Tdarcy_elements.cc

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//LIC// ====================================================================
//LIC// This file forms part of oomph-lib, the object-oriented, 
//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
//LIC// 
//LIC//    Version 1.0; svn revision $LastChangedRevision$
//LIC//
//LIC// $LastChangedDate$
//LIC// 
//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
//LIC// This library is free software; you can redistribute it and/or
//LIC// modify it under the terms of the GNU Lesser General Public
//LIC// License as published by the Free Software Foundation; either
//LIC// version 2.1 of the License, or (at your option) any later version.
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//LIC// Lesser General Public License for more details.
//LIC// 
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//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
//LIC// 
//LIC//====================================================================
#include "Tdarcy_elements.h"

namespace oomph
{


//////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////
/// Lowest-order Raviart-Thomas based Darcy equation element
//////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////


//===========================================================================
 /// \short Constructor. Order 0 elements have 1 pressure dof and no internal
 /// velocity dofs
//===========================================================================
 template<>
 TRaviartThomasDarcyElement<0>::TRaviartThomasDarcyElement() :
  TElement<2,3>(), DarcyEquations<2>(), Sign_edge(3,1)
 {
  P_internal_data_index=this->add_internal_data(new Data(1));
 }

//===========================================================================
 /// Destructor
//===========================================================================
 template<>
 TRaviartThomasDarcyElement<0>::~TRaviartThomasDarcyElement()
 {
 }


//===========================================================================
 /// Return the number of edge basis functions for q
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<0>::nq_basis_edge() const
 {
  return 3;
 }



//===========================================================================
 /// Return the number of internal basis functions for q
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<0>::nq_basis_internal() const
 {
  return 0;
 }

//===========================================================================
 /// Compute the local form of the q basis at local coordinate s
//===========================================================================
 template<>
 void TRaviartThomasDarcyElement<0>::get_q_basis_local(const Vector<double> &s,
                                                       Shape &q_basis) const
 {
  // RT_0 basis functions
  q_basis(0,0) = Sign_edge[0]*std::sqrt(2)*s[0];
  q_basis(0,1) = Sign_edge[0]*std::sqrt(2)*s[1];

  q_basis(1,0) = Sign_edge[1]*(s[0]-1);
  q_basis(1,1) = Sign_edge[1]*s[1];

  q_basis(2,0) = Sign_edge[2]*s[0];
  q_basis(2,1) = Sign_edge[2]*(s[1]-1);
 }

//===========================================================================
 /// Compute the local form of the q basis and dbasis/ds at local coordinate s
//===========================================================================
 template<>
 void TRaviartThomasDarcyElement<0>::get_div_q_basis_local(
   const Vector<double> &s,
   Shape &div_q_basis_ds) const
 {
  div_q_basis_ds(0) = Sign_edge[0]*2*std::sqrt(2);
  div_q_basis_ds(1) = Sign_edge[1]*2;
  div_q_basis_ds(2) = Sign_edge[2]*2;

  // Scale the basis by the ratio of the length of the edge to the length of
  // the corresponding edge on the reference element
  // hierher explain please
  scale_basis(div_q_basis_ds);
 }

//===========================================================================
 /// Return the number of flux interpolation points along each edge 
 /// of the element
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<0>::nedge_flux_interpolation_point() const
 {
  return 1;
 }

//===========================================================================
 /// Return the equation number of the n-th pressure degree of freedom
//===========================================================================
 template<>
 int TRaviartThomasDarcyElement<0>::p_local_eqn(const unsigned &n) const
 {
  return this->internal_local_eqn(P_internal_data_index,n);
 }

//===========================================================================
 /// Return the nth pressure value
//===========================================================================
 template<>
 double TRaviartThomasDarcyElement<0>::p_value(const unsigned &n) const
 {
  return this->internal_data_pt(P_internal_data_index)->value(n);
 }

//===========================================================================
 /// Return the total number of pressure basis functions
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<0>::np_basis() const
 {
  return 1;
 }

//===========================================================================
 /// Compute the pressure basis
//===========================================================================
 template<>
 void TRaviartThomasDarcyElement<0>::get_p_basis(const Vector<double> &s,
                                                 Shape &p_basis) const
 {
  p_basis(0) = 1.0;
 }



//===========================================================================
/// Recovery order for Z2 error estimator
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<0>::nrecovery_order()
 {
  return 2; // Need to experiment with this...
 }

//===========================================================================
 /// The number of values stored at each node: A single flux dof is
 /// stored at each midside node
//===========================================================================
 template<>
 const unsigned TRaviartThomasDarcyElement<0>::Initial_Nvalue[6] =
 {0,0,0,1,1,1};


//===========================================================================
  ///  Face index associated with edge flux degree of freedom
//===========================================================================
 template<>
 const unsigned TRaviartThomasDarcyElement<0>::Face_index_of_edge_flux[3] =
 {2,0,1};


//===========================================================================
 /// Conversion scheme from an edge degree of freedom to the node it's stored at
/// Fluxes are stored at mid-side nodes
//===========================================================================
 template<>
 const unsigned TRaviartThomasDarcyElement<0>::Q_edge_conv[3] = {3,4,5};


//===========================================================================
 /// The points along each edge where the fluxes are taken to be
// hierher explain please
//===========================================================================
 template<>
 const double TRaviartThomasDarcyElement<0>::Flux_interpolation_point[1] = 
 {0.5};




//////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////
/// Second-order Raviart-Thomas based Darcy equation element
//////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////


//===========================================================================
 /// \short Constructor. Order 1 elements have 3 pressure dofs and 2 internal
 /// velocity dofs
//===========================================================================
 template<>
 TRaviartThomasDarcyElement<1>::TRaviartThomasDarcyElement() :
  TElement<2,3>(), DarcyEquations<2>(), Sign_edge(3,1)
 {
  // RT_1 elements have 2 internal degrees of freedom for q, and 3 for p
  Q_internal_data_index=this->add_internal_data(new Data(2));
  P_internal_data_index=this->add_internal_data(new Data(3));
 }

//===========================================================================
 /// Destructor
//===========================================================================
 template<>
 TRaviartThomasDarcyElement<1>::~TRaviartThomasDarcyElement()
 {
 }


//===========================================================================
 /// Return the number of edge basis functions for q
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<1>::nq_basis_edge() const
 {
  return 6;
 }


//===========================================================================
 /// Return the number of internal basis functions for q
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<1>::nq_basis_internal() const
 {
  return 2;
 }

//===========================================================================
 /// Compute the local form of the q basis at local coordinate s
//===========================================================================
 template<>
 void TRaviartThomasDarcyElement<1>::get_q_basis_local(const Vector<double> &s,
                                                       Shape &q_basis) const
 {
  // RT_1 basis functions

  Vector<double> g1_vect=edge_flux_interpolation_point(0,0);
  Vector<double> g2_vect=edge_flux_interpolation_point(0,1);
  double g1=g1_vect[0];
  double g2=g2_vect[0];
  q_basis(0,0) = Sign_edge[0]*std::sqrt(2.0)*s[0]*(s[1]-g2)/(g1-g2);
  q_basis(0,1) = Sign_edge[0]*std::sqrt(2.0)*s[1]*(s[1]-g2)/(g1-g2);

  q_basis(1,0) = Sign_edge[0]*std::sqrt(2.0)*s[0]*(s[1]-g1)/(g2-g1);
  q_basis(1,1) = Sign_edge[0]*std::sqrt(2.0)*s[1]*(s[1]-g1)/(g2-g1);


  g1_vect=edge_flux_interpolation_point(1,0);
  g2_vect=edge_flux_interpolation_point(1,1);
  g1=g1_vect[0];
  g2=g2_vect[0];
  q_basis(2,0) = Sign_edge[1]*(s[0]-1.0)*(s[1]-g1)/(g2-g1);
  q_basis(2,1) = Sign_edge[1]*s[1]*(s[1]-g1)/(g2-g1);

  q_basis(3,0) = Sign_edge[1]*(s[0]-1.0)*(s[1]-g2)/(g1-g2);
  q_basis(3,1) = Sign_edge[1]*s[1]*(s[1]-g2)/(g1-g2);


  g1_vect=edge_flux_interpolation_point(2,0);
  g2_vect=edge_flux_interpolation_point(2,1);
  g1=g1_vect[0];
  g2=g2_vect[0];
  q_basis(4,0) = Sign_edge[2]*s[0]*(s[0]-g2)/(g1-g2);
  q_basis(4,1) = Sign_edge[2]*(s[1]-1.0)*(s[0]-g2)/(g1-g2);

  q_basis(5,0) = Sign_edge[2]*s[0]*(s[0]-g1)/(g2-g1);
  q_basis(5,1) = Sign_edge[2]*(s[1]-1.0)*(s[0]-g1)/(g2-g1);

  q_basis(6,0) = s[1]*s[0];
  q_basis(6,1) = s[1]*(s[1]-1.0);

  q_basis(7,0) = s[0]*(s[0]-1.0);
  q_basis(7,1) = s[0]*s[1];
 }


//===========================================================================
 /// Compute the local form of the q basis and dbasis/ds at local coordinate s
//===========================================================================
 template<>
 void TRaviartThomasDarcyElement<1>::get_div_q_basis_local(
   const Vector<double> &s,
   Shape &div_q_basis_ds) const
 {

  Vector<double> g1_vect=edge_flux_interpolation_point(0,0);
  Vector<double> g2_vect=edge_flux_interpolation_point(0,1);
  double g1=g1_vect[0];
  double g2=g2_vect[0];
  div_q_basis_ds(0) = Sign_edge[0]*std::sqrt(2.0)*(3.0*s[1]-2.0*g2)/(g1-g2);
  div_q_basis_ds(1) = Sign_edge[0]*std::sqrt(2.0)*(2.0*g1-3.0*s[1])/(g1-g2);


  g1_vect=edge_flux_interpolation_point(1,0);
  g2_vect=edge_flux_interpolation_point(1,1);
  g1=g1_vect[0];
  g2=g2_vect[0];
  div_q_basis_ds(2) = Sign_edge[1]*(2.0*g1-3.0*s[1])/(g1-g2);
  div_q_basis_ds(3) = Sign_edge[1]*(3.0*s[1]-2.0*g2)/(g1-g2);



  g1_vect=edge_flux_interpolation_point(2,0);
  g2_vect=edge_flux_interpolation_point(2,1);
  g1=g1_vect[0];
  g2=g2_vect[0];
  div_q_basis_ds(4) = Sign_edge[2]*(3.0*s[0]-2.0*g2)/(g1-g2);
  div_q_basis_ds(5) = Sign_edge[2]*(2.0*g1-3.0*s[0])/(g1-g2);

  div_q_basis_ds(6) = 3.0*s[1]-1.0;
  div_q_basis_ds(7) = 3.0*s[0]-1.0;

  // Scale the basis by the ratio of the length of the edge to the length of
  // the corresponding edge on the reference element
  scale_basis(div_q_basis_ds);
 }

//===========================================================================
/// Return the number of flux_interpolation points along each edge of 
/// the element
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<1>::nedge_flux_interpolation_point() const
 {
  return 2;
 }

//===========================================================================
 /// Return the equation number of the n-th pressure degree of freedom
//===========================================================================
 template<>
 int TRaviartThomasDarcyElement<1>::p_local_eqn(const unsigned &n) const
 {
  return this->internal_local_eqn(P_internal_data_index,n);
 }

//===========================================================================
 /// Return the nth pressure value
//===========================================================================
 template<>
 double TRaviartThomasDarcyElement<1>::p_value(const unsigned &n) const
 {
  return this->internal_data_pt(P_internal_data_index)->value(n);
 }

//===========================================================================
 /// Return the total number of pressure basis functions
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<1>::np_basis() const
 {
  return 3;
 }

//===========================================================================
 /// Compute the pressure basis
//===========================================================================
 template<>
 void TRaviartThomasDarcyElement<1>::get_p_basis(const Vector<double> &s,
                                                 Shape &p_basis) const
 {
  p_basis(0) = 1.0;
  p_basis(1) = s[0];
  p_basis(2) = s[1];
 }


//===========================================================================
/// Recovery order for Z2 error estimator
//===========================================================================
 template<>
 unsigned TRaviartThomasDarcyElement<1>::nrecovery_order()
 {
  return 2; // Need to experiment with this...
 }

//===========================================================================
 /// The number of values stored at each node. Two flux values are stored
 /// at each midside node.
//===========================================================================
 template<>
 const unsigned TRaviartThomasDarcyElement<1>::Initial_Nvalue[6] =
 {0,0,0,2,2,2};


//===========================================================================
  ///  Face index associated with edge flux degree of freedom
//===========================================================================
 template<>
 const unsigned TRaviartThomasDarcyElement<1>::Face_index_of_edge_flux[6] =
 {2,2,0,0,1,1};

//===========================================================================
 /// Conversion scheme from an edge degree of freedom to the node it's stored at
/// Fluxes are stored at midside nodes
//===========================================================================
 template<>
 const unsigned TRaviartThomasDarcyElement<1>::Q_edge_conv[3] = {3,4,5};


//===========================================================================
 /// The points along each edge where the fluxes are taken to be
//===========================================================================
 template<>
 const double TRaviartThomasDarcyElement<1>::Flux_interpolation_point[2] =
  {0.5-std::sqrt(3.0)/6.0,
   0.5+std::sqrt(3.0)/6.0};



//===========================================================================
 // Force building of templates
//===========================================================================
 template class TRaviartThomasDarcyElement<0>;
 template class TRaviartThomasDarcyElement<1>;

} // End of oomph namespace