refineable_spherical_advection_diffusion_elements.h

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// LIC// ====================================================================
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// LIC// multi-physics finite-element library, available
// LIC// at http://www.oomph-lib.org.
// LIC//
// LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
// LIC//
// LIC// This library is free software; you can redistribute it and/or
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// LIC//====================================================================
// Header file for elements that solve the advection diffusion equation
// and that can be refined.
 
#ifndef OOMPH_REFINEABLE_SPHERICAL_ADVECTION_DIFFUSION_ELEMENTS_HEADER
#define OOMPH_REFINEABLE_SPHERICAL_ADVECTION_DIFFUSION_ELEMENTS_HEADER
 
// Config header
#ifdef HAVE_CONFIG_H
#include <oomph-lib-config.h>
#endif
 
// oomph-lib headers
#include "generic/refineable_quad_element.h"
#include "generic/refineable_brick_element.h"
#include "generic/error_estimator.h"
#include "spherical_advection_diffusion_elements.h"
 
namespace oomph
{
  //======================================================================
  /// A version of the Advection Diffusion in spherical
  /// coordinates equations that can be
  /// used with non-uniform mesh refinement. In essence, the class overloads
  /// the fill_in_generic_residual_contribution_spherical_adv_diff()
  /// function so that contributions
  /// from hanging nodes (or alternatively in-compatible function values)
  /// are taken into account.
  //======================================================================
  class RefineableSphericalAdvectionDiffusionEquations
    : public virtual SphericalAdvectionDiffusionEquations,
      public virtual RefineableElement,
      public virtual ElementWithZ2ErrorEstimator
  {
  public:
    /// Empty Constructor
    RefineableSphericalAdvectionDiffusionEquations()
      : SphericalAdvectionDiffusionEquations(),
        RefineableElement(),
        ElementWithZ2ErrorEstimator()
    {
    }
 
 
    /// Broken copy constructor
    RefineableSphericalAdvectionDiffusionEquations(
      const RefineableSphericalAdvectionDiffusionEquations& dummy) = delete;
 
    /// Broken assignment operator
    void operator=(const RefineableSphericalAdvectionDiffusionEquations&) =
      delete;
 
    /// Number of 'flux' terms for Z2 error estimation
    unsigned num_Z2_flux_terms()
    {
      return 2;
    }
 
    /// Get 'flux' for Z2 error recovery:
    /// Standard flux.from AdvectionDiffusion equations
    void get_Z2_flux(const Vector<double>& s, Vector<double>& flux)
    {
      this->get_flux(s, flux);
    }
 
 
    /// Get the function value u in Vector.
    /// Note: Given the generality of the interface (this function
    /// is usually called from black-box documentation or interpolation
    /// routines), the values Vector sets its own size in here.
    void get_interpolated_values(const Vector<double>& s,
                                 Vector<double>& values)
    {
      // Set size of Vector: u
      values.resize(1);
 
      // Find number of nodes
      unsigned n_node = nnode();
 
      // Find the index at which the unknown is stored
      unsigned u_nodal_index = this->u_index_spherical_adv_diff();
 
      // Local shape function
      Shape psi(n_node);
 
      // Find values of shape function
      shape(s, psi);
 
      // Initialise value of u
      values[0] = 0.0;
 
      // Loop over the local nodes and sum
      for (unsigned l = 0; l < n_node; l++)
      {
        values[0] += this->nodal_value(l, u_nodal_index) * psi[l];
      }
    }
 
    /// Get the function value u in Vector.
    /// Note: Given the generality of the interface (this function
    /// is usually called from black-box documentation or interpolation
    /// routines), the values Vector sets its own size in here.
    void get_interpolated_values(const unsigned& t,
                                 const Vector<double>& s,
                                 Vector<double>& values)
    {
      // Set size of Vector: u
      values.resize(1);
 
      // Find number of nodes
      const unsigned n_node = nnode();
 
      // Find the index at which the unknown is stored
      const unsigned u_nodal_index = this->u_index_spherical_adv_diff();
 
      // Local shape function
      Shape psi(n_node);
 
      // Find values of shape function
      shape(s, psi);
 
      // Initialise value of u
      values[0] = 0.0;
 
      // Loop over the local nodes and sum
      for (unsigned l = 0; l < n_node; l++)
      {
        values[0] += this->nodal_value(t, l, u_nodal_index) * psi[l];
      }
      // }
 
      if (t != 0)
      {
        std::string error_message =
          "Time-dependent version of get_interpolated_values() ";
        error_message += "not implemented for this element \n";
        throw OomphLibError(error_message,
                            "RefineableSphericalAdvectionDiffusionEquations::"
                            "get_interpolated_values()",
                            OOMPH_EXCEPTION_LOCATION);
      }
      else
      {
        // Make sure that we call the appropriate steady version
        //(the entire function might be overloaded lower down)
        RefineableSphericalAdvectionDiffusionEquations::get_interpolated_values(
          s, values);
      }
    }
 
    /// Fill in the geometric Jacobian, which in this case is r*r*sin(theta)
    double geometric_jacobian(const Vector<double>& x)
    {
      return x[0] * x[0] * sin(x[1]);
    }
 
    ///  Further build: Copy source function pointer from father element
    void further_build()
    {
      RefineableSphericalAdvectionDiffusionEquations* cast_father_element_pt =
        dynamic_cast<RefineableSphericalAdvectionDiffusionEquations*>(
          this->father_element_pt());
 
      // Set the values of the pointers from the father
      this->Source_fct_pt = cast_father_element_pt->source_fct_pt();
      this->Wind_fct_pt = cast_father_element_pt->wind_fct_pt();
      this->Pe_pt = cast_father_element_pt->pe_pt();
      this->PeSt_pt = cast_father_element_pt->pe_st_pt();
 
      // Set the ALE status
      // this->ALE_is_disabled = cast_father_element_pt->ALE_is_disabled;
    }
 
    /// Compute the derivatives of the i-th component of
    /// velocity at point s with respect
    /// to all data that can affect its value. In addition, return the global
    /// equation numbers corresponding to the data.
    /// Overload the non-refineable version to take account of hanging node
    /// information
    void dinterpolated_u_adv_diff_ddata(const Vector<double>& s,
                                        Vector<double>& du_ddata,
                                        Vector<unsigned>& global_eqn_number)
    {
      // Find number of nodes
      unsigned n_node = this->nnode();
      // Local shape function
      Shape psi(n_node);
      // Find values of shape function at the given local coordinate
      this->shape(s, psi);
 
      // Find the index at which the velocity component is stored
      const unsigned u_nodal_index = this->u_index_spherical_adv_diff();
 
      // Storage for hang info pointer
      HangInfo* hang_info_pt = 0;
      // Storage for global equation
      int global_eqn = 0;
 
      // Find the number of dofs associated with interpolated u
      unsigned n_u_dof = 0;
      for (unsigned l = 0; l < n_node; l++)
      {
        unsigned n_master = 1;
 
        // Local bool (is the node hanging)
        bool is_node_hanging = this->node_pt(l)->is_hanging();
 
        // If the node is hanging, get the number of master nodes
        if (is_node_hanging)
        {
          hang_info_pt = this->node_pt(l)->hanging_pt();
          n_master = hang_info_pt->nmaster();
        }
        // Otherwise there is just one master node, the node itself
        else
        {
          n_master = 1;
        }
 
        // Loop over the master nodes
        for (unsigned m = 0; m < n_master; m++)
        {
          // Get the equation number
          if (is_node_hanging)
          {
            // Get the equation number from the master node
            global_eqn =
              hang_info_pt->master_node_pt(m)->eqn_number(u_nodal_index);
          }
          else
          {
            // Global equation number
            global_eqn = this->node_pt(l)->eqn_number(u_nodal_index);
          }
 
          // If it's positive add to the count
          if (global_eqn >= 0)
          {
            ++n_u_dof;
          }
        }
      }
 
      // Now resize the storage schemes
      du_ddata.resize(n_u_dof, 0.0);
      global_eqn_number.resize(n_u_dof, 0);
 
      // Loop over th nodes again and set the derivatives
      unsigned count = 0;
      // Loop over the local nodes and sum
      for (unsigned l = 0; l < n_node; l++)
      {
        unsigned n_master = 1;
        double hang_weight = 1.0;
 
        // Local bool (is the node hanging)
        bool is_node_hanging = this->node_pt(l)->is_hanging();
 
        // If the node is hanging, get the number of master nodes
        if (is_node_hanging)
        {
          hang_info_pt = this->node_pt(l)->hanging_pt();
          n_master = hang_info_pt->nmaster();
        }
        // Otherwise there is just one master node, the node itself
        else
        {
          n_master = 1;
        }
 
        // Loop over the master nodes
        for (unsigned m = 0; m < n_master; m++)
        {
          // If the node is hanging get weight from master node
          if (is_node_hanging)
          {
            // Get the hang weight from the master node
            hang_weight = hang_info_pt->master_weight(m);
          }
          else
          {
            // Node contributes with full weight
            hang_weight = 1.0;
          }
 
          // Get the equation number
          if (is_node_hanging)
          {
            // Get the equation number from the master node
            global_eqn =
              hang_info_pt->master_node_pt(m)->eqn_number(u_nodal_index);
          }
          else
          {
            // Global equation number
            global_eqn = this->node_pt(l)->eqn_number(u_nodal_index);
          }
 
          if (global_eqn >= 0)
          {
            // Set the global equation number
            global_eqn_number[count] = global_eqn;
            // Set the derivative with respect to the unknown
            du_ddata[count] = psi[l] * hang_weight;
            // Increase the counter
            ++count;
          }
        }
      }
    }
 
 
  protected:
    /// Add the element's contribution to the elemental residual vector
    /// and/or Jacobian matrix
    /// flag=1: compute both
    /// flag=0: compute only residual vector
    void fill_in_generic_residual_contribution_spherical_adv_diff(
      Vector<double>& residuals,
      DenseMatrix<double>& jacobian,
      DenseMatrix<double>& mass_matrix,
      unsigned flag);
  };
 
 
  //======================================================================
  /// Refineable version of QSphericalAdvectionDiffusionElement.
  /// Inherit from the standard QSphericalAdvectionDiffusionElement and the
  /// appropriate refineable geometric element and the refineable equations.
  //======================================================================
  template<unsigned NNODE_1D>
  class RefineableQSphericalAdvectionDiffusionElement
    : public QSphericalAdvectionDiffusionElement<NNODE_1D>,
      public virtual RefineableSphericalAdvectionDiffusionEquations,
      public virtual RefineableQElement<2>
  {
  public:
    /// Empty Constructor:
    RefineableQSphericalAdvectionDiffusionElement()
      : RefineableElement(),
        RefineableSphericalAdvectionDiffusionEquations(),
        RefineableQElement<2>(),
        QSphericalAdvectionDiffusionElement<NNODE_1D>()
    {
    }
 
 
    /// Broken copy constructor
    RefineableQSphericalAdvectionDiffusionElement(
      const RefineableQSphericalAdvectionDiffusionElement<NNODE_1D>& dummy) =
      delete;
 
    /// Broken assignment operator
    void operator=(
      const RefineableQSphericalAdvectionDiffusionElement<NNODE_1D>&) = delete;
 
    /// Number of continuously interpolated values: 1
    unsigned ncont_interpolated_values() const
    {
      return 1;
    }
 
    /// Number of vertex nodes in the element
    unsigned nvertex_node() const
    {
      return QSphericalAdvectionDiffusionElement<NNODE_1D>::nvertex_node();
    }
 
    /// Pointer to the j-th vertex node in the element
    Node* vertex_node_pt(const unsigned& j) const
    {
      return QSphericalAdvectionDiffusionElement<NNODE_1D>::vertex_node_pt(j);
    }
 
    /// Rebuild from sons: empty
    void rebuild_from_sons(Mesh*& mesh_pt) {}
 
    /// Order of recovery shape functions for Z2 error estimation:
    /// Same order as shape functions.
    unsigned nrecovery_order()
    {
      return (NNODE_1D - 1);
    }
 
    ///  Perform additional hanging node procedures for variables
    /// that are not interpolated by all nodes. Empty.
    void further_setup_hanging_nodes() {}
  };
 
  ////////////////////////////////////////////////////////////////////////
  ////////////////////////////////////////////////////////////////////////
  ////////////////////////////////////////////////////////////////////////
 
 
  //=======================================================================
  /// Face geometry for the RefineableQSphericalAdvectionDiffusionElement
  /// elements: The spatial
  /// dimension of the face elements is one lower than that of the
  /// bulk element but they have the same number of points
  /// along their 1D edges.
  //=======================================================================
  template<unsigned NNODE_1D>
  class FaceGeometry<RefineableQSphericalAdvectionDiffusionElement<NNODE_1D>>
    : public virtual QElement<1, NNODE_1D>
  {
  public:
    /// Constructor: Call the constructor for the
    /// appropriate lower-dimensional QElement
    FaceGeometry() : QElement<1, NNODE_1D>() {}
  };
 
} // namespace oomph
 
#endif