LiquidFlowLocalAssembler-impl.h

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#pragma once
 
#include "LiquidFlowLocalAssembler.h"
#include "MaterialLib/MPL/MaterialSpatialDistributionMap.h"
#include "MaterialLib/MPL/Utils/FormEigenTensor.h"
#include "MaterialLib/MPL/VariableType.h"
#include "NumLib/Function/Interpolation.h"
 
namespace ProcessLib
{
namespace LiquidFlow
{
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
void LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    assemble(double const t, double const dt,
             std::vector<double> const& local_x,
             std::vector<double> const& /*local_xdot*/,
             std::vector<double>& local_M_data,
             std::vector<double>& local_K_data,
             std::vector<double>& local_b_data)
{
    ParameterLib::SpatialPosition pos;
    pos.setElementID(_element.getID());
 
    auto const& medium = *_process_data.media_map->getMedium(_element.getID());
    MaterialPropertyLib::VariableArray vars;
    vars[static_cast<int>(MaterialPropertyLib::Variable::temperature)] =
        medium[MaterialPropertyLib::PropertyType::reference_temperature]
            .template value<double>(vars, pos, t, dt);
    vars[static_cast<int>(MaterialPropertyLib::Variable::phase_pressure)] =
        std::numeric_limits<double>::quiet_NaN();
    DimMatrixType const permeability =
        MaterialPropertyLib::formEigenTensor<ShapeFunction::DIM>(
            medium[MaterialPropertyLib::PropertyType::permeability].value(
                vars, pos, t, dt));
    // Note: For Inclined 1D in 2D/3D or 2D element in 3D, the first item in
    //  the assert must be changed to permeability.rows() ==
    //  _element->getDimension()
    assert(permeability.rows() == ShapeFunction::DIM ||
           permeability.rows() == 1);
 
    if (permeability.size() == 1)
    {  // isotropic or 1D problem.
        assembleMatrixAndVector<IsotropicCalculator>(
            t, dt, local_x, local_M_data, local_K_data, local_b_data);
    }
    else
    {
        assembleMatrixAndVector<AnisotropicCalculator>(
            t, dt, local_x, local_M_data, local_K_data, local_b_data);
    }
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
Eigen::Vector3d
LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::getFlux(
    MathLib::Point3d const& p_local_coords, double const t,
    std::vector<double> const& local_x) const
{
    // TODO (tf) Temporary value not used by current material models. Need
    // extension of getFlux interface
    double const dt = std::numeric_limits<double>::quiet_NaN();
 
    // 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,
                                     ShapeFunction::DIM>(
            _element,
            false /*is_axially_symmetric*/,
            std::array{p_local_coords})[0];
 
    // create pos object to access the correct media property
    ParameterLib::SpatialPosition pos;
    pos.setElementID(_element.getID());
 
    auto const& medium = *_process_data.media_map->getMedium(_element.getID());
    auto const& liquid_phase = medium.phase("AqueousLiquid");
 
    MaterialPropertyLib::VariableArray vars;
 
    double pressure = 0.0;
    NumLib::shapeFunctionInterpolate(local_x, shape_matrices.N, pressure);
    vars[static_cast<int>(MaterialPropertyLib::Variable::phase_pressure)] =
        pressure;
 
    DimMatrixType const intrinsic_permeability =
        MaterialPropertyLib::formEigenTensor<ShapeFunction::DIM>(
            medium[MaterialPropertyLib::PropertyType::permeability].value(
                vars, pos, t, dt));
    auto const viscosity =
        liquid_phase[MaterialPropertyLib::PropertyType::viscosity]
            .template value<double>(vars, pos, t, dt);
 
    Eigen::Vector3d flux(0.0, 0.0, 0.0);
    auto const flux_local =
        (-intrinsic_permeability / viscosity * shape_matrices.dNdx *
         Eigen::Map<const NodalVectorType>(local_x.data(), local_x.size()))
            .eval();
 
    flux.head<GlobalDim>() =
        _process_data.element_rotation_matrices[_element.getID()] * flux_local;
 
    return flux;
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
template <typename LaplacianGravityVelocityCalculator>
void LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    assembleMatrixAndVector(double const t, double const dt,
                            std::vector<double> const& local_x,
                            std::vector<double>& local_M_data,
                            std::vector<double>& local_K_data,
                            std::vector<double>& local_b_data)
{
    auto const local_matrix_size = local_x.size();
    assert(local_matrix_size == ShapeFunction::NPOINTS);
 
    auto local_M = MathLib::createZeroedMatrix<NodalMatrixType>(
        local_M_data, local_matrix_size, local_matrix_size);
    auto local_K = MathLib::createZeroedMatrix<NodalMatrixType>(
        local_K_data, local_matrix_size, local_matrix_size);
    auto local_b = MathLib::createZeroedVector<NodalVectorType>(
        local_b_data, local_matrix_size);
 
    unsigned const n_integration_points =
        _integration_method.getNumberOfPoints();
 
    ParameterLib::SpatialPosition pos;
    pos.setElementID(_element.getID());
 
    auto const& medium = *_process_data.media_map->getMedium(_element.getID());
    auto const& liquid_phase = medium.phase("AqueousLiquid");
 
    MaterialPropertyLib::VariableArray vars;
    vars[static_cast<int>(MaterialPropertyLib::Variable::temperature)] =
        medium[MaterialPropertyLib::PropertyType::reference_temperature]
            .template value<double>(vars, pos, t, dt);
 
    DimVectorType const projected_body_force_vector =
        _process_data.element_rotation_matrices[_element.getID()].transpose() *
        _process_data.specific_body_force;
 
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        auto const& ip_data = _ip_data[ip];
 
        double p = 0.;
        NumLib::shapeFunctionInterpolate(local_x, ip_data.N, p);
        vars[static_cast<int>(MaterialPropertyLib::Variable::phase_pressure)] =
            p;
 
        // Compute density:
        auto const fluid_density =
            liquid_phase[MaterialPropertyLib::PropertyType::density]
                .template value<double>(vars, pos, t, dt);
        assert(fluid_density > 0.);
        auto const ddensity_dpressure =
            liquid_phase[MaterialPropertyLib::PropertyType::density]
                .template dValue<double>(
                    vars, MaterialPropertyLib::Variable::phase_pressure, pos, t,
                    dt);
 
        auto const porosity =
            medium[MaterialPropertyLib::PropertyType::porosity]
                .template value<double>(vars, pos, t, dt);
        auto const storage = medium[MaterialPropertyLib::PropertyType::storage]
                                 .template value<double>(vars, pos, t, dt);
 
        // Assemble mass matrix, M
        local_M.noalias() +=
            (porosity * ddensity_dpressure / fluid_density + storage) *
            ip_data.N.transpose() * ip_data.N * ip_data.integration_weight;
 
        // Compute viscosity:
        auto const viscosity =
            liquid_phase[MaterialPropertyLib::PropertyType::viscosity]
                .template value<double>(vars, pos, t, dt);
 
        pos.setIntegrationPoint(ip);
        DimMatrixType const permeability =
            MaterialPropertyLib::formEigenTensor<ShapeFunction::DIM>(
                medium[MaterialPropertyLib::PropertyType::permeability].value(
                    vars, pos, t, dt));
 
        // Assemble Laplacian, K, and RHS by the gravitational term
        LaplacianGravityVelocityCalculator::calculateLaplacianAndGravityTerm(
            local_K, local_b, ip_data, permeability, viscosity, fluid_density,
            projected_body_force_vector, _process_data.has_gravity);
    }
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
template <typename VelocityCacheType>
void LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    computeDarcyVelocity(bool const is_scalar_permeability, const double t,
                         const double dt, std::vector<double> const& local_x,
                         ParameterLib::SpatialPosition const& pos,
                         VelocityCacheType& darcy_velocity_at_ips) const
{
    if (is_scalar_permeability)
    {  // isotropic or 1D problem.
        computeProjectedDarcyVelocity<IsotropicCalculator>(
            t, dt, local_x, pos, darcy_velocity_at_ips);
    }
    else
    {
        computeProjectedDarcyVelocity<AnisotropicCalculator>(
            t, dt, local_x, pos, darcy_velocity_at_ips);
    }
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
std::vector<double> const&
LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    getIntPtDarcyVelocity(
        const double t,
        std::vector<GlobalVector*> const& x,
        std::vector<NumLib::LocalToGlobalIndexMap const*> const& dof_table,
        std::vector<double>& velocity_cache) const
{
    // TODO (tf) Temporary value not used by current material models. Need
    // extension of secondary variable interface.
    double const dt = std::numeric_limits<double>::quiet_NaN();
 
    constexpr int process_id = 0;
    auto const indices =
        NumLib::getIndices(_element.getID(), *dof_table[process_id]);
    auto const local_x = x[process_id]->get(indices);
    auto const n_integration_points = _integration_method.getNumberOfPoints();
    velocity_cache.clear();
 
    ParameterLib::SpatialPosition pos;
    pos.setElementID(_element.getID());
 
    auto const& medium = *_process_data.media_map->getMedium(_element.getID());
    MaterialPropertyLib::VariableArray vars;
    vars[static_cast<int>(MaterialPropertyLib::Variable::temperature)] =
        medium[MaterialPropertyLib::PropertyType::reference_temperature]
            .template value<double>(vars, pos, t, dt);
    vars[static_cast<int>(MaterialPropertyLib::Variable::phase_pressure)] =
        std::numeric_limits<double>::quiet_NaN();
 
    DimMatrixType const permeability =
        MaterialPropertyLib::formEigenTensor<ShapeFunction::DIM>(
            medium[MaterialPropertyLib::PropertyType::permeability].value(
                vars, pos, t, dt));
 
    assert(permeability.rows() == _element.getDimension() ||
           permeability.rows() == 1);
 
    bool const is_scalar_permeability = (permeability.size() == 1);
 
    auto velocity_cache_vectors = MathLib::createZeroedMatrix<
        Eigen::Matrix<double, GlobalDim, Eigen::Dynamic, Eigen::RowMajor>>(
        velocity_cache, GlobalDim, n_integration_points);
 
    computeDarcyVelocity(is_scalar_permeability, t, dt, local_x, pos,
                         velocity_cache_vectors);
 
    return velocity_cache;
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
template <typename LaplacianGravityVelocityCalculator,
          typename VelocityCacheType>
void LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    computeProjectedDarcyVelocity(
        const double t, const double dt, std::vector<double> const& local_x,
        ParameterLib::SpatialPosition const& pos,
        VelocityCacheType& darcy_velocity_at_ips) const
{
    auto const local_matrix_size = local_x.size();
    assert(local_matrix_size == ShapeFunction::NPOINTS);
 
    const auto local_p_vec =
        MathLib::toVector<NodalVectorType>(local_x, local_matrix_size);
 
    unsigned const n_integration_points =
        _integration_method.getNumberOfPoints();
 
    auto const& medium = *_process_data.media_map->getMedium(_element.getID());
    auto const& liquid_phase = medium.phase("AqueousLiquid");
 
    MaterialPropertyLib::VariableArray vars;
    vars[static_cast<int>(MaterialPropertyLib::Variable::temperature)] =
        medium[MaterialPropertyLib::PropertyType::reference_temperature]
            .template value<double>(vars, pos, t, dt);
 
    DimVectorType const projected_body_force_vector =
        _process_data.element_rotation_matrices[_element.getID()].transpose() *
        _process_data.specific_body_force;
 
    for (unsigned ip = 0; ip < n_integration_points; ip++)
    {
        auto const& ip_data = _ip_data[ip];
        double p = 0.;
        NumLib::shapeFunctionInterpolate(local_x, ip_data.N, p);
        vars[static_cast<int>(MaterialPropertyLib::Variable::phase_pressure)] =
            p;
 
        // Compute density:
        auto const fluid_density =
            liquid_phase[MaterialPropertyLib::PropertyType::density]
                .template value<double>(vars, pos, t, dt);
        // Compute viscosity:
        auto const viscosity =
            liquid_phase[MaterialPropertyLib::PropertyType::viscosity]
                .template value<double>(vars, pos, t, dt);
 
        DimMatrixType const permeability =
            MaterialPropertyLib::formEigenTensor<ShapeFunction::DIM>(
                medium[MaterialPropertyLib::PropertyType::permeability].value(
                    vars, pos, t, dt));
 
        Eigen::VectorXd const velocity_at_ip =
            LaplacianGravityVelocityCalculator::calculateVelocity(
                local_p_vec, ip_data, permeability, viscosity, fluid_density,
                projected_body_force_vector, _process_data.has_gravity);
 
        Eigen::MatrixXd const& rotation_matrix =
            _process_data.element_rotation_matrices[_element.getID()];
        darcy_velocity_at_ips.col(ip) = rotation_matrix * velocity_at_ip;
    }
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
void LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    IsotropicCalculator::calculateLaplacianAndGravityTerm(
        Eigen::Map<NodalMatrixType>& local_K,
        Eigen::Map<NodalVectorType>& local_b,
        IntegrationPointData<NodalRowVectorType,
                             GlobalDimNodalMatrixType> const& ip_data,
        DimMatrixType const& permeability, double const mu, double const rho_L,
        DimVectorType const& specific_body_force, bool const has_gravity)
{
    const double K = permeability(0, 0) / mu;
    const double fac = K * ip_data.integration_weight;
    local_K.noalias() += fac * ip_data.dNdx.transpose() * ip_data.dNdx;
 
    if (has_gravity)
    {
        local_b.noalias() +=
            (fac * rho_L) * ip_data.dNdx.transpose() * specific_body_force;
    }
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
Eigen::Matrix<double, ShapeFunction::DIM, 1>
LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    IsotropicCalculator::calculateVelocity(
        Eigen::Map<const NodalVectorType> const& local_p,
        IntegrationPointData<NodalRowVectorType,
                             GlobalDimNodalMatrixType> const& ip_data,
        DimMatrixType const& permeability, double const mu, double const rho_L,
        DimVectorType const& specific_body_force, bool const has_gravity)
{
    const double K = permeability(0, 0) / mu;
    // Compute the velocity
    DimVectorType velocity = -K * ip_data.dNdx * local_p;
    // gravity term
    if (has_gravity)
    {
        velocity += (K * rho_L) * specific_body_force;
    }
    return velocity;
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
void LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    AnisotropicCalculator::calculateLaplacianAndGravityTerm(
        Eigen::Map<NodalMatrixType>& local_K,
        Eigen::Map<NodalVectorType>& local_b,
        IntegrationPointData<NodalRowVectorType,
                             GlobalDimNodalMatrixType> const& ip_data,
        DimMatrixType const& permeability, double const mu, double const rho_L,
        DimVectorType const& specific_body_force, bool const has_gravity)
{
    const double fac = ip_data.integration_weight / mu;
    local_K.noalias() +=
        fac * ip_data.dNdx.transpose() * permeability * ip_data.dNdx;
 
    if (has_gravity)
    {
        local_b.noalias() += (fac * rho_L) * ip_data.dNdx.transpose() *
                             permeability * specific_body_force;
    }
}
 
template <typename ShapeFunction, typename IntegrationMethod, int GlobalDim>
Eigen::Matrix<double, ShapeFunction::DIM, 1>
LiquidFlowLocalAssembler<ShapeFunction, IntegrationMethod, GlobalDim>::
    AnisotropicCalculator::calculateVelocity(
        Eigen::Map<const NodalVectorType> const& local_p,
        IntegrationPointData<NodalRowVectorType,
                             GlobalDimNodalMatrixType> const& ip_data,
        DimMatrixType const& permeability, double const mu, double const rho_L,
        DimVectorType const& specific_body_force, bool const has_gravity)
{
    // Compute the velocity
    DimVectorType velocity = -permeability * ip_data.dNdx * local_p / mu;
 
    // gravity term
    if (has_gravity)
    {
        velocity += (rho_L / mu) * permeability * specific_body_force;
    }
    return velocity;
}
 
}  // namespace LiquidFlow
}  // namespace ProcessLib