PorousFlowDarcyBase.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 "PorousFlowDarcyBase.h"
 
#include "Assembly.h"
#include "MooseMesh.h"
#include "MooseVariable.h"
#include "SystemBase.h"
 
#include "libmesh/quadrature.h"
 
template <bool is_ad>
InputParameters
PorousFlowDarcyBaseTempl<is_ad>::validParams()
{
  InputParameters params = GenericKernel<is_ad>::validParams();
  params.addRequiredParam<RealVectorValue>("gravity",
                                           "Gravitational acceleration vector downwards (m/s^2)");
  params.addRequiredParam<UserObjectName>(
      "PorousFlowDictator", "The UserObject that holds the list of PorousFlow variable names");
  params.addParam<unsigned>("full_upwind_threshold",
                            5,
                            "If, for each timestep, the number of "
                            "upwind-downwind swaps in an element is less than "
                            "this quantity, then full upwinding is used for that element.  "
                            "Otherwise the fallback scheme is employed.");
  MooseEnum fallback_enum("quick harmonic", "quick");
  params.addParam<MooseEnum>("fallback_scheme",
                             fallback_enum,
                             "quick: use nodal mobility without "
                             "preserving mass.  harmonic: use a "
                             "harmonic mean of nodal mobilities "
                             "and preserve fluid mass");
  params.addClassDescription("Fully-upwinded advective Darcy flux");
  return params;
}
 
template <bool is_ad>
PorousFlowDarcyBaseTempl<is_ad>::PorousFlowDarcyBaseTempl(const InputParameters & parameters)
  : GenericKernel<is_ad>(parameters),
    _permeability(this->template getGenericMaterialProperty<RealTensorValue, is_ad>(
        "PorousFlow_permeability_qp")),
    _dpermeability_dvar(is_ad ? nullptr
                              : &this->template getMaterialProperty<std::vector<RealTensorValue>>(
                                    "dPorousFlow_permeability_qp_dvar")),
    _dpermeability_dgradvar(
        is_ad ? nullptr
              : &this->template getMaterialProperty<std::vector<std::vector<RealTensorValue>>>(
                    "dPorousFlow_permeability_qp_dgradvar")),
    _fluid_density_node(this->template getGenericMaterialProperty<std::vector<Real>, is_ad>(
        "PorousFlow_fluid_phase_density_nodal")),
    _dfluid_density_node_dvar(
        is_ad ? nullptr
              : &this->template getMaterialProperty<std::vector<std::vector<Real>>>(
                    "dPorousFlow_fluid_phase_density_nodal_dvar")),
    _fluid_density_qp(this->template getGenericMaterialProperty<std::vector<Real>, is_ad>(
        "PorousFlow_fluid_phase_density_qp")),
    _dfluid_density_qp_dvar(
        is_ad ? nullptr
              : &this->template getMaterialProperty<std::vector<std::vector<Real>>>(
                    "dPorousFlow_fluid_phase_density_qp_dvar")),
    _fluid_viscosity(this->template getGenericMaterialProperty<std::vector<Real>, is_ad>(
        "PorousFlow_viscosity_nodal")),
    _dfluid_viscosity_dvar(
        is_ad ? nullptr
              : &this->template getMaterialProperty<std::vector<std::vector<Real>>>(
                    "dPorousFlow_viscosity_nodal_dvar")),
    _pp(this->template getGenericMaterialProperty<std::vector<Real>, is_ad>(
        "PorousFlow_porepressure_nodal")),
    _grad_p(this->template getGenericMaterialProperty<std::vector<RealGradient>, is_ad>(
        "PorousFlow_grad_porepressure_qp")),
    _dgrad_p_dgrad_var(is_ad ? nullptr
                             : &this->template getMaterialProperty<std::vector<std::vector<Real>>>(
                                   "dPorousFlow_grad_porepressure_qp_dgradvar")),
    _dgrad_p_dvar(is_ad
                      ? nullptr
                      : &this->template getMaterialProperty<std::vector<std::vector<RealGradient>>>(
                            "dPorousFlow_grad_porepressure_qp_dvar")),
    _dictator(this->template getUserObject<PorousFlowDictator>("PorousFlowDictator")),
    _num_phases(_dictator.numPhases()),
    _gravity(this->template getParam<RealVectorValue>("gravity")),
    _perm_derivs(_dictator.usePermDerivs()),
    _full_upwind_threshold(this->template getParam<unsigned>("full_upwind_threshold")),
    _fallback_scheme(
        this->template getParam<MooseEnum>("fallback_scheme").template getEnum<FallbackEnum>()),
    _proto_flux(_num_phases),
    _jacobian(_num_phases),
    _num_upwinds(),
    _num_downwinds()
{
  // The full-upwinding scheme identifies each element test function with a mesh node, which is
  // only valid for nodal (Lagrange) variables.
  if (!_var.isNodal())
    mooseError("The variable '",
               _var.name(),
               "' is not a nodal (Lagrange) variable.  This kernel uses full upwinding, which "
               "requires a nodal variable.  PorousFlow has no discontinuous-Galerkin "
               "finite-element discretisation, so an element-local variable (eg CONSTANT "
               "MONOMIAL) cannot be used as a PorousFlow variable.");
 
#ifdef LIBMESH_HAVE_TBB_API
  if (this->_fe_problem.numThreads() > 1)
    mooseWarning("PorousFlowDarcyBase: num_upwinds and num_downwinds may not be computed "
                 "accurately when using TBB and greater than 1 thread");
#endif
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::timestepSetup()
{
  GenericKernel<is_ad>::timestepSetup();
  _num_upwinds = std::unordered_map<unsigned, std::vector<std::vector<unsigned>>>();
  _num_downwinds = std::unordered_map<unsigned, std::vector<std::vector<unsigned>>>();
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::jacobianSetup()
{
  GenericKernel<is_ad>::jacobianSetup();
  _my_elem_darcy = nullptr;
}
 
template <bool is_ad>
GenericReal<is_ad>
PorousFlowDarcyBaseTempl<is_ad>::darcyQp(unsigned int ph) const
{
  return _grad_test[_i][_qp] *
         (_permeability[_qp] * (_grad_p[_qp][ph] - _fluid_density_qp[_qp][ph] * _gravity));
}
 
template <bool is_ad>
Real
PorousFlowDarcyBaseTempl<is_ad>::darcyQpJacobian(unsigned int jvar, unsigned int ph) const
{
  if constexpr (!is_ad)
  {
    if (_dictator.notPorousFlowVariable(jvar))
      return 0.0;
 
    const unsigned int pvar = _dictator.porousFlowVariableNum(jvar);
 
    RealVectorValue deriv =
        _permeability[_qp] * (_grad_phi[_j][_qp] * (*_dgrad_p_dgrad_var)[_qp][ph][pvar] -
                              _phi[_j][_qp] * (*_dfluid_density_qp_dvar)[_qp][ph][pvar] * _gravity);
 
    deriv += _permeability[_qp] * ((*_dgrad_p_dvar)[_qp][ph][pvar] * _phi[_j][_qp]);
 
    if (_perm_derivs)
    {
      deriv += (*_dpermeability_dvar)[_qp][pvar] * _phi[_j][_qp] *
               (_grad_p[_qp][ph] - _fluid_density_qp[_qp][ph] * _gravity);
      for (const auto i : make_range(Moose::dim))
        deriv += (*_dpermeability_dgradvar)[_qp][i][pvar] * _grad_phi[_j][_qp](i) *
                 (_grad_p[_qp][ph] - _fluid_density_qp[_qp][ph] * _gravity);
    }
 
    return _grad_test[_i][_qp] * deriv;
  }
  else
    libmesh_ignore(jvar, ph);
  return 0.0;
}
 
template <bool is_ad>
GenericReal<is_ad>
PorousFlowDarcyBaseTempl<is_ad>::computeQpResidual()
{
  mooseError("PorousFlowDarcyBase: computeQpResidual called");
  return 0.0;
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::computeResidual()
{
  if constexpr (!is_ad)
    computeResidualOrJacobian(JacRes::CALCULATE_RESIDUAL, 0);
  else
  {
    adComputeProtoFlux(false);
    // Assemble the real-valued residual from the value parts of the ADReal proto fluxes
    assembleProtoFluxResidual();
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::assembleProtoFluxResidual()
{
  this->prepareVectorTag(this->_assembly, _var.number());
  for (_i = 0; _i < _test.size(); _i++)
    for (unsigned int ph = 0; ph < _num_phases; ++ph)
      this->_local_re(_i) += MetaPhysicL::raw_value(_proto_flux[ph][_i]);
  this->accumulateTaggedLocalResidual();
 
  if (this->_has_save_in)
    for (unsigned int i = 0; i < this->_save_in.size(); i++)
      this->_save_in[i]->sys().solution().add_vector(this->_local_re,
                                                     this->_save_in[i]->dofIndices());
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::computeJacobian()
{
  if constexpr (!is_ad)
    computeResidualOrJacobian(JacRes::CALCULATE_JACOBIAN, _var.number());
  else
    // Block-diagonal (e.g. PJFNK) assembly path: this is the only Jacobian call we get.
    adComputeJacobian();
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::adComputeJacobian()
{
  if constexpr (is_ad)
  {
    // Compute ADReal proto fluxes with upwind counting, then extract the Jacobian.
    // Every block (diagonal and off-diagonal) is encoded in the ADReal derivatives, so a
    // single call to addJacobianWithoutConstraints captures all variable sensitivities.
    //
    // See PorousFlowLumpedKernelBase.C::computeJacobian for the detailed rationale of why
    // addJacobianWithoutConstraints (rather than the default ADKernel addJacobian) is required:
    // each residual row's column set must be read from its own derivatives instead of being shared
    // from row 0. There it is forced by mass-lumped nodal materials; here it is forced by the
    // upwinding scheme, which makes each node's proto flux depend on a different set of nodal DOFs.
    adComputeProtoFlux(true);
 
    const unsigned int num_nodes = _test.size();
    std::vector<ADReal> darcy_residuals(num_nodes, 0.0);
    for (const auto n : make_range(num_nodes))
      for (const auto ph : make_range(_num_phases))
        darcy_residuals[n] += _proto_flux[ph][n];
 
    this->addJacobianWithoutConstraints(
        this->_assembly, darcy_residuals, this->dofIndices(), _var.scalingFactor());
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::computeOffDiagJacobian(const unsigned int jvar)
{
  if constexpr (!is_ad)
    computeResidualOrJacobian(JacRes::CALCULATE_JACOBIAN, jvar);
  else
  {
    libmesh_ignore(jvar);
    // Full (SMP) assembly calls this once per coupled variable; the first call performs the
    // single AD pass that fills every block, and the guard makes the rest no-ops. This mirrors
    // ADKernel::computeOffDiagJacobian and avoids the ADD-semantics double-counting.
    if (_my_elem_darcy != this->_current_elem)
    {
      adComputeJacobian();
      _my_elem_darcy = this->_current_elem;
    }
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::computeProtoFluxWithoutMobility()
{
  const unsigned int num_nodes = _test.size();
  for (unsigned ph = 0; ph < _num_phases; ++ph)
  {
    _proto_flux[ph].assign(num_nodes, 0.0);
    for (_qp = 0; _qp < this->_qrule->n_points(); _qp++)
    {
      // The AD weight carries the displacement derivatives on a displaced mesh. Elsewhere use the
      // Real weight, as ADKernel does: XFEM rescales only the Real weight.
      GenericReal<is_ad> jxw_coord = this->_JxW[_qp] * this->_coord[_qp];
      if constexpr (is_ad)
        if (this->_use_displaced_mesh)
          jxw_coord = this->_ad_JxW[_qp] * this->_ad_coord[_qp];
      for (_i = 0; _i < num_nodes; ++_i)
        _proto_flux[ph][_i] += jxw_coord * darcyQp(ph);
    }
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::initializeUpwindTracking(unsigned elem, unsigned int num_nodes)
{
  if (_num_upwinds.find(elem) == _num_upwinds.end())
  {
    _num_upwinds[elem] = std::vector<std::vector<unsigned>>(_num_phases);
    _num_downwinds[elem] = std::vector<std::vector<unsigned>>(_num_phases);
    for (unsigned ph = 0; ph < _num_phases; ++ph)
    {
      _num_upwinds[elem][ph].assign(num_nodes, 0);
      _num_downwinds[elem][ph].assign(num_nodes, 0);
    }
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::updateUpwindCounts(unsigned elem, unsigned int num_nodes)
{
  for (unsigned ph = 0; ph < _num_phases; ++ph)
    for (unsigned nod = 0; nod < num_nodes; ++nod)
    {
      if (_proto_flux[ph][nod] > 0)
        _num_upwinds[elem][ph][nod]++;
      else if (_proto_flux[ph][nod] < 0)
        _num_downwinds[elem][ph][nod]++;
    }
}
 
template <bool is_ad>
std::vector<unsigned>
PorousFlowDarcyBaseTempl<is_ad>::computeMaxSwaps(unsigned elem, unsigned int num_nodes) const
{
  std::vector<unsigned> max_swaps(_num_phases, 0);
  for (unsigned ph = 0; ph < _num_phases; ++ph)
    for (unsigned nod = 0; nod < num_nodes; ++nod)
      max_swaps[ph] =
          std::max(max_swaps[ph],
                   std::min(_num_upwinds.at(elem)[ph][nod], _num_downwinds.at(elem)[ph][nod]));
  return max_swaps;
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::applyUpwinding(const std::vector<unsigned> & max_swaps,
                                                JacRes res_or_jac,
                                                unsigned int pvar)
{
  for (unsigned int ph = 0; ph < _num_phases; ++ph)
  {
    if (max_swaps[ph] < _full_upwind_threshold)
      fullyUpwind(res_or_jac, ph, pvar);
    else
    {
      switch (_fallback_scheme)
      {
        case FallbackEnum::QUICK:
          quickUpwind(res_or_jac, ph, pvar);
          break;
        case FallbackEnum::HARMONIC:
          harmonicMean(res_or_jac, ph, pvar);
          break;
      }
    }
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::adComputeProtoFlux(bool do_counting)
{
  const unsigned int num_nodes = _test.size();
  computeProtoFluxWithoutMobility();
 
  // Initialise upwind-tracking maps for this element on first encounter
  const unsigned elem = this->_current_elem->id();
  initializeUpwindTracking(elem, num_nodes);
 
  if (do_counting)
    updateUpwindCounts(elem, num_nodes);
 
  // Determine how many upwind-downwind swaps have occurred this timestep
  const std::vector<unsigned> max_swaps = computeMaxSwaps(elem, num_nodes);
 
  // Apply mobility via the chosen upwinding scheme (always in residual mode for AD)
  applyUpwinding(max_swaps, JacRes::CALCULATE_RESIDUAL, 0);
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::computeResidualOrJacobian(JacRes res_or_jac, unsigned int jvar)
{
  if ((res_or_jac == JacRes::CALCULATE_JACOBIAN) && _dictator.notPorousFlowVariable(jvar))
    return;
 
  // The PorousFlow variable index corresponding to the variable number jvar
  const unsigned int pvar =
      ((res_or_jac == JacRes::CALCULATE_JACOBIAN) ? _dictator.porousFlowVariableNum(jvar) : 0);
 
  this->prepareMatrixTag(this->_assembly, _var.number(), jvar);
  if ((this->_local_ke.n() == 0) &&
      (res_or_jac == JacRes::CALCULATE_JACOBIAN)) // this removes a problem
                                                  // encountered in the
                                                  // initial timestep when
                                                  // use_displaced_mesh=true
    return;
 
  // The number of nodes in the element
  const unsigned int num_nodes = _test.size();
 
  // Compute the residual and jacobian without the mobility terms. Even if we are computing the
  // Jacobian we still need this in order to see which nodes are upwind and which are downwind.
  computeProtoFluxWithoutMobility();
 
  // for this element, record whether each node is "upwind" or "downwind" (or neither)
  const unsigned elem = this->_current_elem->id();
  initializeUpwindTracking(elem, num_nodes);
  // record the information once per nonlinear iteration
  if (res_or_jac == JacRes::CALCULATE_JACOBIAN && jvar == _var.number())
    updateUpwindCounts(elem, num_nodes);
 
  // based on _num_upwinds and _num_downwinds, calculate the maximum number
  // of upwind-downwind swaps that have been encountered in this timestep
  // for this element
  const std::vector<unsigned> max_swaps = computeMaxSwaps(elem, num_nodes);
 
  // size the _jacobian correctly and calculate it for the case residual = _proto_flux
  if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
  {
    for (unsigned ph = 0; ph < _num_phases; ++ph)
    {
      _jacobian[ph].resize(this->_local_ke.m());
      for (_i = 0; _i < _test.size(); _i++)
      {
        _jacobian[ph][_i].assign(this->_local_ke.n(), 0.0);
        for (_j = 0; _j < _phi.size(); _j++)
          for (_qp = 0; _qp < this->_qrule->n_points(); _qp++)
            _jacobian[ph][_i][_j] +=
                this->_JxW[_qp] * this->_coord[_qp] * darcyQpJacobian(jvar, ph);
      }
    }
  }
 
  // Loop over all the phases, computing the mass flux, which
  // gets placed into _proto_flux, and the derivative of this
  // which gets placed into _jacobian
  applyUpwinding(max_swaps, res_or_jac, pvar);
 
  // Add results to the Residual or Jacobian
  if (res_or_jac == JacRes::CALCULATE_RESIDUAL)
    assembleProtoFluxResidual();
 
  if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
  {
    for (_i = 0; _i < _test.size(); _i++)
      for (_j = 0; _j < _phi.size(); _j++)
        for (unsigned int ph = 0; ph < _num_phases; ++ph)
          this->_local_ke(_i, _j) += _jacobian[ph][_i][_j];
 
    this->accumulateTaggedLocalMatrix();
 
    if (this->_has_diag_save_in && jvar == _var.number())
    {
      unsigned int rows = this->_local_ke.m();
      DenseVector<Number> diag(rows);
      for (unsigned int i = 0; i < rows; i++)
        diag(i) = this->_local_ke(i, i);
 
      for (unsigned int i = 0; i < this->_diag_save_in.size(); i++)
        this->_diag_save_in[i]->sys().solution().add_vector(diag,
                                                            this->_diag_save_in[i]->dofIndices());
    }
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::fullyUpwind(JacRes res_or_jac, unsigned int ph, unsigned int pvar)
{
  // res_or_jac and pvar drive the hand-coded non-AD Jacobian only; the AD path ignores them
  if constexpr (is_ad)
    libmesh_ignore(res_or_jac, pvar);
 
  // The number of nodes in the element
  const unsigned int num_nodes = _test.size();
 
  GenericReal<is_ad> mob;
  // Define variables used to ensure mass conservation
  GenericReal<is_ad> total_mass_out = 0.0;
  GenericReal<is_ad> total_in = 0.0;
 
  // The following holds derivatives of these (non-AD path only)
  std::vector<Real> dtotal_mass_out;
  std::vector<Real> dtotal_in;
 
  // These accumulate Jacobian columns, so they must be sized by the column variable's
  // DOF count (_phi.size(), not by num_nodes = _test.size() (which is the row variable's)
  if constexpr (!is_ad)
    if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
    {
      dtotal_mass_out.assign(_phi.size(), 0.0);
      dtotal_in.assign(_phi.size(), 0.0);
    }
 
  // Perform the upwinding using the mobility
  std::vector<bool> upwind_node(num_nodes);
  for (unsigned int n = 0; n < num_nodes; ++n)
  {
    if (_proto_flux[ph][n] >= 0.0) // upstream node
    {
      upwind_node[n] = true;
      // The mobility at the upstream node
      mob = mobility(n, ph);
      if constexpr (!is_ad)
        if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
        {
          // The derivative of the mobility wrt the PorousFlow variable
          const Real dmob = dmobility(n, ph, pvar);
 
          for (_j = 0; _j < _phi.size(); _j++)
            _jacobian[ph][n][_j] *= mob;
 
          if (_test.size() == _phi.size())
            /* mobility at node=n depends only on the variables at node=n, by construction.  For
             * linear-lagrange variables, this means that Jacobian entries involving the derivative
             * of mobility will only be nonzero for derivatives wrt variables at node=n.  Hence the
             * [n][n] in the line below.  However, for other variable types (eg constant monomials)
             * I cannot tell what variable number contributes to the derivative.  However, in all
             * cases I can possibly imagine, the derivative is zero anyway, since in the full
             * upwinding scheme, mobility shouldn't depend on these other sorts of variables.
             */
            _jacobian[ph][n][n] += dmob * MetaPhysicL::raw_value(_proto_flux[ph][n]);
 
          for (_j = 0; _j < _phi.size(); _j++)
            dtotal_mass_out[_j] += _jacobian[ph][n][_j];
        }
      _proto_flux[ph][n] *= mob;
      total_mass_out += _proto_flux[ph][n];
    }
    else
    {
      upwind_node[n] = false;
      total_in -= _proto_flux[ph][n]; 
      if constexpr (!is_ad)
        if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
          for (_j = 0; _j < _phi.size(); _j++)
            dtotal_in[_j] -= _jacobian[ph][n][_j];
    }
  }
 
  // Conserve mass over all phases by proportioning the total_mass_out mass to the inflow nodes,
  // weighted by their proto_flux values
  for (unsigned int n = 0; n < num_nodes; ++n)
  {
    if (!upwind_node[n]) // downstream node
    {
      if constexpr (!is_ad)
        if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
          for (_j = 0; _j < _phi.size(); _j++)
          {
            _jacobian[ph][n][_j] *= MetaPhysicL::raw_value(total_mass_out / total_in);
            _jacobian[ph][n][_j] +=
                MetaPhysicL::raw_value(_proto_flux[ph][n]) *
                (dtotal_mass_out[_j] / MetaPhysicL::raw_value(total_in) -
                 dtotal_in[_j] * MetaPhysicL::raw_value(total_mass_out) /
                     MetaPhysicL::raw_value(total_in) / MetaPhysicL::raw_value(total_in));
          }
      _proto_flux[ph][n] *= total_mass_out / total_in;
    }
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::quickUpwind(JacRes res_or_jac, unsigned int ph, unsigned int pvar)
{
  // res_or_jac and pvar drive the hand-coded non-AD Jacobian only; the AD path ignores them
  if constexpr (is_ad)
    libmesh_ignore(res_or_jac, pvar);
 
  // The number of nodes in the element
  const unsigned int num_nodes = _test.size();
 
  // Use the raw nodal mobility
  for (unsigned int n = 0; n < num_nodes; ++n)
  {
    // The mobility at the node
    const GenericReal<is_ad> mob = mobility(n, ph);
    if constexpr (!is_ad)
      if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
      {
        // The derivative of the mobility wrt the PorousFlow variable
        const Real dmob = dmobility(n, ph, pvar);
 
        for (_j = 0; _j < _phi.size(); _j++)
          _jacobian[ph][n][_j] *= mob;
 
        if (_test.size() == _phi.size())
          /* mobility at node=n depends only on the variables at node=n, by construction.  For
           * linear-lagrange variables, this means that Jacobian entries involving the derivative
           * of mobility will only be nonzero for derivatives wrt variables at node=n.  Hence the
           * [n][n] in the line below.  However, for other variable types (eg constant monomials)
           * I cannot tell what variable number contributes to the derivative.  However, in all
           * cases I can possibly imagine, the derivative is zero anyway, since in the full
           * upwinding scheme, mobility shouldn't depend on these other sorts of variables.
           */
          _jacobian[ph][n][n] += dmob * MetaPhysicL::raw_value(_proto_flux[ph][n]);
      }
    _proto_flux[ph][n] *= mob;
  }
}
 
template <bool is_ad>
void
PorousFlowDarcyBaseTempl<is_ad>::harmonicMean(JacRes res_or_jac, unsigned int ph, unsigned int pvar)
{
  // res_or_jac and pvar drive the hand-coded non-AD Jacobian only; the AD path ignores them
  if constexpr (is_ad)
    libmesh_ignore(res_or_jac, pvar);
 
  // The number of nodes in the element
  const unsigned int num_nodes = _test.size();
 
  std::vector<GenericReal<is_ad>> mob(num_nodes);
  unsigned num_zero = 0;
  GenericReal<is_ad> harmonic_mob = 0;
  for (unsigned n = 0; n < num_nodes; ++n)
  {
    mob[n] = mobility(n, ph);
    if (MetaPhysicL::raw_value(mob[n]) == 0.0)
    {
      num_zero++;
    }
    else
      harmonic_mob += 1.0 / mob[n];
  }
  if (num_zero > 0)
    harmonic_mob = 0.0;
  else
    harmonic_mob = (1.0 * num_nodes) / harmonic_mob;
 
  // d(harmonic_mob)/d(PorousFlow variable at node n) -- non-AD path only
  std::vector<Real> dharmonic_mob(num_nodes, 0.0);
  if constexpr (!is_ad)
    if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
    {
      const Real harm2 = std::pow(MetaPhysicL::raw_value(harmonic_mob), 2) / (1.0 * num_nodes);
      if (num_zero == 0)
        for (unsigned n = 0; n < num_nodes; ++n)
          dharmonic_mob[n] =
              dmobility(n, ph, pvar) * harm2 / std::pow(MetaPhysicL::raw_value(mob[n]), 2);
      else if (num_zero == 1)
        for (unsigned n = 0; n < num_nodes; ++n)
          if (MetaPhysicL::raw_value(mob[n]) == 0.0)
          {
            dharmonic_mob[n] = num_nodes * dmobility(n, ph, pvar); // other derivs are zero
            break;
          }
      // if num_zero > 1 then all dharmonic_mob = 0.0
    }
 
  if constexpr (!is_ad)
    if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
      for (unsigned n = 0; n < num_nodes; ++n)
        for (_j = 0; _j < _phi.size(); _j++)
        {
          _jacobian[ph][n][_j] *= MetaPhysicL::raw_value(harmonic_mob);
          if (_test.size() == _phi.size())
            _jacobian[ph][n][_j] += dharmonic_mob[_j] * MetaPhysicL::raw_value(_proto_flux[ph][n]);
        }
 
  for (unsigned n = 0; n < num_nodes; ++n)
    _proto_flux[ph][n] *= harmonic_mob;
}
 
template <bool is_ad>
GenericReal<is_ad>
PorousFlowDarcyBaseTempl<is_ad>::mobility(unsigned nodenum, unsigned phase) const
{
  return _fluid_density_node[nodenum][phase] / _fluid_viscosity[nodenum][phase];
}
 
template <bool is_ad>
Real
PorousFlowDarcyBaseTempl<is_ad>::dmobility(unsigned nodenum, unsigned phase, unsigned pvar) const
{
  if constexpr (!is_ad)
  {
    Real dm = (*_dfluid_density_node_dvar)[nodenum][phase][pvar] / _fluid_viscosity[nodenum][phase];
    dm -= _fluid_density_node[nodenum][phase] * (*_dfluid_viscosity_dvar)[nodenum][phase][pvar] /
          std::pow(_fluid_viscosity[nodenum][phase], 2);
    return dm;
  }
  else
    libmesh_ignore(nodenum, phase, pvar);
  return 0.0;
}
 
template class PorousFlowDarcyBaseTempl<false>;
template class PorousFlowDarcyBaseTempl<true>;