TriSubChannel1PhaseProblem.C

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//* This file is part of the MOOSE framework
//* https://mooseframework.inl.gov
//*
//* All rights reserved, see COPYRIGHT for full restrictions
//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
//*
//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html

#include "TriSubChannel1PhaseProblem.h"
#include "AuxiliarySystem.h"
#include "TriSubChannelMesh.h"
#include "SubChannel1PhaseProblem.h"
#include "SinglePhaseFluidProperties.h"
#include "SCM.h"
#include <limits> // for std::numeric_limits
#include <cmath>  // for std::isnan
#include "SCMMixingClosureBase.h"

registerMooseObject("SubChannelApp", TriSubChannel1PhaseProblem);

InputParameters
TriSubChannel1PhaseProblem::validParams()
{
  InputParameters params = SubChannel1PhaseProblem::validParams();
  params.addClassDescription("Solver class for subchannels in a triangular lattice assembly and "
                             "bare/wire-wrapped fuel pins");
  return params;
}

TriSubChannel1PhaseProblem::TriSubChannel1PhaseProblem(const InputParameters & params)
  : SubChannel1PhaseProblem(params),
    _tri_sch_mesh(SCM::getMesh<TriSubChannelMesh>(_subchannel_mesh))
{
  // Initializing heat conduction system
  LibmeshPetscCall(createPetscMatrix(
      _hc_axial_heat_conduction_mat, _block_size * _n_channels, _block_size * _n_channels));
  LibmeshPetscCall(createPetscVector(_hc_axial_heat_conduction_rhs, _block_size * _n_channels));
  LibmeshPetscCall(createPetscMatrix(
      _hc_radial_heat_conduction_mat, _block_size * _n_channels, _block_size * _n_channels));
  LibmeshPetscCall(createPetscVector(_hc_radial_heat_conduction_rhs, _block_size * _n_channels));
  LibmeshPetscCall(createPetscMatrix(
      _hc_sweep_enthalpy_mat, _block_size * _n_channels, _block_size * _n_channels));
  LibmeshPetscCall(createPetscVector(_hc_sweep_enthalpy_rhs, _block_size * _n_channels));
}

TriSubChannel1PhaseProblem::~TriSubChannel1PhaseProblem()
{
  PetscErrorCode ierr = cleanUp();
  if (ierr)
    mooseError(name(), ": Error in memory cleanup");
}

PetscErrorCode
TriSubChannel1PhaseProblem::cleanUp()
{
  PetscFunctionBegin;
  // Clean up heat conduction system
  LibmeshPetscCall(MatDestroy(&_hc_axial_heat_conduction_mat));
  LibmeshPetscCall(VecDestroy(&_hc_axial_heat_conduction_rhs));
  LibmeshPetscCall(MatDestroy(&_hc_radial_heat_conduction_mat));
  LibmeshPetscCall(VecDestroy(&_hc_radial_heat_conduction_rhs));
  LibmeshPetscCall(MatDestroy(&_hc_sweep_enthalpy_mat));
  LibmeshPetscCall(VecDestroy(&_hc_sweep_enthalpy_rhs));
  PetscFunctionReturn(LIBMESH_PETSC_SUCCESS);
}

void
TriSubChannel1PhaseProblem::initializeSolution()
{
  detectDeformation();

  if (_deformation)
  {
    // update surface area, wetted perimeter based on: Dpin, displacement
    Real standard_area, wire_area, additional_area, wetted_perimeter, displaced_area;
    auto flat_to_flat = _tri_sch_mesh.getFlatToFlat();
    auto n_rings = _tri_sch_mesh.getNumOfRings();
    auto pitch = _subchannel_mesh.getPitch();
    auto pin_diameter = _subchannel_mesh.getPinDiameter();
    auto wire_diameter = _tri_sch_mesh.getWireDiameter();
    auto wire_lead_length = _tri_sch_mesh.getWireLeadLength();
    auto gap = _tri_sch_mesh.getDuctToPinGap();
    auto z_blockage = _subchannel_mesh.getZBlockage();
    auto index_blockage = _subchannel_mesh.getIndexBlockage();
    auto reduction_blockage = _subchannel_mesh.getReductionBlockage();
    auto theta =
        std::acos(wire_lead_length /
                  std::sqrt(Utility::pow<2>(wire_lead_length) +
                            Utility::pow<2>(libMesh::pi * (pin_diameter + wire_diameter))));
    for (unsigned int iz = 0; iz < _n_cells + 1; iz++)
    {
      for (unsigned int i_ch = 0; i_ch < _n_channels; i_ch++)
      {
        auto subch_type = _subchannel_mesh.getSubchannelType(i_ch);
        auto * node = _subchannel_mesh.getChannelNode(i_ch, iz);
        auto Z = _z_grid[iz];
        Real rod_area = 0.0;
        Real rod_perimeter = 0.0;
        for (auto i_pin : _subchannel_mesh.getChannelPins(i_ch))
        {
          auto * pin_node = _subchannel_mesh.getPinNode(i_pin, iz);
          if (subch_type == EChannelType::CENTER || subch_type == EChannelType::CORNER)
          {
            rod_area +=
                (1.0 / 6.0) * 0.25 * M_PI * (*_Dpin_soln)(pin_node) * (*_Dpin_soln)(pin_node);
            rod_perimeter += (1.0 / 6.0) * M_PI * (*_Dpin_soln)(pin_node);
          }
          else
          {
            rod_area +=
                (1.0 / 4.0) * 0.25 * M_PI * (*_Dpin_soln)(pin_node) * (*_Dpin_soln)(pin_node);
            rod_perimeter += (1.0 / 4.0) * M_PI * (*_Dpin_soln)(pin_node);
          }
        }

        if (subch_type == EChannelType::CENTER)
        {
          standard_area = Utility::pow<2>(pitch) * std::sqrt(3.0) / 4.0;
          additional_area = 0.0;
          displaced_area = 0.0;
          wire_area = libMesh::pi * Utility::pow<2>(wire_diameter) / 8.0 / std::cos(theta);
          wetted_perimeter = rod_perimeter + 0.5 * libMesh::pi * wire_diameter / std::cos(theta);
        }
        else if (subch_type == EChannelType::EDGE)
        {
          standard_area = pitch * (pin_diameter / 2.0 + gap);
          additional_area = 0.0;
          displaced_area = (*_displacement_soln)(node)*pitch;
          wire_area = libMesh::pi * Utility::pow<2>(wire_diameter) / 8.0 / std::cos(theta);
          wetted_perimeter =
              rod_perimeter + 0.5 * libMesh::pi * wire_diameter / std::cos(theta) + pitch;
        }
        else
        {
          standard_area = 1.0 / std::sqrt(3.0) * Utility::pow<2>(pin_diameter / 2.0 + gap);
          additional_area = 0.0;
          displaced_area = 1.0 / std::sqrt(3.0) *
                           (pin_diameter + 2.0 * gap + (*_displacement_soln)(node)) *
                           (*_displacement_soln)(node);
          wire_area = libMesh::pi / 24.0 * Utility::pow<2>(wire_diameter) / std::cos(theta);
          wetted_perimeter =
              rod_perimeter + libMesh::pi * wire_diameter / std::cos(theta) / 6.0 +
              2.0 / std::sqrt(3.0) * (pin_diameter / 2.0 + gap + (*_displacement_soln)(node));
        }

        // Calculate subchannel area
        auto subchannel_area =
            standard_area + additional_area + displaced_area - rod_area - wire_area;

        // Correct subchannel area and wetted perimeter in case of overlapping pins
        auto overlapping_pin_area = 0.0;
        auto overlapping_wetted_perimeter = 0.0;
        for (auto i_gap : _subchannel_mesh.getChannelGaps(i_ch))
        {
          auto gap_pins = _subchannel_mesh.getGapPins(i_gap);
          auto pin_1 = gap_pins.first;
          auto pin_2 = gap_pins.second;
          auto * pin_node_1 = _subchannel_mesh.getPinNode(pin_1, iz);
          auto * pin_node_2 = _subchannel_mesh.getPinNode(pin_2, iz);
          auto Diameter1 = (*_Dpin_soln)(pin_node_1);
          auto Radius1 = Diameter1 / 2.0;
          auto Diameter2 = (*_Dpin_soln)(pin_node_2);
          auto Radius2 = Diameter2 / 2.0;
          auto pitch = _subchannel_mesh.getPitch();

          if (pitch < (Radius1 + Radius2)) // overlapping pins
          {
            mooseWarning(" The gap of index : '", i_gap, " at axial cell ", iz, " ' is blocked.");
            auto cos1 =
                (pitch * pitch + Radius1 * Radius1 - Radius2 * Radius2) / (2 * pitch * Radius1);
            auto cos2 =
                (pitch * pitch + Radius2 * Radius2 - Radius1 * Radius1) / (2 * pitch * Radius2);
            auto angle1 = 2.0 * acos(cos1);
            auto angle2 = 2.0 * acos(cos2);
            // half of the intersecting arc-length
            overlapping_wetted_perimeter += 0.5 * angle1 * Radius1 + 0.5 * angle2 * Radius2;
            // Half of the overlapping area
            overlapping_pin_area +=
                0.5 * Radius1 * Radius1 * acos(cos1) + 0.5 * Radius2 * Radius2 * acos(cos2) -
                0.25 * sqrt((-pitch + Radius1 + Radius2) * (pitch + Radius1 - Radius2) *
                            (pitch - Radius1 + Radius2) * (pitch + Radius1 + Radius2));
          }
        }
        subchannel_area += overlapping_pin_area;           // correct surface area
        wetted_perimeter += -overlapping_wetted_perimeter; // correct wetted perimeter

        // Apply area reduction on subchannels affected by blockage
        auto index = 0;
        for (const auto & i_blockage : index_blockage)
        {
          if (i_ch == i_blockage && (Z >= z_blockage.front() && Z <= z_blockage.back()))
          {
            subchannel_area *= reduction_blockage[index];
          }
          index++;
        }
        _S_flow_soln->set(node, subchannel_area);
        _w_perim_soln->set(node, wetted_perimeter);
      }
    }
    // update map of gap between pins (gij) based on: Dpin, displacement
    for (unsigned int iz = 0; iz < _n_cells + 1; iz++)
    {
      for (unsigned int i_gap = 0; i_gap < _n_gaps; i_gap++)
      {
        auto gap_pins = _subchannel_mesh.getGapPins(i_gap);
        auto pin_1 = gap_pins.first;
        auto pin_2 = gap_pins.second;
        auto * pin_node_1 = _subchannel_mesh.getPinNode(pin_1, iz);
        auto * pin_node_2 = _subchannel_mesh.getPinNode(pin_2, iz);

        if (pin_1 == pin_2) // Corner or edge gap
        {
          auto displacement = 0.0;
          auto counter = 0.0;
          for (auto i_ch : _subchannel_mesh.getPinChannels(pin_1))
          {
            auto subch_type = _subchannel_mesh.getSubchannelType(i_ch);
            auto * node = _subchannel_mesh.getChannelNode(i_ch, iz);
            if (subch_type == EChannelType::EDGE || subch_type == EChannelType::CORNER)
            {
              displacement += (*_displacement_soln)(node);
              counter += 1.0;
            }
          }
          displacement = displacement / counter;
          _tri_sch_mesh.setGapWidth(iz,
                                    i_gap,
                                    0.5 * (flat_to_flat - (n_rings - 1) * pitch * std::sqrt(3.0) -
                                           (*_Dpin_soln)(pin_node_1)) +
                                        displacement);
        }
        else // center gap
        {
          _tri_sch_mesh.setGapWidth(
              iz, i_gap, pitch - (*_Dpin_soln)(pin_node_1) / 2.0 - (*_Dpin_soln)(pin_node_2) / 2.0);
        }
        // if pins come in contact, the gap is zero
        if (_tri_sch_mesh.getGapWidth(iz, i_gap) <= 0.0)
          _tri_sch_mesh.setGapWidth(iz, i_gap, 0.0);
      }
    }
  }

  for (unsigned int iz = 1; iz < _n_cells + 1; iz++)
  {
    for (unsigned int i_ch = 0; i_ch < _n_channels; i_ch++)
    {
      auto * node_out = _subchannel_mesh.getChannelNode(i_ch, iz);
      auto * node_in = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
      _mdot_soln->set(node_out, (*_mdot_soln)(node_in));
    }
  }

  // We must do a global assembly to make sure data is parallel consistent before we do things
  // like compute L2 norms
  _aux->solution().close();
}

Real
TriSubChannel1PhaseProblem::computeAddedHeatPin(unsigned int i_ch, unsigned int iz) const
{
  if (!_pin_mesh_exist)
    return 0.0;

  // Compute axial location of nodes.
  auto z2 = _z_grid[iz];
  auto z1 = _z_grid[iz - 1];
  auto heated_length = _subchannel_mesh.getHeatedLength();
  auto unheated_length_entry = _subchannel_mesh.getHeatedLengthEntry();
  if (MooseUtils::absoluteFuzzyGreaterThan(z2, unheated_length_entry) &&
      MooseUtils::absoluteFuzzyLessThan(z1, unheated_length_entry + heated_length))
  {
    // Compute the height of this element.
    auto dz = z2 - z1;
    Real factor;
    auto subch_type = _subchannel_mesh.getSubchannelType(i_ch);
    switch (subch_type)
    {
      case EChannelType::CENTER:
        factor = 1.0 / 6.0;
        break;
      case EChannelType::EDGE:
        factor = 1.0 / 4.0;
        break;
      case EChannelType::CORNER:
        factor = 1.0 / 6.0;
        break;
      default:
        return 0.0; // handle invalid subch_type if needed
    }
    double heat_rate_in = 0.0;
    double heat_rate_out = 0.0;
    for (auto i_pin : _subchannel_mesh.getChannelPins(i_ch))
    {
      auto * node_in = _subchannel_mesh.getPinNode(i_pin, iz - 1);
      auto * node_out = _subchannel_mesh.getPinNode(i_pin, iz);
      heat_rate_out += factor * (*_q_prime_soln)(node_out);
      heat_rate_in += factor * (*_q_prime_soln)(node_in);
    }
    return (heat_rate_in + heat_rate_out) * dz / 2.0;
  }
  else
    return 0.0;
}

Real
TriSubChannel1PhaseProblem::getSubChannelPeripheralDuctWidth(unsigned int i_ch) const
{
  auto subch_type = _subchannel_mesh.getSubchannelType(i_ch);
  if (subch_type == EChannelType::EDGE || subch_type == EChannelType::CORNER)
  {
    auto width = _subchannel_mesh.getPitch();
    if (subch_type == EChannelType::CORNER)
      width = 2.0 / std::sqrt(3.0) *
              (_subchannel_mesh.getPinDiameter() / 2.0 + _tri_sch_mesh.getDuctToPinGap());
    return width;
  }
  else
    mooseError("Channel is not a perimetric subchannel ");
}

void
TriSubChannel1PhaseProblem::computeh(int iblock)
{
  unsigned int last_node = (iblock + 1) * _block_size;
  unsigned int first_node = iblock * _block_size + 1;
  const Real & wire_lead_length = _tri_sch_mesh.getWireLeadLength();
  const Real & wire_diameter = _tri_sch_mesh.getWireDiameter();
  const Real & pitch = _subchannel_mesh.getPitch();
  const Real & pin_diameter = _subchannel_mesh.getPinDiameter();

  if (iblock == 0)
  {
    for (unsigned int i_ch = 0; i_ch < _n_channels; i_ch++)
    {
      auto * node = _subchannel_mesh.getChannelNode(i_ch, 0);
      auto h_out = _fp->h_from_p_T((*_P_soln)(node) + _P_out, (*_T_soln)(node));
      if (h_out < 0)
      {
        mooseError(
            name(), " : Calculation of negative Enthalpy h_out = : ", h_out, " Axial Level= : ", 0);
      }
      _h_soln->set(node, h_out);
    }
  }

  if (!_implicit_bool)
  {
    for (unsigned int iz = first_node; iz < last_node + 1; iz++)
    {
      auto z_grid = _subchannel_mesh.getZGrid();
      auto dz = z_grid[iz] - z_grid[iz - 1];
      // Calculation of average mass flux of all periphery subchannels
      Real edge_flux_ave = 0.0;
      Real mdot_sum = 0.0;
      Real si_sum = 0.0;
      for (unsigned int i_ch = 0; i_ch < _n_channels; i_ch++)
      {
        auto subch_type = _subchannel_mesh.getSubchannelType(i_ch);
        if (subch_type == EChannelType::EDGE || subch_type == EChannelType::CORNER)
        {
          auto * node_in = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
          auto Si = (*_S_flow_soln)(node_in);
          auto mdot_in = (*_mdot_soln)(node_in);
          mdot_sum = mdot_sum + mdot_in;
          si_sum = si_sum + Si;
        }
      }
      edge_flux_ave = mdot_sum / si_sum;

      for (unsigned int i_ch = 0; i_ch < _n_channels; i_ch++)
      {
        auto * node_in = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
        auto * node_out = _subchannel_mesh.getChannelNode(i_ch, iz);
        auto mdot_in = (*_mdot_soln)(node_in);
        auto h_in = (*_h_soln)(node_in); // J/kg
        auto volume = dz * (*_S_flow_soln)(node_in);
        auto mdot_out = (*_mdot_soln)(node_out);
        auto h_out = 0.0;
        Real sumWijh = 0.0;
        Real sumWijPrimeDhij = 0.0;
        Real sweep_enthalpy = 0.0;
        Real e_cond = 0.0;

        // Calculate added enthalpy from heatflux (Pin, Duct)
        Real added_enthalpy = computeAddedHeatPin(i_ch, iz);
        added_enthalpy += computeAddedHeatDuct(i_ch, iz);

        // Calculate net sum of enthalpy into/out-of channel i from channels j around i
        // (Turbulent diffusion, Diversion Crossflow, Sweep flow Enthalpy, Radial heat conduction)
        unsigned int counter = 0;
        for (auto i_gap : _subchannel_mesh.getChannelGaps(i_ch))
        {
          auto chans = _subchannel_mesh.getGapChannels(i_gap);
          auto gap = _subchannel_mesh.getGapWidth(iz, i_gap);
          auto Sij = dz * gap;
          unsigned int ii_ch = chans.first;  // the first subchannel next to gap i_gap
          unsigned int jj_ch = chans.second; // the second subchannel next to gap i_gap
          auto * node_in_i = _subchannel_mesh.getChannelNode(ii_ch, iz - 1);
          auto * node_in_j = _subchannel_mesh.getChannelNode(jj_ch, iz - 1);
          auto subch_type_i = _subchannel_mesh.getSubchannelType(ii_ch);
          auto subch_type_j = _subchannel_mesh.getSubchannelType(jj_ch);
          // Define donor enthalpy
          auto h_star = 0.0;
          if (_Wij(i_gap, iz) > 0.0)
            h_star = (*_h_soln)(node_in_i);
          else if (_Wij(i_gap, iz) < 0.0)
            h_star = (*_h_soln)(node_in_j);
          // Diversion crossflow
          // take care of the sign by applying the map, use donor cell
          sumWijh += _subchannel_mesh.getCrossflowSign(i_ch, counter) * _Wij(i_gap, iz) * h_star;
          counter++;
          // SWEEP FLOW is calculated if i_gap is located in the periphery
          // and we have a wire-wrap (if i_gap is in the periphery then i_ch is in the periphery)
          // There are two gaps per periphery subchannel that this is true.
          if ((subch_type_i == EChannelType::CORNER || subch_type_i == EChannelType::EDGE) &&
              (subch_type_j == EChannelType::CORNER || subch_type_j == EChannelType::EDGE) &&
              (wire_lead_length != 0) && (wire_diameter != 0))
          {
            // donor subchannel and node of sweep flow. The donor subchannel is the subchannel next
            // to i_ch that sweep flow, flows from and into i_ch
            auto sweep_donor = _tri_sch_mesh.getSweepFlowChans(i_ch).first;
            auto * node_sweep_donor = _subchannel_mesh.getChannelNode(sweep_donor, iz - 1);
            // if one of the neighbor subchannels of the periphery gap is the donor subchannel
            //(the other would be the i_ch) sweep enthalpy flows into i_ch
            if ((ii_ch == sweep_donor) || (jj_ch == sweep_donor))
            {
              sweep_enthalpy += computeSweepFlowMixingParameter(i_gap, iz) * edge_flux_ave * Sij *
                                (*_h_soln)(node_sweep_donor);
            }
            // else sweep enthalpy flows out of i_ch
            else
            {
              sweep_enthalpy -= computeSweepFlowMixingParameter(i_gap, iz) * edge_flux_ave * Sij *
                                (*_h_soln)(node_in);
            }
          }
          // Inner gap
          // Turbulent Diffusion
          else
          {
            sumWijPrimeDhij +=
                _WijPrime(i_gap, iz) * (2 * h_in - (*_h_soln)(node_in_j) - (*_h_soln)(node_in_i));
          }

          // compute the radial heat conduction through the gaps
          Real dist_ij = pitch;

          if (subch_type_i == EChannelType::EDGE && subch_type_j == EChannelType::EDGE)
          {
            dist_ij = pitch;
          }
          else if ((subch_type_i == EChannelType::CORNER && subch_type_j == EChannelType::EDGE) ||
                   (subch_type_i == EChannelType::EDGE && subch_type_j == EChannelType::CORNER))
          {
            dist_ij = pitch;
          }
          else
          {
            dist_ij = pitch / std::sqrt(3);
          }

          auto thcon_i = _fp->k_from_p_T((*_P_soln)(node_in_i) + _P_out, (*_T_soln)(node_in_i));
          auto thcon_j = _fp->k_from_p_T((*_P_soln)(node_in_j) + _P_out, (*_T_soln)(node_in_j));
          auto shape_factor =
              0.66 * (pitch / pin_diameter) *
              std::pow((_subchannel_mesh.getGapWidth(iz, i_gap) / pin_diameter), -0.3);
          if (ii_ch == i_ch)
          {
            e_cond += 0.5 * (thcon_i + thcon_j) * Sij * shape_factor *
                      ((*_T_soln)(node_in_j) - (*_T_soln)(node_in_i)) / dist_ij;
          }
          else
          {
            e_cond += -0.5 * (thcon_i + thcon_j) * Sij * shape_factor *
                      ((*_T_soln)(node_in_j) - (*_T_soln)(node_in_i)) / dist_ij;
          }
        }

        // compute the axial heat conduction between current and lower axial node
        auto * node_in_i = _subchannel_mesh.getChannelNode(i_ch, iz);
        auto * node_in_j = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
        auto thcon_i = _fp->k_from_p_T((*_P_soln)(node_in_i) + _P_out, (*_T_soln)(node_in_i));
        auto thcon_j = _fp->k_from_p_T((*_P_soln)(node_in_j) + _P_out, (*_T_soln)(node_in_j));
        auto Si = (*_S_flow_soln)(node_in_i);
        auto dist_ij = z_grid[iz] - z_grid[iz - 1];

        e_cond += 0.5 * (thcon_i + thcon_j) * Si * ((*_T_soln)(node_in_j) - (*_T_soln)(node_in_i)) /
                  dist_ij;

        unsigned int nz = _subchannel_mesh.getNumOfAxialCells();
        // compute the axial heat conduction between current and upper axial node
        if (iz < nz)
        {
          auto * node_in_i = _subchannel_mesh.getChannelNode(i_ch, iz);
          auto * node_in_j = _subchannel_mesh.getChannelNode(i_ch, iz + 1);
          auto thcon_i = _fp->k_from_p_T((*_P_soln)(node_in_i) + _P_out, (*_T_soln)(node_in_i));
          auto thcon_j = _fp->k_from_p_T((*_P_soln)(node_in_j) + _P_out, (*_T_soln)(node_in_j));
          auto Si = (*_S_flow_soln)(node_in_i);
          auto dist_ij = z_grid[iz + 1] - z_grid[iz];
          e_cond += 0.5 * (thcon_i + thcon_j) * Si *
                    ((*_T_soln)(node_in_j) - (*_T_soln)(node_in_i)) / dist_ij;
        }

        // end of radial heat conduction calc.
        h_out =
            (mdot_in * h_in - sumWijh - sumWijPrimeDhij + added_enthalpy + e_cond + sweep_enthalpy +
             _TR * _rho_soln->old(node_out) * _h_soln->old(node_out) * volume / _dt) /
            (mdot_out + _TR * (*_rho_soln)(node_out)*volume / _dt);
        if (h_out < 0)
        {
          mooseError(name(),
                     " : Calculation of negative Enthalpy h_out = : ",
                     h_out,
                     " Axial Level= : ",
                     iz);
        }
        _h_soln->set(node_out, h_out); // J/kg
      }
    }
  }
  else
  {
    LibmeshPetscCall(MatZeroEntries(_hc_time_derivative_mat));
    LibmeshPetscCall(MatZeroEntries(_hc_advective_derivative_mat));
    LibmeshPetscCall(MatZeroEntries(_hc_cross_derivative_mat));
    LibmeshPetscCall(MatZeroEntries(_hc_axial_heat_conduction_mat));
    LibmeshPetscCall(MatZeroEntries(_hc_radial_heat_conduction_mat));
    LibmeshPetscCall(MatZeroEntries(_hc_sweep_enthalpy_mat));

    LibmeshPetscCall(VecZeroEntries(_hc_time_derivative_rhs));
    LibmeshPetscCall(VecZeroEntries(_hc_advective_derivative_rhs));
    LibmeshPetscCall(VecZeroEntries(_hc_cross_derivative_rhs));
    LibmeshPetscCall(VecZeroEntries(_hc_added_heat_rhs));
    LibmeshPetscCall(VecZeroEntries(_hc_axial_heat_conduction_rhs));
    LibmeshPetscCall(VecZeroEntries(_hc_radial_heat_conduction_rhs));
    LibmeshPetscCall(VecZeroEntries(_hc_sweep_enthalpy_rhs));

    LibmeshPetscCall(MatZeroEntries(_hc_sys_h_mat));
    LibmeshPetscCall(VecZeroEntries(_hc_sys_h_rhs));

    for (unsigned int iz = first_node; iz < last_node + 1; iz++)
    {
      auto dz = _z_grid[iz] - _z_grid[iz - 1];
      auto pitch = _subchannel_mesh.getPitch();
      auto pin_diameter = _subchannel_mesh.getPinDiameter();
      auto iz_ind = iz - first_node;

      for (unsigned int i_ch = 0; i_ch < _n_channels; i_ch++)
      {
        auto * node_in = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
        auto * node_out = _subchannel_mesh.getChannelNode(i_ch, iz);
        auto S_in = (*_S_flow_soln)(node_in);
        auto S_out = (*_S_flow_soln)(node_out);
        auto S_interp = computeInterpolatedValue(S_out, S_in, 0.5);
        auto volume = dz * S_interp;

        PetscScalar Pe = 0.5;
        if (_interpolation_scheme == 3)
        {
          // Compute the Peclet number
          auto w_perim_in = (*_w_perim_soln)(node_in);
          auto w_perim_out = (*_w_perim_soln)(node_out);
          auto w_perim_interp = this->computeInterpolatedValue(w_perim_out, w_perim_in, 0.5);
          auto K_in = _fp->k_from_p_T((*_P_soln)(node_in) + _P_out, (*_T_soln)(node_in));
          auto K_out = _fp->k_from_p_T((*_P_soln)(node_out) + _P_out, (*_T_soln)(node_out));
          auto K = this->computeInterpolatedValue(K_out, K_in, 0.5);
          auto cp_in = _fp->cp_from_p_T((*_P_soln)(node_in) + _P_out, (*_T_soln)(node_in));
          auto cp_out = _fp->cp_from_p_T((*_P_soln)(node_out) + _P_out, (*_T_soln)(node_out));
          auto cp = this->computeInterpolatedValue(cp_out, cp_in, 0.5);
          auto mdot_loc =
              this->computeInterpolatedValue((*_mdot_soln)(node_out), (*_mdot_soln)(node_in), 0.5);
          // hydraulic diameter in the i direction
          auto Dh_i = 4.0 * S_interp / w_perim_interp;
          Pe = mdot_loc * Dh_i * cp / (K * S_interp) * (mdot_loc / std::abs(mdot_loc));
        }
        auto alpha = computeInterpolationCoefficients(Pe);

        // Time derivative term
        if (iz == first_node)
        {
          PetscScalar value_vec_tt =
              -1.0 * _TR * alpha * (*_rho_soln)(node_in) * (*_h_soln)(node_in)*volume / _dt;
          PetscInt row_vec_tt = i_ch + _n_channels * iz_ind;
          LibmeshPetscCall(
              VecSetValues(_hc_time_derivative_rhs, 1, &row_vec_tt, &value_vec_tt, ADD_VALUES));
        }
        else
        {
          PetscInt row_tt = i_ch + _n_channels * iz_ind;
          PetscInt col_tt = i_ch + _n_channels * (iz_ind - 1);
          PetscScalar value_tt = _TR * alpha * (*_rho_soln)(node_in)*volume / _dt;
          LibmeshPetscCall(MatSetValues(
              _hc_time_derivative_mat, 1, &row_tt, 1, &col_tt, &value_tt, INSERT_VALUES));
        }

        // Adding diagonal elements
        PetscInt row_tt = i_ch + _n_channels * iz_ind;
        PetscInt col_tt = i_ch + _n_channels * iz_ind;
        PetscScalar value_tt = _TR * (1.0 - alpha) * (*_rho_soln)(node_out)*volume / _dt;
        LibmeshPetscCall(MatSetValues(
            _hc_time_derivative_mat, 1, &row_tt, 1, &col_tt, &value_tt, INSERT_VALUES));

        // Adding RHS elements
        PetscScalar rho_old_interp =
            computeInterpolatedValue(_rho_soln->old(node_out), _rho_soln->old(node_in), Pe);
        PetscScalar h_old_interp =
            computeInterpolatedValue(_h_soln->old(node_out), _h_soln->old(node_in), Pe);
        PetscScalar value_vec_tt = _TR * rho_old_interp * h_old_interp * volume / _dt;
        PetscInt row_vec_tt = i_ch + _n_channels * iz_ind;
        LibmeshPetscCall(
            VecSetValues(_hc_time_derivative_rhs, 1, &row_vec_tt, &value_vec_tt, ADD_VALUES));

        // Advective derivative term
        if (iz == first_node)
        {
          PetscInt row_at = i_ch + _n_channels * iz_ind;
          PetscScalar value_at = alpha * (*_mdot_soln)(node_in) * (*_h_soln)(node_in);
          LibmeshPetscCall(
              VecSetValues(_hc_advective_derivative_rhs, 1, &row_at, &value_at, ADD_VALUES));

          value_at = alpha * (*_mdot_soln)(node_out) - (1 - alpha) * (*_mdot_soln)(node_in);
          PetscInt col_at = i_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_advective_derivative_mat, 1, &row_at, 1, &col_at, &value_at, ADD_VALUES));

          value_at = (1 - alpha) * (*_mdot_soln)(node_out);
          col_at = i_ch + _n_channels * (iz_ind + 1);
          LibmeshPetscCall(MatSetValues(
              _hc_advective_derivative_mat, 1, &row_at, 1, &col_at, &value_at, ADD_VALUES));
        }
        else if (iz == last_node)
        {
          PetscInt row_at = i_ch + _n_channels * iz_ind;
          PetscScalar value_at = 1.0 * (*_mdot_soln)(node_out);
          PetscInt col_at = i_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_advective_derivative_mat, 1, &row_at, 1, &col_at, &value_at, ADD_VALUES));

          value_at = -1.0 * (*_mdot_soln)(node_in);
          col_at = i_ch + _n_channels * (iz_ind - 1);
          LibmeshPetscCall(MatSetValues(
              _hc_advective_derivative_mat, 1, &row_at, 1, &col_at, &value_at, ADD_VALUES));
        }
        else
        {
          PetscInt row_at = i_ch + _n_channels * iz_ind;
          PetscInt col_at;

          PetscScalar value_at = -alpha * (*_mdot_soln)(node_in);
          col_at = i_ch + _n_channels * (iz_ind - 1);
          LibmeshPetscCall(MatSetValues(
              _hc_advective_derivative_mat, 1, &row_at, 1, &col_at, &value_at, ADD_VALUES));

          value_at = alpha * (*_mdot_soln)(node_out) - (1 - alpha) * (*_mdot_soln)(node_in);
          col_at = i_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_advective_derivative_mat, 1, &row_at, 1, &col_at, &value_at, ADD_VALUES));

          value_at = (1 - alpha) * (*_mdot_soln)(node_out);
          col_at = i_ch + _n_channels * (iz_ind + 1);
          LibmeshPetscCall(MatSetValues(
              _hc_advective_derivative_mat, 1, &row_at, 1, &col_at, &value_at, ADD_VALUES));
        }

        // Axial heat conduction
        auto * node_center = _subchannel_mesh.getChannelNode(i_ch, iz);
        auto K_center = _fp->k_from_p_T((*_P_soln)(node_center) + _P_out, (*_T_soln)(node_center));
        auto cp_center =
            _fp->cp_from_p_T((*_P_soln)(node_center) + _P_out, (*_T_soln)(node_center));
        auto diff_center = K_center / (cp_center + 1e-15);

        if (iz == first_node)
        {
          auto * node_top = _subchannel_mesh.getChannelNode(i_ch, iz + 1);
          auto * node_bottom = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
          auto K_bottom =
              _fp->k_from_p_T((*_P_soln)(node_bottom) + _P_out, (*_T_soln)(node_bottom));
          auto K_top = _fp->k_from_p_T((*_P_soln)(node_top) + _P_out, (*_T_soln)(node_top));
          auto cp_bottom =
              _fp->cp_from_p_T((*_P_soln)(node_bottom) + _P_out, (*_T_soln)(node_bottom));
          auto cp_top = _fp->cp_from_p_T((*_P_soln)(node_top) + _P_out, (*_T_soln)(node_top));
          auto diff_bottom = K_bottom / (cp_bottom + 1e-15);
          auto diff_top = K_top / (cp_top + 1e-15);

          auto dz_up = _z_grid[iz + 1] - _z_grid[iz];
          auto dz_down = _z_grid[iz] - _z_grid[iz - 1];
          auto S_up =
              computeInterpolatedValue((*_S_flow_soln)(node_top), (*_S_flow_soln)(node_center));
          auto S_down =
              computeInterpolatedValue((*_S_flow_soln)(node_center), (*_S_flow_soln)(node_bottom));
          auto diff_up = computeInterpolatedValue(diff_top, diff_center);
          auto diff_down = computeInterpolatedValue(diff_center, diff_bottom);

          // Diagonal  value
          PetscInt row_at = i_ch + _n_channels * iz_ind;
          PetscInt col_at = i_ch + _n_channels * iz_ind;
          PetscScalar value_at = diff_up * S_up / dz_up + diff_down * S_down / dz_down;
          LibmeshPetscCall(MatSetValues(
              _hc_axial_heat_conduction_mat, 1, &row_at, 1, &col_at, &value_at, INSERT_VALUES));

          // Bottom value
          value_at = 1.0 * diff_down * S_down / dz_down * (*_h_soln)(node_bottom);
          LibmeshPetscCall(
              VecSetValues(_hc_axial_heat_conduction_rhs, 1, &row_at, &value_at, ADD_VALUES));

          // Top value
          col_at = i_ch + _n_channels * (iz_ind + 1);
          value_at = -diff_up * S_up / dz_up;
          LibmeshPetscCall(MatSetValues(
              _hc_axial_heat_conduction_mat, 1, &row_at, 1, &col_at, &value_at, INSERT_VALUES));
        }
        else if (iz == last_node)
        {
          auto * node_bottom = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
          auto K_bottom =
              _fp->k_from_p_T((*_P_soln)(node_bottom) + _P_out, (*_T_soln)(node_bottom));
          auto cp_bottom =
              _fp->cp_from_p_T((*_P_soln)(node_bottom) + _P_out, (*_T_soln)(node_bottom));
          auto diff_bottom = K_bottom / (cp_bottom + 1e-15);

          auto dz_down = _z_grid[iz] - _z_grid[iz - 1];
          auto S_down = 0.5 * ((*_S_flow_soln)(node_center) + (*_S_flow_soln)(node_bottom));
          auto diff_down = 0.5 * (diff_center + diff_bottom);

          // Diagonal  value
          PetscInt row_at = i_ch + _n_channels * iz_ind;
          PetscInt col_at = i_ch + _n_channels * iz_ind;
          PetscScalar value_at = diff_down * S_down / dz_down;
          LibmeshPetscCall(MatSetValues(
              _hc_axial_heat_conduction_mat, 1, &row_at, 1, &col_at, &value_at, INSERT_VALUES));

          // Bottom value
          col_at = i_ch + _n_channels * (iz_ind - 1);
          value_at = -diff_down * S_down / dz_down;
          LibmeshPetscCall(MatSetValues(
              _hc_axial_heat_conduction_mat, 1, &row_at, 1, &col_at, &value_at, INSERT_VALUES));

          // Outflow derivative
          // value_at = -1.0 * (*_mdot_soln)(node_center) * (*_h_soln)(node_center);
          // VecSetValues(_hc_axial_heat_conduction_rhs, 1, &row_at, &value_at, ADD_VALUES);
        }
        else
        {
          auto * node_top = _subchannel_mesh.getChannelNode(i_ch, iz + 1);
          auto * node_bottom = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
          auto K_bottom =
              _fp->k_from_p_T((*_P_soln)(node_bottom) + _P_out, (*_T_soln)(node_bottom));
          auto K_top = _fp->k_from_p_T((*_P_soln)(node_top) + _P_out, (*_T_soln)(node_top));
          auto cp_bottom =
              _fp->cp_from_p_T((*_P_soln)(node_bottom) + _P_out, (*_T_soln)(node_bottom));
          auto cp_top = _fp->cp_from_p_T((*_P_soln)(node_top) + _P_out, (*_T_soln)(node_top));
          auto diff_bottom = K_bottom / (cp_bottom + 1e-15);
          auto diff_top = K_top / (cp_top + 1e-15);

          auto dz_up = _z_grid[iz + 1] - _z_grid[iz];
          auto dz_down = _z_grid[iz] - _z_grid[iz - 1];
          auto S_up =
              computeInterpolatedValue((*_S_flow_soln)(node_top), (*_S_flow_soln)(node_center));
          auto S_down =
              computeInterpolatedValue((*_S_flow_soln)(node_center), (*_S_flow_soln)(node_bottom));
          auto diff_up = computeInterpolatedValue(diff_top, diff_center);
          auto diff_down = computeInterpolatedValue(diff_center, diff_bottom);

          // Diagonal value
          PetscInt row_at = i_ch + _n_channels * iz_ind;
          PetscInt col_at = i_ch + _n_channels * iz_ind;
          PetscScalar value_at = diff_up * S_up / dz_up + diff_down * S_down / dz_down;
          LibmeshPetscCall(MatSetValues(
              _hc_axial_heat_conduction_mat, 1, &row_at, 1, &col_at, &value_at, INSERT_VALUES));

          // Bottom value
          col_at = i_ch + _n_channels * (iz_ind - 1);
          value_at = -diff_down * S_down / dz_down;
          LibmeshPetscCall(MatSetValues(
              _hc_axial_heat_conduction_mat, 1, &row_at, 1, &col_at, &value_at, INSERT_VALUES));

          // Top value
          col_at = i_ch + _n_channels * (iz_ind + 1);
          value_at = -diff_up * S_up / dz_up;
          LibmeshPetscCall(MatSetValues(
              _hc_axial_heat_conduction_mat, 1, &row_at, 1, &col_at, &value_at, INSERT_VALUES));
        }

        // Radial Terms
        unsigned int counter = 0;
        unsigned int cross_index = iz;
        // Real radial_heat_conduction(0.0);
        for (auto i_gap : _subchannel_mesh.getChannelGaps(i_ch))
        {
          auto chans = _subchannel_mesh.getGapChannels(i_gap);
          unsigned int ii_ch = chans.first;
          unsigned int jj_ch = chans.second;
          auto * node_in_i = _subchannel_mesh.getChannelNode(ii_ch, iz - 1);
          auto * node_in_j = _subchannel_mesh.getChannelNode(jj_ch, iz - 1);
          PetscScalar h_star;
          // figure out donor axial velocity
          if (_Wij(i_gap, cross_index) > 0.0)
          {
            if (iz == first_node)
            {
              h_star = (*_h_soln)(node_in_i);
              PetscScalar value_vec_ct = -1.0 * alpha *
                                         _subchannel_mesh.getCrossflowSign(i_ch, counter) *
                                         _Wij(i_gap, cross_index) * h_star;
              PetscInt row_vec_ct = i_ch + _n_channels * iz_ind;
              LibmeshPetscCall(VecSetValues(
                  _hc_cross_derivative_rhs, 1, &row_vec_ct, &value_vec_ct, ADD_VALUES));
            }
            else
            {
              PetscScalar value_ct = alpha * _subchannel_mesh.getCrossflowSign(i_ch, counter) *
                                     _Wij(i_gap, cross_index);
              PetscInt row_ct = i_ch + _n_channels * iz_ind;
              PetscInt col_ct = ii_ch + _n_channels * (iz_ind - 1);
              LibmeshPetscCall(MatSetValues(
                  _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_ct, ADD_VALUES));
            }
            PetscScalar value_ct = (1.0 - alpha) *
                                   _subchannel_mesh.getCrossflowSign(i_ch, counter) *
                                   _Wij(i_gap, cross_index);
            PetscInt row_ct = i_ch + _n_channels * iz_ind;
            PetscInt col_ct = ii_ch + _n_channels * iz_ind;
            LibmeshPetscCall(MatSetValues(
                _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_ct, ADD_VALUES));
          }
          else if (_Wij(i_gap, cross_index) < 0.0) // _Wij=0 operations not necessary
          {
            if (iz == first_node)
            {
              h_star = (*_h_soln)(node_in_j);
              PetscScalar value_vec_ct = -1.0 * alpha *
                                         _subchannel_mesh.getCrossflowSign(i_ch, counter) *
                                         _Wij(i_gap, cross_index) * h_star;
              PetscInt row_vec_ct = i_ch + _n_channels * iz_ind;
              LibmeshPetscCall(VecSetValues(
                  _hc_cross_derivative_rhs, 1, &row_vec_ct, &value_vec_ct, ADD_VALUES));
            }
            else
            {
              PetscScalar value_ct = alpha * _subchannel_mesh.getCrossflowSign(i_ch, counter) *
                                     _Wij(i_gap, cross_index);
              PetscInt row_ct = i_ch + _n_channels * iz_ind;
              PetscInt col_ct = jj_ch + _n_channels * (iz_ind - 1);
              LibmeshPetscCall(MatSetValues(
                  _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_ct, ADD_VALUES));
            }
            PetscScalar value_ct = (1.0 - alpha) *
                                   _subchannel_mesh.getCrossflowSign(i_ch, counter) *
                                   _Wij(i_gap, cross_index);
            PetscInt row_ct = i_ch + _n_channels * iz_ind;
            PetscInt col_ct = jj_ch + _n_channels * iz_ind;
            LibmeshPetscCall(MatSetValues(
                _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_ct, ADD_VALUES));
          }

          // Turbulent cross flows
          if (iz == first_node)
          {
            PetscScalar value_vec_ct =
                -2.0 * alpha * (*_h_soln)(node_in)*_WijPrime(i_gap, cross_index);
            value_vec_ct += alpha * (*_h_soln)(node_in_j)*_WijPrime(i_gap, cross_index);
            value_vec_ct += alpha * (*_h_soln)(node_in_i)*_WijPrime(i_gap, cross_index);
            PetscInt row_vec_ct = i_ch + _n_channels * iz_ind;
            LibmeshPetscCall(
                VecSetValues(_hc_cross_derivative_rhs, 1, &row_vec_ct, &value_vec_ct, ADD_VALUES));
          }
          else
          {
            PetscScalar value_center_ct = 2.0 * alpha * _WijPrime(i_gap, cross_index);
            PetscInt row_ct = i_ch + _n_channels * iz_ind;
            PetscInt col_ct = i_ch + _n_channels * (iz_ind - 1);
            LibmeshPetscCall(MatSetValues(
                _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_center_ct, ADD_VALUES));

            PetscScalar value_left_ct = -1.0 * alpha * _WijPrime(i_gap, cross_index);
            row_ct = i_ch + _n_channels * iz_ind;
            col_ct = jj_ch + _n_channels * (iz_ind - 1);
            LibmeshPetscCall(MatSetValues(
                _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_left_ct, ADD_VALUES));

            PetscScalar value_right_ct = -1.0 * alpha * _WijPrime(i_gap, cross_index);
            row_ct = i_ch + _n_channels * iz_ind;
            col_ct = ii_ch + _n_channels * (iz_ind - 1);
            LibmeshPetscCall(MatSetValues(
                _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_right_ct, ADD_VALUES));
          }
          PetscScalar value_center_ct = 2.0 * (1.0 - alpha) * _WijPrime(i_gap, cross_index);
          PetscInt row_ct = i_ch + _n_channels * iz_ind;
          PetscInt col_ct = i_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_center_ct, ADD_VALUES));

          PetscScalar value_left_ct = -1.0 * (1.0 - alpha) * _WijPrime(i_gap, cross_index);
          row_ct = i_ch + _n_channels * iz_ind;
          col_ct = jj_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_left_ct, ADD_VALUES));

          PetscScalar value_right_ct = -1.0 * (1.0 - alpha) * _WijPrime(i_gap, cross_index);
          row_ct = i_ch + _n_channels * iz_ind;
          col_ct = ii_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_cross_derivative_mat, 1, &row_ct, 1, &col_ct, &value_right_ct, ADD_VALUES));

          // Radial heat conduction
          auto subch_type_i = _subchannel_mesh.getSubchannelType(ii_ch);
          auto subch_type_j = _subchannel_mesh.getSubchannelType(jj_ch);
          Real dist_ij = pitch;

          if (subch_type_i == EChannelType::EDGE && subch_type_j == EChannelType::EDGE)
          {
            dist_ij = pitch;
          }
          else if ((subch_type_i == EChannelType::CORNER && subch_type_j == EChannelType::EDGE) ||
                   (subch_type_i == EChannelType::EDGE && subch_type_j == EChannelType::CORNER))
          {
            dist_ij = pitch;
          }
          else
          {
            dist_ij = pitch / std::sqrt(3);
          }

          auto Sij = dz * _subchannel_mesh.getGapWidth(iz, i_gap);
          auto K_i = _fp->k_from_p_T((*_P_soln)(node_in_i) + _P_out, (*_T_soln)(node_in_i));
          auto K_j = _fp->k_from_p_T((*_P_soln)(node_in_j) + _P_out, (*_T_soln)(node_in_j));
          auto cp_i = _fp->cp_from_p_T((*_P_soln)(node_in_i) + _P_out, (*_T_soln)(node_in_i));
          auto cp_j = _fp->cp_from_p_T((*_P_soln)(node_in_j) + _P_out, (*_T_soln)(node_in_j));
          auto A_i = K_i / cp_i;
          auto A_j = K_j / cp_j;
          auto harm_A = 2.0 * A_i * A_j / (A_i + A_j);
          auto shape_factor =
              0.66 * (pitch / pin_diameter) *
              std::pow((_subchannel_mesh.getGapWidth(iz, i_gap) / pin_diameter), -0.3);
          // auto base_value =  0.5 * (A_i + A_j) * Sij * shape_factor / dist_ij;
          auto base_value = harm_A * shape_factor * Sij / dist_ij;
          auto neg_base_value = -1.0 * base_value;

          row_ct = ii_ch + _n_channels * iz_ind;
          col_ct = ii_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_radial_heat_conduction_mat, 1, &row_ct, 1, &col_ct, &base_value, ADD_VALUES));

          row_ct = jj_ch + _n_channels * iz_ind;
          col_ct = jj_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_radial_heat_conduction_mat, 1, &row_ct, 1, &col_ct, &base_value, ADD_VALUES));

          row_ct = ii_ch + _n_channels * iz_ind;
          col_ct = jj_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_radial_heat_conduction_mat, 1, &row_ct, 1, &col_ct, &neg_base_value, ADD_VALUES));

          row_ct = jj_ch + _n_channels * iz_ind;
          col_ct = ii_ch + _n_channels * iz_ind;
          LibmeshPetscCall(MatSetValues(
              _hc_radial_heat_conduction_mat, 1, &row_ct, 1, &col_ct, &neg_base_value, ADD_VALUES));
          counter++;
        }

        // Compute the sweep flow enthalpy change
        // Calculation of average mass flux of all periphery subchannels
        Real edge_flux_ave = 0.0;
        Real mdot_sum = 0.0;
        Real si_sum = 0.0;
        for (unsigned int i_ch = 0; i_ch < _n_channels; i_ch++)
        {
          auto subch_type = _subchannel_mesh.getSubchannelType(i_ch);
          if (subch_type == EChannelType::EDGE || subch_type == EChannelType::CORNER)
          {
            auto * node_in = _subchannel_mesh.getChannelNode(i_ch, iz - 1);
            auto Si = (*_S_flow_soln)(node_in);
            auto mdot_in = (*_mdot_soln)(node_in);
            mdot_sum = mdot_sum + mdot_in;
            si_sum = si_sum + Si;
          }
        }
        edge_flux_ave = mdot_sum / si_sum;
        auto subch_type = _subchannel_mesh.getSubchannelType(i_ch);
        PetscScalar sweep_enthalpy = 0.0;
        if ((subch_type == EChannelType::EDGE || subch_type == EChannelType::CORNER) &&
            (wire_diameter != 0.0) && (wire_lead_length != 0.0))
        {
          auto beta_in = std::numeric_limits<double>::quiet_NaN();
          auto beta_out = std::numeric_limits<double>::quiet_NaN();
          // donor sweep channel for i_ch
          auto sweep_donor = _tri_sch_mesh.getSweepFlowChans(i_ch).first;
          auto * node_sweep_donor = _subchannel_mesh.getChannelNode(sweep_donor, iz - 1);
          // Calculation of turbulent mixing parameter
          for (auto i_gap : _subchannel_mesh.getChannelGaps(i_ch))
          {
            auto chans = _subchannel_mesh.getGapChannels(i_gap);
            unsigned int ii_ch = chans.first;
            unsigned int jj_ch = chans.second;
            auto subch_type_i = _subchannel_mesh.getSubchannelType(ii_ch);
            auto subch_type_j = _subchannel_mesh.getSubchannelType(jj_ch);
            if ((subch_type_i == EChannelType::CORNER || subch_type_i == EChannelType::EDGE) &&
                (subch_type_j == EChannelType::CORNER || subch_type_j == EChannelType::EDGE))
            {
              if ((ii_ch == sweep_donor) || (jj_ch == sweep_donor))
              {
                beta_in = computeSweepFlowMixingParameter(i_gap, iz);
              }
              else
              {
                beta_out = computeSweepFlowMixingParameter(i_gap, iz);
              }
            }
          }
          // Abort execution if required values are unset
          mooseAssert(!std::isnan(beta_in),
                      "beta_in was not set. Check gap logic for i_ch = " + std::to_string(i_ch) +
                          ", iz = " + std::to_string(iz));
          mooseAssert(!std::isnan(beta_out),
                      "beta_out was not set. Check gap logic for i_ch = " + std::to_string(i_ch) +
                          ", iz = " + std::to_string(iz));

          auto gap = _tri_sch_mesh.getDuctToPinGap();
          auto Sij = dz * gap;
          auto wsweep_in = edge_flux_ave * beta_in * Sij;
          auto wsweep_out = edge_flux_ave * beta_out * Sij;
          auto sweep_hin = (*_h_soln)(node_sweep_donor);
          auto sweep_hout = (*_h_soln)(node_in);
          sweep_enthalpy = (wsweep_in * sweep_hin - wsweep_out * sweep_hout);

          if (iz == first_node)
          {
            PetscInt row_sh = i_ch + _n_channels * iz_ind;
            PetscScalar value_hs = -sweep_enthalpy;
            LibmeshPetscCall(
                VecSetValues(_hc_sweep_enthalpy_rhs, 1, &row_sh, &value_hs, ADD_VALUES));
          }
          else
          {
            // coefficient of sweep_hin
            PetscInt row_sh = i_ch + _n_channels * (iz_ind - 1);
            PetscInt col_sh = i_ch + _n_channels * (iz_ind - 1);
            LibmeshPetscCall(MatSetValues(
                _hc_sweep_enthalpy_mat, 1, &row_sh, 1, &col_sh, &wsweep_out, ADD_VALUES));
            PetscInt col_sh_l = sweep_donor + _n_channels * (iz_ind - 1);
            PetscScalar neg_sweep_in = -1.0 * wsweep_in;
            // coefficient of sweep_hout
            LibmeshPetscCall(MatSetValues(
                _hc_sweep_enthalpy_mat, 1, &row_sh, 1, &col_sh_l, &(neg_sweep_in), ADD_VALUES));
          }
        }

        // Add heat enthalpy from pin and/or duct
        PetscScalar added_enthalpy = computeAddedHeatPin(i_ch, iz);
        added_enthalpy += computeAddedHeatDuct(i_ch, iz);
        PetscInt row_vec_ht = i_ch + _n_channels * iz_ind;
        LibmeshPetscCall(
            VecSetValues(_hc_added_heat_rhs, 1, &row_vec_ht, &added_enthalpy, ADD_VALUES));
      }
    }
    // Assembling system
    LibmeshPetscCall(MatAssemblyBegin(_hc_time_derivative_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_time_derivative_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyBegin(_hc_advective_derivative_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_advective_derivative_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyBegin(_hc_cross_derivative_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_cross_derivative_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyBegin(_hc_axial_heat_conduction_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_axial_heat_conduction_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyBegin(_hc_radial_heat_conduction_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_radial_heat_conduction_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyBegin(_hc_sweep_enthalpy_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_sweep_enthalpy_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyBegin(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    // Add all matrices together
    LibmeshPetscCall(
        MatAXPY(_hc_sys_h_mat, 1.0, _hc_time_derivative_mat, DIFFERENT_NONZERO_PATTERN));
    LibmeshPetscCall(MatAssemblyBegin(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(
        MatAXPY(_hc_sys_h_mat, 1.0, _hc_advective_derivative_mat, DIFFERENT_NONZERO_PATTERN));
    LibmeshPetscCall(MatAssemblyBegin(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(
        MatAXPY(_hc_sys_h_mat, 1.0, _hc_cross_derivative_mat, DIFFERENT_NONZERO_PATTERN));
    LibmeshPetscCall(MatAssemblyBegin(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(
        MatAXPY(_hc_sys_h_mat, 1.0, _hc_axial_heat_conduction_mat, DIFFERENT_NONZERO_PATTERN));
    LibmeshPetscCall(MatAssemblyBegin(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(
        MatAXPY(_hc_sys_h_mat, 1.0, _hc_radial_heat_conduction_mat, DIFFERENT_NONZERO_PATTERN));
    LibmeshPetscCall(MatAssemblyBegin(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(
        MatAXPY(_hc_sys_h_mat, 1.0, _hc_sweep_enthalpy_mat, DIFFERENT_NONZERO_PATTERN));
    LibmeshPetscCall(MatAssemblyBegin(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    LibmeshPetscCall(MatAssemblyEnd(_hc_sys_h_mat, MAT_FINAL_ASSEMBLY));
    if (_verbose_subchannel)
      _console << "Block: " << iblock << " - Enthalpy conservation matrix assembled" << std::endl;
    // RHS
    LibmeshPetscCall(VecAXPY(_hc_sys_h_rhs, 1.0, _hc_time_derivative_rhs));
    LibmeshPetscCall(VecAXPY(_hc_sys_h_rhs, 1.0, _hc_advective_derivative_rhs));
    LibmeshPetscCall(VecAXPY(_hc_sys_h_rhs, 1.0, _hc_cross_derivative_rhs));
    LibmeshPetscCall(VecAXPY(_hc_sys_h_rhs, 1.0, _hc_added_heat_rhs));
    LibmeshPetscCall(VecAXPY(_hc_sys_h_rhs, 1.0, _hc_axial_heat_conduction_rhs));
    LibmeshPetscCall(VecAXPY(_hc_sys_h_rhs, 1.0, _hc_radial_heat_conduction_rhs));
    LibmeshPetscCall(VecAXPY(_hc_sys_h_rhs, 1.0, _hc_sweep_enthalpy_rhs));

    // Use system to solve for and populate enthalpy
    LibmeshPetscCall(this->solveAndPopulateEnthalpy(
        _hc_sys_h_mat, _hc_sys_h_rhs, first_node, last_node, "h_sys_"));
  }
}