heat_model.cc

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/*!
 *
 * Copyright (C) 2015 Technical University of Liberec.  All rights reserved.
 * 
 * This program is free software; you can redistribute it and/or modify it under
 * the terms of the GNU General Public License version 3 as published by the
 * Free Software Foundation. (http://www.gnu.org/licenses/gpl-3.0.en.html)
 * 
 * This program 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.
 *
 * 
 * @file    heat_model.cc
 * @brief   Discontinuous Galerkin method for equation of transport with dispersion.
 * @author  Jan Stebel
 */

#include "input/input_type.hh"
#include "mesh/mesh.h"
#include "mesh/accessors.hh"
//#include "transport/transport_operator_splitting.hh"
#include "heat_model.hh"
#include "tools/unit_si.hh"
#include "coupling/balance.hh"



using namespace std;
using namespace Input::Type;








const Selection & HeatTransferModel::ModelEqData::get_bc_type_selection() {
    return Selection("Heat_BC_Type", "Types of boundary conditions for heat transfer model.")
            .add_value(bc_inflow, "inflow",
                  "Default heat transfer boundary condition.\n"
                  "On water inflow (($(q_w \\le 0)$)), total energy flux is given by the reference temperature 'bc_temperature'. "
                  "On water outflow we prescribe zero diffusive flux, "
                  "i.e. the energy flows out only due to advection.")
            .add_value(bc_dirichlet, "dirichlet",
                  "Dirichlet boundary condition (($T = T_D $)).\n"
                  "The prescribed temperature (($T_D$)) is specified by the field 'bc_temperature'.")
            .add_value(bc_total_flux, "total_flux",
                  "Total energy flux boundary condition.\n"
                  "The prescribed incoming total flux can have the general form (($\\delta(f_N+\\sigma_R(T_R-T) )$)), "
                  "where the absolute flux (($f_N$)) is specified by the field 'bc_flux', "
                  "the transition parameter (($\\sigma_R$)) by 'bc_robin_sigma', "
                  "and the reference temperature (($T_R$)) by 'bc_temperature'.")
            .add_value(bc_diffusive_flux, "diffusive_flux",
                  "Diffusive flux boundary condition.\n"
                  "The prescribed incoming energy flux due to diffusion can have the general form (($\\delta(f_N+\\sigma_R(T_R-T) )$)), "
                  "where the absolute flux (($f_N$)) is specified by the field 'bc_flux', "
                  "the transition parameter (($\\sigma_R$)) by 'bc_robin_sigma', "
                  "and the reference temperature (($T_R$)) by 'bc_temperature'.")
              .close();
}


HeatTransferModel::ModelEqData::ModelEqData()
{
    *this+=bc_type
            .name("bc_type")
            .description(
            "Type of boundary condition.")
            .units( UnitSI::dimensionless() )
            .input_default("\"inflow\"")
            .input_selection( get_bc_type_selection() )
            .flags_add(FieldFlag::in_rhs & FieldFlag::in_main_matrix);
    *this+=bc_dirichlet_value
            .name("bc_temperature")
            .description("Boundary value of temperature.")
            .units( UnitSI().K() )
            .input_default("0.0")
            .flags_add(in_rhs);
    *this+=bc_flux
            .disable_where(bc_type, { bc_dirichlet, bc_inflow })
            .name("bc_flux")
            .description("Flux in Neumann boundary condition.")
            .units( UnitSI().kg().m().s(-1).md() )
            .input_default("0.0")
            .flags_add(FieldFlag::in_rhs);
    *this+=bc_robin_sigma
            .disable_where(bc_type, { bc_dirichlet, bc_inflow })
            .name("bc_robin_sigma")
            .description("Conductivity coefficient in Robin boundary condition.")
            .units( UnitSI().m(4).s(-1).md() )
            .input_default("0.0")
            .flags_add(FieldFlag::in_rhs & FieldFlag::in_main_matrix);

    *this+=init_temperature
            .name("init_temperature")
            .description("Initial temperature.")
            .units( UnitSI().K() )
            .input_default("0.0");

    *this+=porosity
            .name("porosity")
            .description("Porosity.")
            .units( UnitSI::dimensionless() )
            .input_default("1.0")
            .flags_add(in_main_matrix & in_time_term)
            .set_limits(0.0);

    *this+=water_content
            .name("water_content")
            .units( UnitSI::dimensionless() )
            .input_default("1.0")
            .flags_add(input_copy & in_main_matrix & in_time_term);

    *this += flow_flux.name("flow_flux")
               .flags( FieldFlag::input_copy )
               .flags_add(in_time_term & in_main_matrix & in_rhs);

    *this+=fluid_density
            .name("fluid_density")
            .description("Density of fluid.")
            .units( UnitSI().kg().m(-3) )
            .input_default("1000")
            .flags_add(in_main_matrix & in_time_term);

    *this+=fluid_heat_capacity
            .name("fluid_heat_capacity")
            .description("Heat capacity of fluid.")
            .units( UnitSI::J() * UnitSI().kg(-1).K(-1) )
            .flags_add(in_main_matrix & in_time_term);

    *this+=fluid_heat_conductivity
            .name("fluid_heat_conductivity")
            .description("Heat conductivity of fluid.")
            .units( UnitSI::W() * UnitSI().m(-1).K(-1) )
            .flags_add(in_main_matrix)
            .set_limits(0.0);


    *this+=solid_density
            .name("solid_density")
            .description("Density of solid (rock).")
            .units( UnitSI().kg().m(-3) )
            .flags_add(in_time_term);

    *this+=solid_heat_capacity
            .name("solid_heat_capacity")
            .description("Heat capacity of solid (rock).")
            .units( UnitSI::J() * UnitSI().kg(-1).K(-1) )
            .flags_add(in_time_term);

    *this+=solid_heat_conductivity
            .name("solid_heat_conductivity")
            .description("Heat conductivity of solid (rock).")
            .units( UnitSI::W() * UnitSI().m(-1).K(-1) )
            .flags_add(in_main_matrix)
            .set_limits(0.0);

    *this+=disp_l
            .name("disp_l")
            .description("Longitudinal heat dispersivity in fluid.")
            .units( UnitSI().m() )
            .input_default("0.0")
            .flags_add(in_main_matrix);

    *this+=disp_t
            .name("disp_t")
            .description("Transverse heat dispersivity in fluid.")
            .units( UnitSI().m() )
            .input_default("0.0")
            .flags_add(in_main_matrix);

    *this+=fluid_thermal_source
            .name("fluid_thermal_source")
            .description("Density of thermal source in fluid.")
            .units( UnitSI::W() * UnitSI().m(-3) )
            .input_default("0.0")
            .flags_add(in_rhs);

    *this+=solid_thermal_source
            .name("solid_thermal_source")
            .description("Density of thermal source in solid.")
            .units( UnitSI::W() * UnitSI().m(-3) )
            .input_default("0.0")
            .flags_add(in_rhs);

    *this+=fluid_heat_exchange_rate
            .name("fluid_heat_exchange_rate")
            .description("Heat exchange rate of source in fluid.")
            .units( UnitSI().s(-1) )
            .input_default("0.0")
            .flags_add(in_rhs);

    *this+=solid_heat_exchange_rate
            .name("solid_heat_exchange_rate")
            .description("Heat exchange rate of source in solid.")
            .units( UnitSI().s(-1) )
            .input_default("0.0")
            .flags_add(in_rhs);

    *this+=fluid_ref_temperature
            .name("fluid_ref_temperature")
            .description("Reference temperature of source in fluid.")
            .units( UnitSI().K() )
            .input_default("0.0")
            .flags_add(in_rhs);

    *this+=solid_ref_temperature
            .name("solid_ref_temperature")
            .description("Reference temperature in solid.")
            .units( UnitSI().K() )
            .input_default("0.0")
            .flags_add(in_rhs);

    *this+=cross_section
            .name("cross_section")
            .units( UnitSI().m(3).md() )
            .flags(input_copy & in_time_term & in_main_matrix);

    *this+=output_field
            .name("temperature")
            .description("Temperature solution.")
            .units( UnitSI().K() )
            .flags(equation_result);
}



IT::Record HeatTransferModel::get_input_type(const string &implementation, const string &description)
{
    return IT::Record(
                std::string(ModelEqData::name()) + "_" + implementation,
                description + " for heat transfer.")
            .derive_from(AdvectionProcessBase::get_input_type())
            .copy_keys(EquationBase::record_template())
            .declare_key("balance", Balance::get_input_type(), Default("{}"),
                    "Settings for computing balance.")
            .declare_key("output_stream", OutputTime::get_input_type(), Default("{}"),
                    "Parameters of output stream.");
}


IT::Selection HeatTransferModel::ModelEqData::get_output_selection()
{
    // Return empty selection just to provide model specific selection name and description.
    // The fields are added by TransportDG using an auxiliary selection.
    return IT::Selection(
                std::string(ModelEqData::name()) + "_DG_output_fields",
                "Selection of output fields for Heat Transfer DG model.");
}


HeatTransferModel::HeatTransferModel(Mesh &mesh, const Input::Record in_rec) :
        AdvectionProcessBase(mesh, in_rec)
{
    time_ = new TimeGovernor(in_rec.val<Input::Record>("time"));
    ASSERT( time_->is_default() == false ).error("Missing key 'time' in Heat_AdvectionDiffusion_DG.");
    substances_.initialize({""});

    output_stream_ = OutputTime::create_output_stream("heat", in_rec.val<Input::Record>("output_stream"), time().get_unit_string());
    //output_stream_->add_admissible_field_names(in_rec.val<Input::Array>("output_fields"));

    balance_ = std::make_shared<Balance>("energy", mesh_);
    balance_->init_from_input(in_rec.val<Input::Record>("balance"), *time_);
    // initialization of balance object
    subst_idx = {balance_->add_quantity("energy")};
    balance_->units(UnitSI().m(2).kg().s(-2));
}


void HeatTransferModel::output_data()
{
    output_stream_->write_time_frame();
}


void HeatTransferModel::compute_mass_matrix_coefficient(const Armor::array &point_list,
        const ElementAccessor<3> &ele_acc,
        std::vector<double> &mm_coef)
{
    vector<double> elem_csec(point_list.size()),
            por(point_list.size()),
            f_rho(point_list.size()),
            s_rho(point_list.size()),
            f_c(point_list.size()),
            s_c(point_list.size());

    data().cross_section.value_list(point_list, ele_acc, elem_csec);
    data().porosity.value_list(point_list, ele_acc, por);
    data().fluid_density.value_list(point_list, ele_acc, f_rho);
    data().fluid_heat_capacity.value_list(point_list, ele_acc, f_c);
    data().solid_density.value_list(point_list, ele_acc, s_rho);
    data().solid_heat_capacity.value_list(point_list, ele_acc, s_c);

    for (unsigned int i=0; i<point_list.size(); i++)
        mm_coef[i] = elem_csec[i]*(por[i]*f_rho[i]*f_c[i] + (1.-por[i])*s_rho[i]*s_c[i]);
}


void HeatTransferModel::compute_advection_diffusion_coefficients(const Armor::array &point_list,
        const std::vector<arma::vec3> &velocity,
        const ElementAccessor<3> &ele_acc,
        std::vector<std::vector<arma::vec3> > &ad_coef,
        std::vector<std::vector<arma::mat33> > &dif_coef)
{
    const unsigned int qsize = point_list.size();
    std::vector<double> f_rho(qsize), f_cap(qsize), f_cond(qsize),
            s_cond(qsize), por(qsize), csection(qsize), disp_l(qsize), disp_t(qsize);

    data().fluid_density.value_list(point_list, ele_acc, f_rho);
    data().fluid_heat_capacity.value_list(point_list, ele_acc, f_cap);
    data().fluid_heat_conductivity.value_list(point_list, ele_acc, f_cond);
    data().solid_heat_conductivity.value_list(point_list, ele_acc, s_cond);
    data().disp_l.value_list(point_list, ele_acc, disp_l);
    data().disp_t.value_list(point_list, ele_acc, disp_t);
    data().porosity.value_list(point_list, ele_acc, por);
    data().cross_section.value_list(point_list, ele_acc, csection);

    for (unsigned int k=0; k<qsize; k++) {
        ad_coef[0][k] = velocity[k]*f_rho[k]*f_cap[k];

        // dispersive part of thermal diffusion
        // Note that the velocity vector is in fact the Darcian flux,
        // so to obtain |v| we have to divide vnorm by porosity and cross_section.
        double vnorm = arma::norm(velocity[k], 2);
        if (fabs(vnorm) > 0)
            for (int i=0; i<3; i++)
                for (int j=0; j<3; j++)
                    dif_coef[0][k](i,j) = ((velocity[k][i]/vnorm)*(velocity[k][j]/vnorm)*(disp_l[k]-disp_t[k]) + disp_t[k]*(i==j?1:0))
                                            *vnorm*f_rho[k]*f_cond[k];
        else
            dif_coef[0][k].zeros();

        // conductive part of thermal diffusion
        dif_coef[0][k] += csection[k]*(por[k]*f_cond[k] + (1.-por[k])*s_cond[k])*arma::eye(3,3);
    }
}


void HeatTransferModel::compute_init_cond(const Armor::array &point_list,
        const ElementAccessor<3> &ele_acc,
        std::vector<std::vector<double> > &init_values)
{
    data().init_temperature.value_list(point_list, ele_acc, init_values[0]);
}


void HeatTransferModel::get_bc_type(const ElementAccessor<3> &ele_acc,
            arma::uvec &bc_types)
{
    // Currently the bc types for HeatTransfer are numbered in the same way as in TransportDG.
    // In general we should use some map here.
    bc_types = { data().bc_type.value(ele_acc.centre(), ele_acc) };
}


void HeatTransferModel::get_flux_bc_data(unsigned int index,
        const Armor::array &point_list,
        const ElementAccessor<3> &ele_acc,
        std::vector< double > &bc_flux,
        std::vector< double > &bc_sigma,
        std::vector< double > &bc_ref_value)
{
    data().bc_flux.value_list(point_list, ele_acc, bc_flux);
    data().bc_robin_sigma.value_list(point_list, ele_acc, bc_sigma);
    data().bc_dirichlet_value[index].value_list(point_list, ele_acc, bc_ref_value);
    
    // Change sign in bc_flux since internally we work with outgoing fluxes.
    for (auto f : bc_flux) f = -f;
}

void HeatTransferModel::get_flux_bc_sigma(FMT_UNUSED unsigned int index,
        const Armor::array &point_list,
        const ElementAccessor<3> &ele_acc,
        std::vector< double > &bc_sigma)
{
    data().bc_robin_sigma.value_list(point_list, ele_acc, bc_sigma);
}


void HeatTransferModel::compute_source_coefficients(const Armor::array &point_list,
            const ElementAccessor<3> &ele_acc,
            std::vector<std::vector<double> > &sources_value,
            std::vector<std::vector<double> > &sources_density,
            std::vector<std::vector<double> > &sources_sigma)
{
    const unsigned int qsize = point_list.size();
    std::vector<double> por(qsize), csection(qsize), f_rho(qsize), s_rho(qsize), f_cap(qsize), s_cap(qsize),
            f_source(qsize), s_source(qsize), f_sigma(qsize), s_sigma(qsize), f_temp(qsize), s_temp(qsize);
    data().porosity.value_list(point_list, ele_acc, por);
    data().cross_section.value_list(point_list, ele_acc, csection);
    data().fluid_density.value_list(point_list, ele_acc, f_rho);
    data().solid_density.value_list(point_list, ele_acc, s_rho);
    data().fluid_heat_capacity.value_list(point_list, ele_acc, f_cap);
    data().solid_heat_capacity.value_list(point_list, ele_acc, s_cap);
    data().fluid_thermal_source.value_list(point_list, ele_acc, f_source);
    data().solid_thermal_source.value_list(point_list, ele_acc, s_source);
    data().fluid_heat_exchange_rate.value_list(point_list, ele_acc, f_sigma);
    data().solid_heat_exchange_rate.value_list(point_list, ele_acc, s_sigma);
    data().fluid_ref_temperature.value_list(point_list, ele_acc, f_temp);
    data().solid_ref_temperature.value_list(point_list, ele_acc, s_temp);

    sources_density[0].resize(point_list.size());
    sources_sigma[0].resize(point_list.size());
    sources_value[0].resize(point_list.size());
    for (unsigned int k=0; k<point_list.size(); k++)
    {
        sources_density[0][k] = csection[k]*(por[k]*f_source[k] + (1.-por[k])*s_source[k]);
        sources_sigma[0][k] = csection[k]*(por[k]*f_rho[k]*f_cap[k]*f_sigma[k] + (1.-por[k])*s_rho[k]*s_cap[k]*s_sigma[k]);
        if (fabs(sources_sigma[0][k]) > numeric_limits<double>::epsilon())
            sources_value[0][k] = csection[k]*(por[k]*f_rho[k]*f_cap[k]*f_sigma[k]*f_temp[k]
                           + (1.-por[k])*s_rho[k]*s_cap[k]*s_sigma[k]*s_temp[k])/sources_sigma[0][k];
        else
            sources_value[0][k] = 0;
    }
}


void HeatTransferModel::compute_sources_sigma(const Armor::array &point_list,
            const ElementAccessor<3> &ele_acc,
            std::vector<std::vector<double> > &sources_sigma)
{
    const unsigned int qsize = point_list.size();
    std::vector<double> por(qsize), csection(qsize), f_rho(qsize), s_rho(qsize), f_cap(qsize), s_cap(qsize),
            f_source(qsize), s_source(qsize), f_sigma(qsize), s_sigma(qsize), f_temp(qsize), s_temp(qsize);
    data().porosity.value_list(point_list, ele_acc, por);
    data().cross_section.value_list(point_list, ele_acc, csection);
    data().fluid_density.value_list(point_list, ele_acc, f_rho);
    data().solid_density.value_list(point_list, ele_acc, s_rho);
    data().fluid_heat_capacity.value_list(point_list, ele_acc, f_cap);
    data().solid_heat_capacity.value_list(point_list, ele_acc, s_cap);
    data().fluid_heat_exchange_rate.value_list(point_list, ele_acc, f_sigma);
    data().solid_heat_exchange_rate.value_list(point_list, ele_acc, s_sigma);
    sources_sigma[0].resize(point_list.size());
    for (unsigned int k=0; k<point_list.size(); k++)
    {
        sources_sigma[0][k] = csection[k]*(por[k]*f_rho[k]*f_cap[k]*f_sigma[k] + (1.-por[k])*s_rho[k]*s_cap[k]*s_sigma[k]);
    }
}


HeatTransferModel::~HeatTransferModel()
{}