dim>::
execute (internal::Assembly::Scratch::ScratchBase<dim> &scratch_base,
internal::Assembly::CopyData::CopyDataBase<dim> &data_base) const
{
internal::Assembly::Scratch::StokesSystem<dim> &scratch = dynamic_cast<internal::Assembly::Scratch::StokesSystem<dim>& > (scratch_base);
internal::Assembly::CopyData::StokesSystem<dim> &data = dynamic_cast<internal::Assembly::CopyData::StokesSystem<dim>& > (data_base);
const Introspection<dim> &introspection = this->introspection();
const FiniteElement<dim> &fe = this->get_fe();
const unsigned int n_face_q_points = scratch.face_finite_element_values.n_quadrature_points;
const unsigned int stokes_dofs_per_cell = data.local_dof_indices.size();
const FEValuesExtractors::Scalar ex_p_f = introspection.variable("fluid pressure").extractor_scalar();
const unsigned int p_f_component_index = introspection.variable("fluid pressure").first_component_index;
const unsigned int p_c_component_index = introspection.variable("compaction pressure").first_component_index;
const double p_c_scale = dynamic_cast<const MaterialModel::MeltInterface<dim>*>(&this->get_material_model())->p_c_scale(scratch.material_model_inputs, scratch.material_model_outputs, this->get_melt_handler(), true);
const typename DoFHandler<dim>::face_iterator face = scratch.face_material_model_inputs.current_cell->face(scratch.face_number);
MaterialModel::MeltOutputs<dim> *melt_outputs = scratch.face_material_model_outputs.template get_additional_output<MaterialModel::MeltOutputs<dim> >();
std::vector<double> grad_p_f(n_face_q_points);
this->get_melt_handler().boundary_fluid_pressure->fluid_pressure_gradient(
face->boundary_id(),
scratch.face_material_model_inputs,
scratch.face_material_model_outputs,
#if DEAL_II_VERSION_GTE(9,0,0)
scratch.face_finite_element_values.get_normal_vectors(),
#else
scratch.face_finite_element_values.get_all_normal_vectors(),
#endif
grad_p_f);
for (unsigned int q=0; q<n_face_q_points; ++q)
{
const Tensor<1,dim>
gravity = this->get_gravity_model().gravity_vector (scratch.face_finite_element_values.quadrature_point(q));
const double density_f = melt_outputs->fluid_densities[q];
const double K_D = this->get_melt_handler().limited_darcy_coefficient(melt_outputs->permeabilities[q] / melt_outputs->fluid_viscosities[q], p_c_scale > 0);
for (unsigned int i=0, i_stokes=0; i_stokes<stokes_dofs_per_cell; /*increment at end of loop*/)
{
const unsigned int component_index_i = fe.system_to_component_index(i).first;
if (is_velocity_or_pressures(introspection,p_c_component_index,p_f_component_index,component_index_i))
{
// apply the fluid pressure boundary condition
data.local_rhs(i_stokes) += (scratch.face_finite_element_values[ex_p_f].value(i, q)
* this->get_pressure_scaling() * K_D *
(density_f
* (scratch.face_finite_element_values.normal_vector(q) * gravity)
- grad_p_f[q])
* scratch.face_finite_element_values.JxW(q));
++i_stokes;
}
++i;
}
}
}
namespace
{
/**
* Compute the right-hand side for the porosity system.
* It includes the melting rate and a term dependent
* on the density and velocity.
*
* This function is implemented in
* <code>source/simulator/melt.cc</code>.
*/
template <int dim>
double
compute_melting_RHS(const SimulatorAccess<dim> *simulator_access,
const internal::Assembly::Scratch::AdvectionSystem<dim> &scratch,
const unsigned int q_point,
const double divergence_u)
{
Assert (scratch.material_model_outputs.densities[q_point] > 0,
ExcMessage ("The density needs to be a positive quantity "
"when melt transport is included in the simulation."));
const double melting_rate = scratch.material_model_outputs.reaction_terms[q_point][scratch.advection_field->compositional_variable];
const double density = scratch.material_model_outputs.densities[q_point];
const double compressibility = (simulator_access->get_material_model().is_compressible()
?
scratch.material_model_outputs.compressibilities[q_point]
:
0.0);
const Tensor<1,dim> current_u = scratch.current_velocity_values[q_point];
const Tensor<1,dim>
gravity = simulator_access->get_gravity_model().gravity_vector (scratch.finite_element_values.quadrature_point(q_point));
// Note that the full advection term would be (1 - phi) * (div u + kappa rho u g),
// but we expanded the term and move the part (- phi) * (div u + kappa rho u g) over to the LHS.
double melt_transport_RHS = melting_rate / density
+ divergence_u + compressibility * density * (current_u * gravity);
if (!simulator_access->get_melt_handler().is_melt_cell(scratch.material_model_inputs.current_cell))
melt_transport_RHS = melting_rate / density;
return melt_transport_RHS;
}
}
template <int dim>
void
MeltAdvectionSystem<dim>::
execute (internal::Assembly::Scratch::ScratchBase<dim> &scratch_base,
internal::Assembly::CopyData::CopyDataBase<dim> &data_base) const
{
internal::Assembly::Scratch::AdvectionSystem<dim> &scratch = dynamic_cast<internal::Assembly::Scratch::AdvectionSystem<dim>& > (scratch_base);
internal::Assembly::CopyData::AdvectionSystem<dim> &data = dynamic_cast<internal::Assembly::CopyData::AdvectionSystem<dim>& > (data_base);
const Introspection<dim> &introspection = this->introspection();
const FiniteElement<dim> &fe = this->get_fe();
const bool use_bdf2_scheme = (this->get_timestep_number() > 1);
const unsigned int n_q_points = scratch.finite_element_values.n_quadrature_points;
const unsigned int advection_dofs_per_cell = data.local_dof_indices.size();
const double time_step = this->get_timestep();
const double old_time_step = this->get_old_timestep();
const unsigned int solution_component = scratch.advection_field->component_index(introspection);
const FEValuesExtractors::Scalar solution_field = scratch.advection_field->scalar_extractor(introspection);
MaterialModel::MeltOutputs<dim> *melt_outputs = scratch.material_model_outputs.template get_additional_output<MaterialModel::MeltOutputs<dim> >();
Assert(melt_outputs->compaction_viscosities[0] > 0.0,
ExcMessage ("MeltOutputs have to be filled for models with melt transport. "
"At the moment, these outputs are not filled, or they do not have "
"reasonable values."));
std::vector<Tensor<1,dim> > fluid_velocity_values(n_q_points);
const FEValuesExtractors::Vector ex_u_f = introspection.variable("fluid velocity").extractor_vector();
scratch.finite_element_values[ex_u_f].get_function_values (this->get_solution(),fluid_velocity_values);
// average divergence u over the cell (needed for porosity advection)
double divergence_u = 0.0;
if (this->get_melt_handler().is_porosity(*scratch.advection_field))
for (unsigned int q=0; q<n_q_points; ++q)
divergence_u += scratch.current_velocity_divergences[q] * 1./n_q_points;
for (unsigned int q=0; q<n_q_points; ++q)
{
// precompute the values of shape functions and their gradients.
// We only need to look up values of shape functions if they
// belong to 'our' component. They are zero otherwise anyway.
// Note that we later only look at the values that we do set here.
for (unsigned int i=0, i_advection=0; i_advection<advection_dofs_per_cell; /*increment at end of loop*/)
{
if (fe.system_to_component_index(i).first == solution_component)
{
scratch.grad_phi_field[i_advection] = scratch.finite_element_values[solution_field].gradient (i,q);
scratch.phi_field[i_advection] = scratch.finite_element_values[solution_field].value (i,q);
++i_advection;
}
++i;
}
const unsigned int porosity_index = introspection.compositional_index_for_name("porosity");
const double porosity = std::max(scratch.material_model_inputs.composition[q][porosity_index],0.0);
const double bulk_density = (1.0 - porosity) * scratch.material_model_outputs.densities[q] + porosity * melt_outputs->fluid_densities[q];
const double density_c_P =
((scratch.advection_field->is_temperature())
?
bulk_density *
scratch.material_model_outputs.specific_heat[q]
:
1.0);
Assert (density_c_P >= 0,
ExcMessage ("The product of density and c_P needs to be a "
"non-negative quantity."));
const double conductivity =
(scratch.advection_field->is_temperature()
?
scratch.material_model_outputs.thermal_conductivities[q]
:
0.0);
const double latent_heat_LHS =
((scratch.advection_field->is_temperature())
?
scratch.heating_model_outputs.lhs_latent_heat_terms[q]
:
0.0);
Assert (density_c_P + latent_heat_LHS >= 0,
ExcMessage ("The sum of density times c_P and the latent heat contribution "
"to the left hand side needs to be a non-negative quantity."));
const double gamma =
((scratch.advection_field->is_temperature())
?
scratch.heating_model_outputs.heating_source_terms[q]
:
0.0);
const double reaction_term =
((scratch.advection_field->is_temperature() || this->get_melt_handler().is_porosity(*scratch.advection_field))
?
0.0
:
scratch.material_model_outputs.reaction_terms[q][scratch.advection_field->compositional_variable]);
const double melt_transport_RHS = (this->get_melt_handler().is_porosity(*scratch.advection_field) ?
compute_melting_RHS (this,
scratch,
q,
divergence_u)
:
0.0);
const double field_term_for_rhs
= (use_bdf2_scheme ?
((scratch.old_field_values)[q] *
(1 + time_step/old_time_step)
-
(scratch.old_old_field_values)[q] *
(time_step * time_step) /
(old_time_step * (time_step + old_time_step)))
:
(scratch.old_field_values)[q])
*
(density_c_P + latent_heat_LHS);
Tensor<1,dim> current_u = scratch.current_velocity_values[q];
// Subtract off the mesh velocity for ALE corrections if necessary
if (this->get_parameters().free_surface_enabled)
current_u -= scratch.mesh_velocity_values[q];
const double melt_transport_LHS =
(this->get_melt_handler().is_porosity(*scratch.advection_field)
?
divergence_u
+ (this->get_material_model().is_compressible()
?
scratch.material_model_outputs.compressibilities[q]
* scratch.material_model_outputs.densities[q]
* current_u
* this->get_gravity_model().gravity_vector (scratch.finite_element_values.quadrature_point(q))
:
0.0)
:
0.0);
const double factor = (use_bdf2_scheme)? ((2*time_step + old_time_step) /
(time_step + old_time_step)) : 1.0;
// for advective transport of heat by melt, we have to consider melt velocities
const Tensor<1,dim> current_u_f = fluid_velocity_values[q];
double density_c_P_solid = density_c_P;
double density_c_P_melt = 0.0;
if (scratch.advection_field->is_temperature() && this->get_melt_handler().is_melt_cell(scratch.cell)
&& this->get_melt_handler().heat_advection_by_melt)
{
density_c_P_solid = (1.0 - porosity) * scratch.material_model_outputs.densities[q] * scratch.material_model_outputs.specific_heat[q];
density_c_P_melt = porosity * melt_outputs->fluid_densities[q] * scratch.material_model_outputs.specific_heat[q];
}
// do the actual assembly. note that we only need to loop over the advection
// shape functions because these are the only contributions we compute here
for (unsigned int i=0; i<advection_dofs_per_cell; ++i)
{
data.local_rhs(i)
+= (field_term_for_rhs * scratch.phi_field[i]
+ time_step *
scratch.phi_field[i]
* (gamma + melt_transport_RHS)
+ scratch.phi_field[i]
* reaction_term)
*
scratch.finite_element_values.JxW(q);
for (unsigned int j=0; j<advection_dofs_per_cell; ++j)
{
data.local_matrix(i,j)
+= (
(time_step * (conductivity + scratch.artificial_viscosity)
* (scratch.grad_phi_field[i] * scratch.grad_phi_field[j]))
+ ((time_step * (scratch.phi_field[i] * (current_u * scratch.grad_phi_field[j])))
+ (factor * scratch.phi_field[i] * scratch.phi_field[j])) *
(density_c_P_solid + latent_heat_LHS)
+ ((time_step * (scratch.phi_field[i] * (current_u_f * scratch.grad_phi_field[j])))
+ (factor * scratch.phi_field[i] * scratch.phi_field[j])) *
(density_c_P_melt)
+ time_step * scratch.phi_field[i] * scratch.phi_field[j] * melt_transport_LHS
)
* scratch.finite_element_values.JxW(q);
}
}
}
}
template <int dim>
std::vector<double>
MeltAdvectionSystem<dim>::
compute_residual(internal::Assembly::Scratch::ScratchBase<dim> &scratch_base) const
{
internal::Assembly::Scratch::AdvectionSystem<dim> &scratch =
dynamic_cast<internal::Assembly::Scratch::AdvectionSystem<dim>& > (scratch_base);
const unsigned int n_q_points = scratch.finite_element_values.n_quadrature_points;
std::vector<double> residuals(n_q_points);
this->get_heating_model_manager().evaluate(scratch.material_model_inputs,
scratch.material_model_outputs,
scratch.heating_model_outputs);
// average divergence u over the cell (needed for porosity advection)
double divergence_u = 0.0;
if (this->get_melt_handler().is_porosity(*scratch.advection_field))
for (unsigned int q=0; q<n_q_points; ++q)
divergence_u += scratch.current_velocity_divergences[q] * 1./n_q_points;
for (unsigned int q=0; q < n_q_points; ++q)
{
const Tensor<1,dim> u = (scratch.old_velocity_values[q] +
scratch.old_old_velocity_values[q]) / 2;
const double dField_dt = (this->get_old_timestep() == 0.0) ? 0.0 :
(
((scratch.old_field_values)[q] - (scratch.old_old_field_values)[q])
/ this->get_old_timestep());
const double u_grad_field = u * (scratch.old_field_grads[q] +
scratch.old_old_field_grads[q]) / 2;
if (scratch.advection_field->is_temperature())
{
const double density = scratch.material_model_outputs.densities[q];
const double conductivity = scratch.material_model_outputs.thermal_conductivities[q];
const double c_P = scratch.material_model_outputs.specific_heat[q];
const double k_Delta_field = conductivity * (scratch.old_field_laplacians[q] +
scratch.old_old_field_laplacians[q]) / 2;
const double gamma = scratch.heating_model_outputs.heating_source_terms[q];
const double latent_heat_LHS = scratch.heating_model_outputs.lhs_latent_heat_terms[q];
residuals[q]
= std::abs((density * c_P + latent_heat_LHS) * (dField_dt + u_grad_field) - k_Delta_field - gamma);
}
else
{
const double field = ((scratch.old_field_values)[q] + (scratch.old_old_field_values)[q]) / 2;
const double dreaction_term_dt =
(this->get_old_timestep() == 0 || this->get_melt_handler().is_porosity(*scratch.advection_field))
?
0.0
:
(scratch.material_model_outputs.reaction_terms[q][scratch.advection_field->compositional_variable]
/ this->get_old_timestep());
const double melt_transport_RHS = (this->get_melt_handler().is_porosity(*scratch.advection_field) ?
compute_melting_RHS (this,
scratch,
q,
divergence_u)
:
0.0);
const double melt_transport_LHS =
(this->get_melt_handler().is_porosity(*scratch.advection_field)
?
scratch.current_velocity_divergences[q]
+ (this->get_material_model().is_compressible()
?
scratch.material_model_outputs.compressibilities[q]
* scratch.material_model_outputs.densities[q]
* u
* this->get_gravity_model().gravity_vector (scratch.finite_element_values.quadrature_point(q))
:
0.0)
:
0.0);
residuals[q]
= std::abs(dField_dt + u_grad_field + melt_transport_LHS * field
- melt_transport_RHS - dreaction_term_dt);
}
}
return residuals;
}
template <int dim>
void
MeltPressureRHSCompatibilityModification<dim>::
execute (internal::Assembly::Scratch::ScratchBase<dim> &scratch_base,
internal::Assembly::CopyData::CopyDataBase<dim> &data_base) const
{
internal::Assembly::Scratch::StokesSystem<dim> &scratch = dynamic_cast<internal::Assembly::Scratch::StokesSystem<dim>& > (scratch_base);
internal::Assembly::CopyData::StokesSystem<dim> &data = dynamic_cast<internal::Assembly::CopyData::StokesSystem<dim>& > (data_base);
const Introspection<dim> &introspection = this->introspection();
const FiniteElement<dim> &fe = scratch.finite_element_values.get_fe();
const unsigned int stokes_dofs_per_cell = data.local_dof_indices.size();
const unsigned int p_f_component_index = introspection.variable("fluid pressure").first_component_index;
const unsigned int p_c_component_index = introspection.variable("compaction pressure").first_component_index;
const unsigned int n_q_points = scratch.finite_element_values.n_quadrature_points;
const FEValuesExtractors::Scalar ex_p_f = introspection.variable("fluid pressure").extractor_scalar();
for (unsigned int q=0; q<n_q_points; ++q)
for (unsigned int i=0, i_stokes=0; i_stokes<stokes_dofs_per_cell; /*increment at end of loop*/)
{
const unsigned int component_index_i = fe.system_to_component_index(i).first;
if (is_velocity_or_pressures(introspection,p_c_component_index,p_f_component_index,component_index_i))
{
scratch.phi_p[i_stokes] = scratch.finite_element_values[ex_p_f].value (i, q);
data.local_pressure_shape_function_integrals(i_stokes) += scratch.phi_p[i_stokes] * scratch.finite_element_values.JxW(q);
++i_stokes;
}
++i;
}
}
template <int dim>
void
MeltBoundaryTraction<dim>::
execute (internal::Assembly::Scratch::ScratchBase<dim> &scratch_base,
internal::Assembly::CopyData::CopyDataBase<dim> &data_base) const
{
internal::Assembly::Scratch::StokesSystem<dim> &scratch = dynamic_cast<internal::Assembly::Scratch::StokesSystem<dim>& > (scratch_base);
internal::Assembly::CopyData::StokesSystem<dim> &data = dynamic_cast<internal::Assembly::CopyData::StokesSystem<dim>& > (data_base);
const Introspection<dim> &introspection = this->introspection();
const FiniteElement<dim> &fe = this->get_fe();
// see if any of the faces are traction boundaries for which
// we need to assemble force terms for the right hand side
const unsigned int stokes_dofs_per_cell = data.local_dof_indices.size();
const unsigned int p_f_component_index = introspection.variable("fluid pressure").first_component_index;
const unsigned int p_c_component_index = introspection.variable("compaction pressure").first_component_index;
const typename DoFHandler<dim>::active_cell_iterator cell (&this->get_triangulation(),
scratch.face_finite_element_values.get_cell()->level(),
scratch.face_finite_element_values.get_cell()->index(),
&this->get_dof_handler());
unsigned int face_no = numbers::invalid_unsigned_int;
for (face_no=0; face_no<GeometryInfo<dim>::faces_per_cell; ++face_no)
if (scratch.face_finite_element_values.get_face_index() == cell->face_index(face_no))
break;
Assert(face_no != numbers::invalid_unsigned_int,ExcInternalError());
const typename DoFHandler<dim>::face_iterator face = cell->face(face_no);
if (this->get_boundary_traction()
.find (face->boundary_id())
!=
this->get_boundary_traction().end())
{
scratch.face_finite_element_values.reinit (cell, face_no);
for (unsigned int q=0; q<scratch.face_finite_element_values.n_quadrature_points; ++q)
{
const Tensor<1,dim> traction
= this->get_boundary_traction().find(
face->boundary_id()
)->second
->boundary_traction (face->boundary_id(),
scratch.face_finite_element_values.quadrature_point(q),
scratch.face_finite_element_values.normal_vector(q));
for (unsigned int i=0, i_stokes=0; i_stokes<stokes_dofs_per_cell; /*increment at end of loop*/)
{
const unsigned int component_index_i = fe.system_to_component_index(i).first;