MonolithicHTFEM.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 <typeinfo>
#include <vector>
 
#include "HTFEM.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/ShapeMatrixPolicy.h"
#include "NumLib/NumericalStability/AdvectionMatrixAssembler.h"
#include "NumLib/NumericalStability/HydrodynamicDispersion.h"
#include "ParameterLib/Parameter.h"
 
namespace ProcessLib
{
namespace HT
{
const unsigned NUM_NODAL_DOF = 2;
 
template <typename ShapeFunction, int GlobalDim>
class MonolithicHTFEM : public HTFEM<ShapeFunction, GlobalDim>
{
    using ShapeMatricesType = ShapeMatrixPolicyType<ShapeFunction, GlobalDim>;
    using ShapeMatrices = typename ShapeMatricesType::ShapeMatrices;
 
    using LocalMatrixType = typename ShapeMatricesType::template MatrixType<
        NUM_NODAL_DOF * ShapeFunction::NPOINTS,
        NUM_NODAL_DOF * ShapeFunction::NPOINTS>;
    using LocalVectorType =
        typename ShapeMatricesType::template VectorType<NUM_NODAL_DOF *
                                                        ShapeFunction::NPOINTS>;
 
    using NodalVectorType = typename ShapeMatricesType::NodalVectorType;
    using NodalMatrixType = typename ShapeMatricesType::NodalMatrixType;
    using NodalRowVectorType = typename ShapeMatricesType::NodalRowVectorType;
 
    using GlobalDimVectorType = typename ShapeMatricesType::GlobalDimVectorType;
    using GlobalDimMatrixType = typename ShapeMatricesType::GlobalDimMatrixType;
 
public:
    MonolithicHTFEM(MeshLib::Element const& element,
                    std::size_t const local_matrix_size,
                    NumLib::GenericIntegrationMethod const& integration_method,
                    bool is_axially_symmetric,
                    HTProcessData const& process_data)
        : HTFEM<ShapeFunction, GlobalDim>(
              element, local_matrix_size, integration_method,
              is_axially_symmetric, process_data, NUM_NODAL_DOF)
    {
    }
 
    void assemble(double const t, double const dt,
                  std::vector<double> const& local_x,
                  std::vector<double> const& local_x_prev,
                  std::vector<double>& local_M_data,
                  std::vector<double>& local_K_data,
                  std::vector<double>& local_b_data) override
    {
        auto const local_matrix_size = local_x.size();
        // This assertion is valid only if all nodal d.o.f. use the same shape
        // matrices.
        assert(local_matrix_size == ShapeFunction::NPOINTS * NUM_NODAL_DOF);
 
        auto local_M = MathLib::createZeroedMatrix<LocalMatrixType>(
            local_M_data, local_matrix_size, local_matrix_size);
        auto local_K = MathLib::createZeroedMatrix<LocalMatrixType>(
            local_K_data, local_matrix_size, local_matrix_size);
        auto local_b = MathLib::createZeroedVector<LocalVectorType>(
            local_b_data, local_matrix_size);
 
        auto KTT = local_K.template block<temperature_size, temperature_size>(
            temperature_index, temperature_index);
        auto MTT = local_M.template block<temperature_size, temperature_size>(
            temperature_index, temperature_index);
        auto Kpp = local_K.template block<pressure_size, pressure_size>(
            pressure_index, pressure_index);
        auto Mpp = local_M.template block<pressure_size, pressure_size>(
            pressure_index, pressure_index);
        auto Bp = local_b.template block<pressure_size, 1>(pressure_index, 0);
 
        auto const& process_data = this->_process_data;
 
        auto p_nodal_values = Eigen::Map<const NodalVectorType>(
            &local_x[pressure_index], pressure_size);
 
        auto const& medium =
            *process_data.media_map.getMedium(this->_element.getID());
        auto const& liquid_phase =
            medium.phase(MaterialPropertyLib::PhaseName::AqueousLiquid);
        auto const& solid_phase =
            medium.phase(MaterialPropertyLib::PhaseName::Solid);
 
        auto const& b =
            process_data
                .projected_specific_body_force_vectors[this->_element.getID()];
 
        MaterialPropertyLib::VariableArray vars;
 
        unsigned const n_integration_points =
            this->_integration_method.getNumberOfPoints();
 
        std::vector<GlobalDimVectorType> ip_flux_vector;
        double average_velocity_norm = 0.0;
        ip_flux_vector.reserve(n_integration_points);
 
        auto const& Ns =
            process_data.shape_matrix_cache
                .template NsHigherOrder<typename ShapeFunction::MeshElement>();
 
        for (unsigned ip(0); ip < n_integration_points; ip++)
        {
            auto const& ip_data = this->_ip_data[ip];
            auto const& dNdx = ip_data.dNdx;
            auto const& N = Ns[ip];
            auto const& w = ip_data.integration_weight;
 
            ParameterLib::SpatialPosition const pos{
                std::nullopt, this->_element.getID(),
                MathLib::Point3d(
                    NumLib::interpolateCoordinates<ShapeFunction,
                                                   ShapeMatricesType>(
                        this->_element, N))};
 
            double T_int_pt = 0.0;
            double p_int_pt = 0.0;
            // Order matters: First T, then P!
            NumLib::shapeFunctionInterpolate(local_x, N, T_int_pt, p_int_pt);
 
            vars.temperature = T_int_pt;
            vars.liquid_phase_pressure = p_int_pt;
 
            vars.liquid_saturation = 1.0;
            // \todo the argument to getValue() has to be changed for non
            // constant storage model
            auto const specific_storage =
                solid_phase.property(MaterialPropertyLib::PropertyType::storage)
                    .template value<double>(vars, pos, t, dt);
 
            auto const porosity =
                medium.property(MaterialPropertyLib::PropertyType::porosity)
                    .template value<double>(vars, pos, t, dt);
            vars.porosity = porosity;
 
            auto const intrinsic_permeability =
                MaterialPropertyLib::formEigenTensor<GlobalDim>(
                    medium
                        .property(
                            MaterialPropertyLib::PropertyType::permeability)
                        .value(vars, pos, t, dt));
 
            auto const specific_heat_capacity_fluid =
                liquid_phase
                    .property(MaterialPropertyLib::specific_heat_capacity)
                    .template value<double>(vars, pos, t, dt);
 
            // Use the fluid density model to compute the density
            auto const fluid_density =
                liquid_phase
                    .property(MaterialPropertyLib::PropertyType::density)
                    .template value<double>(vars, pos, t, dt);
 
            vars.density = fluid_density;
            const double dfluid_density_dp =
                liquid_phase
                    .property(MaterialPropertyLib::PropertyType::density)
                    .template dValue<double>(
                        vars,
                        MaterialPropertyLib::Variable::liquid_phase_pressure,
                        pos, t, dt);
 
            // Use the viscosity model to compute the viscosity
            auto const viscosity =
                liquid_phase
                    .property(MaterialPropertyLib::PropertyType::viscosity)
                    .template value<double>(vars, pos, t, dt);
            GlobalDimMatrixType K_over_mu = intrinsic_permeability / viscosity;
 
            GlobalDimVectorType const velocity =
                process_data.has_gravity
                    ? GlobalDimVectorType(-K_over_mu * (dNdx * p_nodal_values -
                                                        fluid_density * b))
                    : GlobalDimVectorType(-K_over_mu * dNdx * p_nodal_values);
 
            // matrix assembly
            GlobalDimMatrixType const thermal_conductivity_dispersivity =
                this->getThermalConductivityDispersivity(
                    vars, fluid_density, specific_heat_capacity_fluid, velocity,
                    pos, t, dt);
 
            KTT.noalias() +=
                dNdx.transpose() * thermal_conductivity_dispersivity * dNdx * w;
 
            ip_flux_vector.emplace_back(velocity * fluid_density *
                                        specific_heat_capacity_fluid);
            average_velocity_norm += velocity.norm();
 
            Kpp.noalias() += w * dNdx.transpose() * K_over_mu * dNdx;
            MTT.noalias() += w *
                             this->getHeatEnergyCoefficient(
                                 vars, porosity, fluid_density,
                                 specific_heat_capacity_fluid, pos, t, dt) *
                             N.transpose() * N;
            Mpp.noalias() += w *
                             (porosity * dfluid_density_dp / fluid_density +
                              specific_storage) *
                             N.transpose() * N;
            if (process_data.has_gravity)
            {
                Bp += w * fluid_density * dNdx.transpose() * K_over_mu * b;
            }
 
            if (process_data.has_fluid_thermal_expansion)
            {
                double const solid_thermal_expansion =
                    process_data.solid_thermal_expansion(t, pos)[0];
                double const dfluid_density_dT =
                    liquid_phase
                        .property(MaterialPropertyLib::PropertyType::density)
                        .template dValue<double>(
                            vars, MaterialPropertyLib::Variable::temperature,
                            pos, t, dt);
                double const Tdot_int_pt =
                    (T_int_pt -
                     Eigen::Map<const NodalVectorType>(
                         &local_x_prev[temperature_index], temperature_size)
                         .dot(N)) /
                    dt;
                double const biot_constant =
                    process_data.biot_constant(t, pos)[0];
                double const eff_thermal_expansion =
                    3.0 * (biot_constant - porosity) * solid_thermal_expansion -
                    porosity * dfluid_density_dT / fluid_density;
                Bp.noalias() += eff_thermal_expansion * Tdot_int_pt * w * N;
            }
        }
 
        NumLib::assembleAdvectionMatrix<typename ShapeFunction::MeshElement>(
            process_data.stabilizer, this->_ip_data,
            process_data.shape_matrix_cache, ip_flux_vector,
            average_velocity_norm / static_cast<double>(n_integration_points),
            KTT);
    }
 
    std::vector<double> const& getIntPtDarcyVelocity(
        const double t,
        std::vector<GlobalVector*> const& x,
        std::vector<NumLib::LocalToGlobalIndexMap const*> const& dof_table,
        std::vector<double>& cache) const override
    {
        int const process_id = 0;  // monolithic case.
        auto const indices =
            NumLib::getIndices(this->_element.getID(), *dof_table[process_id]);
        assert(!indices.empty());
        auto const& local_x = x[process_id]->get(indices);
 
        return this->getIntPtDarcyVelocityLocal(t, local_x, cache);
    }
 
private:
    using HTFEM<ShapeFunction, GlobalDim>::pressure_index;
    using HTFEM<ShapeFunction, GlobalDim>::pressure_size;
    using HTFEM<ShapeFunction, GlobalDim>::temperature_index;
    using HTFEM<ShapeFunction, GlobalDim>::temperature_size;
};
 
}  // namespace HT
}  // namespace ProcessLib