HTFEM.h

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// SPDX-FileCopyrightText: Copyright (c) OpenGeoSys Community (opengeosys.org)
// SPDX-License-Identifier: BSD-3-Clause
 
#pragma once
 
#include <Eigen/Core>
#include <optional>
#include <vector>
 
#include "HTLocalAssemblerInterface.h"
#include "HTProcessData.h"
#include "MaterialLib/MPL/Medium.h"
#include "MaterialLib/MPL/Utils/FormEigenTensor.h"
#include "NumLib/DOF/DOFTableUtil.h"
#include "NumLib/Extrapolation/ExtrapolatableElement.h"
#include "NumLib/Fem/FiniteElement/TemplateIsoparametric.h"
#include "NumLib/Fem/InitShapeMatrices.h"
#include "NumLib/Fem/Integration/GenericIntegrationMethod.h"
#include "NumLib/Fem/ShapeMatrixPolicy.h"
#include "NumLib/NumericalStability/HydrodynamicDispersion.h"
#include "ParameterLib/Parameter.h"
 
namespace ProcessLib
{
namespace HT
{
double evalEffectiveThermalExpansivity(
    double const t, double const dt, ParameterLib::SpatialPosition const& pos,
    MaterialPropertyLib::VariableArray const& vars,
    MaterialPropertyLib::Medium const& medium,
    MaterialPropertyLib::Phase const& liquid_phase,
    MaterialPropertyLib::Phase const& solid_phase,
    bool const has_solid_thermal_expansivity, double const specific_storage);

void checkBiotStorageRelation(double const t, double const dt,
                              ParameterLib::SpatialPosition const& pos,
                              MaterialPropertyLib::VariableArray const& vars,
                              MaterialPropertyLib::Medium const& medium,
                              MaterialPropertyLib::Phase const& solid_phase);
 
template <typename ShapeFunction, int GlobalDim>
class HTFEM : public HTLocalAssemblerInterface
{
    using ShapeMatricesType = ShapeMatrixPolicyType<ShapeFunction, GlobalDim>;
    using ShapeMatrices = typename ShapeMatricesType::ShapeMatrices;
 
    using NodalVectorType = typename ShapeMatricesType::NodalVectorType;
    using NodalRowVectorType = typename ShapeMatricesType::NodalRowVectorType;
 
    using GlobalDimVectorType = typename ShapeMatricesType::GlobalDimVectorType;
    using GlobalDimNodalMatrixType =
        typename ShapeMatricesType::GlobalDimNodalMatrixType;
    using GlobalDimMatrixType = typename ShapeMatricesType::GlobalDimMatrixType;
 
public:
    HTFEM(MeshLib::Element const& element,
          std::size_t const local_matrix_size,
          NumLib::GenericIntegrationMethod const& integration_method,
          bool const is_axially_symmetric,
          HTProcessData const& process_data,
          const unsigned dof_per_node)
        : HTLocalAssemblerInterface(),
          _element(element),
          _process_data(process_data),
          _integration_method(integration_method)
    {
        // This assertion is valid only if all nodal d.o.f. use the same shape
        // matrices.
        assert(local_matrix_size == ShapeFunction::NPOINTS * dof_per_node);
        (void)local_matrix_size;
        (void)dof_per_node;
 
        unsigned const n_integration_points =
            _integration_method.getNumberOfPoints();
        _ip_data.reserve(n_integration_points);
 
        ParameterLib::SpatialPosition pos;
        pos.setElementID(_element.getID());
 
        double const aperture_size = _process_data.aperture_size(0.0, pos)[0];
 
        auto const shape_matrices =
            NumLib::initShapeMatrices<ShapeFunction, ShapeMatricesType,
                                      GlobalDim>(element, is_axially_symmetric,
                                                 _integration_method);
 
        for (unsigned ip = 0; ip < n_integration_points; ip++)
        {
            _ip_data.emplace_back(
                shape_matrices[ip].dNdx,
                _integration_method.getWeightedPoint(ip).getWeight() *
                    shape_matrices[ip].integralMeasure *
                    shape_matrices[ip].detJ * aperture_size);
        }
    }
 
    void initializeConcrete() override
    {
        auto const& medium =
            *_process_data.media_map.getMedium(_element.getID());
        auto const& solid_phase =
            medium.phase(MaterialPropertyLib::PhaseName::Solid);
 
        // The Biot coefficient is read only together with the solid thermal
        // expansivity, see evalEffectiveThermalExpansivity().
        if (!solid_phase.hasProperty(
                MaterialPropertyLib::PropertyType::thermal_expansivity))
        {
            return;
        }
 
        MaterialPropertyLib::VariableArray vars;
        vars.liquid_saturation = 1.0;
 
        auto const& Ns =
            _process_data.shape_matrix_cache
                .template NsHigherOrder<typename ShapeFunction::MeshElement>();
 
        unsigned const n_integration_points =
            _integration_method.getNumberOfPoints();
        for (unsigned ip = 0; ip < n_integration_points; ip++)
        {
            ParameterLib::SpatialPosition const pos{
                std::nullopt, _element.getID(),
                MathLib::Point3d(
                    NumLib::interpolateCoordinates<ShapeFunction,
                                                   ShapeMatricesType>(_element,
                                                                      Ns[ip]))};
 
            checkBiotStorageRelation(0.0 /* t */, 0.0 /* dt */, pos, vars,
                                     medium, solid_phase);
        }
    }
 
    Eigen::Map<const Eigen::RowVectorXd> getShapeMatrix(
        const unsigned integration_point) const override
    {
        auto const& N = _process_data.shape_matrix_cache.NsHigherOrder<
            typename ShapeFunction::MeshElement>()[integration_point];
 
        // assumes N is stored contiguously in memory
        return Eigen::Map<const Eigen::RowVectorXd>(N.data(), N.size());
    }

    Eigen::Vector3d getFlux(MathLib::Point3d const& pnt_local_coords,
                            double const t,
                            std::vector<double> const& local_x) const override
    {
        // Eval shape matrices at given point
        // Note: Axial symmetry is set to false here, because we only need dNdx
        // here, which is not affected by axial symmetry.
        auto const shape_matrices =
            NumLib::computeShapeMatrices<ShapeFunction, ShapeMatricesType,
                                         GlobalDim>(
                _element, false /*is_axially_symmetric*/,
                std::array{pnt_local_coords})[0];
 
        ParameterLib::SpatialPosition pos;
        pos.setElementID(this->_element.getID());
 
        MaterialPropertyLib::VariableArray vars;
 
        // local_x contains the local temperature and pressure values
        double T_int_pt = 0.0;
        double p_int_pt = 0.0;
        NumLib::shapeFunctionInterpolate(local_x, shape_matrices.N, T_int_pt,
                                         p_int_pt);
 
        vars.temperature = T_int_pt;
        vars.liquid_phase_pressure = p_int_pt;
 
        auto const& medium =
            *_process_data.media_map.getMedium(_element.getID());
        auto const& liquid_phase =
            medium.phase(MaterialPropertyLib::PhaseName::AqueousLiquid);
 
        // TODO (naumov) Temporary value not used by current material models.
        // Need extension of secondary variables interface.
        double const dt = std::numeric_limits<double>::quiet_NaN();
        // fetch permeability, viscosity, density
        auto const K = MaterialPropertyLib::formEigenTensor<GlobalDim>(
            medium.property(MaterialPropertyLib::PropertyType::permeability)
                .value(vars, pos, t, dt));
 
        auto const mu =
            liquid_phase.property(MaterialPropertyLib::PropertyType::viscosity)
                .template value<double>(vars, pos, t, dt);
        GlobalDimMatrixType const K_over_mu = K / mu;
 
        auto const p_nodal_values = Eigen::Map<const NodalVectorType>(
            &local_x[local_x.size() / 2], ShapeFunction::NPOINTS);
        GlobalDimVectorType q =
            -K_over_mu * shape_matrices.dNdx * p_nodal_values;
 
        if (this->_process_data.has_gravity)
        {
            auto const rho_w =
                liquid_phase
                    .property(MaterialPropertyLib::PropertyType::density)
                    .template value<double>(vars, pos, t, dt);
            auto const b =
                this->_process_data.projected_specific_body_force_vectors
                    [this->_element.getID()];
            q += K_over_mu * rho_w * b;
        }
 
        Eigen::Vector3d flux;
        flux.head<GlobalDim>() = q;
        return flux;
    }
 
protected:
    MeshLib::Element const& _element;
    HTProcessData const& _process_data;
 
    NumLib::GenericIntegrationMethod const& _integration_method;
    std::vector<IntegrationPointData<GlobalDimNodalMatrixType>> _ip_data;
 
    double getHeatEnergyCoefficient(
        MaterialPropertyLib::VariableArray const& vars, const double porosity,
        const double fluid_density, const double specific_heat_capacity_fluid,
        ParameterLib::SpatialPosition const& pos, double const t,
        double const dt)
    {
        auto const& medium =
            *_process_data.media_map.getMedium(this->_element.getID());
        auto const& solid_phase =
            medium.phase(MaterialPropertyLib::PhaseName::Solid);
 
        auto const specific_heat_capacity_solid =
            solid_phase
                .property(
                    MaterialPropertyLib::PropertyType::specific_heat_capacity)
                .template value<double>(vars, pos, t, dt);
 
        auto const solid_density =
            solid_phase.property(MaterialPropertyLib::PropertyType::density)
                .template value<double>(vars, pos, t, dt);
 
        return solid_density * specific_heat_capacity_solid * (1 - porosity) +
               fluid_density * specific_heat_capacity_fluid * porosity;
    }
 
    GlobalDimMatrixType getThermalConductivityDispersivity(
        MaterialPropertyLib::VariableArray const& vars,
        const double fluid_density, const double specific_heat_capacity_fluid,
        const GlobalDimVectorType& velocity,
        ParameterLib::SpatialPosition const& pos, double const t,
        double const dt)
    {
        auto const& medium =
            *_process_data.media_map.getMedium(_element.getID());
 
        auto thermal_conductivity =
            MaterialPropertyLib::formEigenTensor<GlobalDim>(
                medium
                    .property(
                        MaterialPropertyLib::PropertyType::thermal_conductivity)
                    .value(vars, pos, t, dt));
 
        auto const thermal_dispersivity_transversal =
            medium
                .property(MaterialPropertyLib::PropertyType::
                              thermal_transversal_dispersivity)
                .template value<double>();
 
        auto const thermal_dispersivity_longitudinal =
            medium
                .property(MaterialPropertyLib::PropertyType::
                              thermal_longitudinal_dispersivity)
                .template value<double>();
 
        // Thermal conductivity is moved outside and zero matrix is passed
        // instead due to multiplication with fluid's density times specific
        // heat capacity.
        return thermal_conductivity +
               fluid_density * specific_heat_capacity_fluid *
                   NumLib::computeHydrodynamicDispersion(
                       _process_data.stabilizer, _element.getID(),
                       GlobalDimMatrixType::Zero(GlobalDim, GlobalDim),
                       velocity, 0 /* phi */, thermal_dispersivity_transversal,
                       thermal_dispersivity_longitudinal);
    }
 
    std::vector<double> const& getIntPtDarcyVelocityLocal(
        const double t, std::vector<double> const& local_x,
        std::vector<double>& cache) const
    {
        std::vector<double> local_p{
            local_x.data() + pressure_index,
            local_x.data() + pressure_index + pressure_size};
        std::vector<double> local_T{
            local_x.data() + temperature_index,
            local_x.data() + temperature_index + temperature_size};
 
        auto const n_integration_points =
            _integration_method.getNumberOfPoints();
 
        cache.clear();
        auto cache_mat = MathLib::createZeroedMatrix<
            Eigen::Matrix<double, GlobalDim, Eigen::Dynamic, Eigen::RowMajor>>(
            cache, GlobalDim, n_integration_points);
 
        ParameterLib::SpatialPosition pos;
        pos.setElementID(_element.getID());
 
        MaterialPropertyLib::VariableArray vars;
 
        auto const p_nodal_values = Eigen::Map<const NodalVectorType>(
            &local_p[0], ShapeFunction::NPOINTS);
 
        auto const& medium =
            *_process_data.media_map.getMedium(_element.getID());
        auto const& liquid_phase =
            medium.phase(MaterialPropertyLib::PhaseName::AqueousLiquid);
 
        auto const& Ns =
            _process_data.shape_matrix_cache
                .NsHigherOrder<typename ShapeFunction::MeshElement>();
 
        for (unsigned ip = 0; ip < n_integration_points; ++ip)
        {
            auto const& ip_data = _ip_data[ip];
            auto const& dNdx = ip_data.dNdx;
            auto const& N = Ns[ip];
 
            double T_int_pt = 0.0;
            double p_int_pt = 0.0;
            NumLib::shapeFunctionInterpolate(local_p, N, p_int_pt);
            NumLib::shapeFunctionInterpolate(local_T, N, T_int_pt);
 
            vars.temperature = T_int_pt;
            vars.liquid_phase_pressure = p_int_pt;
 
            // TODO (naumov) Temporary value not used by current material
            // models. Need extension of secondary variables interface.
            double const dt = std::numeric_limits<double>::quiet_NaN();
            auto const K = MaterialPropertyLib::formEigenTensor<GlobalDim>(
                medium.property(MaterialPropertyLib::PropertyType::permeability)
                    .value(vars, pos, t, dt));
 
            auto const mu =
                liquid_phase
                    .property(MaterialPropertyLib::PropertyType::viscosity)
                    .template value<double>(vars, pos, t, dt);
            GlobalDimMatrixType const K_over_mu = K / mu;
 
            cache_mat.col(ip).noalias() = -K_over_mu * dNdx * p_nodal_values;
 
            if (_process_data.has_gravity)
            {
                auto const rho_w =
                    liquid_phase
                        .property(MaterialPropertyLib::PropertyType::density)
                        .template value<double>(vars, pos, t, dt);
                auto const b =
                    _process_data.projected_specific_body_force_vectors
                        [_element.getID()];
                // here it is assumed that the vector b is directed 'downwards'
                cache_mat.col(ip).noalias() += K_over_mu * rho_w * b;
            }
        }
 
        return cache;
    }
 
protected:
    static const int pressure_index = ShapeFunction::NPOINTS;
    static const int pressure_size = ShapeFunction::NPOINTS;
    static const int temperature_index = 0;
    static const int temperature_size = ShapeFunction::NPOINTS;
};
 
}  // namespace HT
}  // namespace ProcessLib