refineable_spherical_advection_diffusion_elements.h

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//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 generated by autoconfig
#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
{

//======================================================================
/// \short 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:

 /// \short Empty Constructor
 RefineableSphericalAdvectionDiffusionEquations() : 
 SphericalAdvectionDiffusionEquations(),
  RefineableElement(),
  ElementWithZ2ErrorEstimator()
   {} 
 
 
  /// Broken copy constructor
 RefineableSphericalAdvectionDiffusionEquations(
  const RefineableSphericalAdvectionDiffusionEquations& dummy) 
  { 
   BrokenCopy::broken_copy("RefineableSphericalAdvectionDiffusionEquations");
  } 
 
 /// Broken assignment operator
 void operator=(const RefineableSphericalAdvectionDiffusionEquations&) 
  {
   BrokenCopy::broken_assign("RefineableSphericalAdvectionDiffusionEquations");
  }
 
 /// Number of 'flux' terms for Z2 error estimation 
 unsigned num_Z2_flux_terms() {return 2;}
 
 /// \short 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);}


 /// \short 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];
    }
 }

 /// \short 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;
  }

 /// \short 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:
 
/// \short 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); 

};


//======================================================================
/// \short 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:

 /// \short Empty Constructor: 
  RefineableQSphericalAdvectionDiffusionElement() : 
   RefineableElement(),
   RefineableSphericalAdvectionDiffusionEquations(),
   RefineableQElement<2>(),
   QSphericalAdvectionDiffusionElement<NNODE_1D>()
   {} 


 /// Broken copy constructor
 RefineableQSphericalAdvectionDiffusionElement(
  const RefineableQSphericalAdvectionDiffusionElement<NNODE_1D>& 
  dummy) 
  { 
   BrokenCopy::broken_copy("RefineableQSphericalAdvectionDiffusionElement");
  } 
 
 /// Broken assignment operator
 void operator=(const 
                RefineableQSphericalAdvectionDiffusionElement<NNODE_1D>&) 
  {
   BrokenCopy::broken_assign("RefineableQSphericalAdvectionDiffusionElement");
  }
 
 /// Number of continuously interpolated values: 1
 unsigned ncont_interpolated_values() const {return 1;}

 /// \short Number of vertex nodes in the element
 unsigned nvertex_node() const
  {return QSphericalAdvectionDiffusionElement<NNODE_1D>::nvertex_node();}

 /// \short 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) {}

 /// \short Order of recovery shape functions for Z2 error estimation:
 /// Same order as shape functions.
 unsigned nrecovery_order() {return (NNODE_1D-1);}

 ///  \short 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:
 
 /// \short Constructor: Call the constructor for the
 /// appropriate lower-dimensional QElement
 FaceGeometry() : QElement<1,NNODE_1D>() {}

};

}

#endif