refineable_spherical_advection_diffusion_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.
//LIC// 
//LIC// This library is distributed in the hope that it will be useful,
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//LIC// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
//LIC// Lesser General Public License for more details.
//LIC// 
//LIC// You should have received a copy of the GNU Lesser General Public
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//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
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//LIC//====================================================================
#include "refineable_spherical_advection_diffusion_elements.h"

namespace oomph
{


//==========================================================================
/// Add  the element's contribution to the elemental residual vector 
/// and/or elemental jacobian matrix.
/// This function overloads the standard version so that the possible
/// presence of hanging nodes is taken into account.
//=========================================================================
void RefineableSphericalAdvectionDiffusionEquations::
fill_in_generic_residual_contribution_spherical_adv_diff(
 Vector<double> &residuals, 
 DenseMatrix<double> &jacobian, 
 DenseMatrix<double> 
 &mass_matrix,
 unsigned flag)
{

//Find out how many nodes there are in the element
const unsigned n_node = nnode();
 
//Get the nodal index at which the unknown is stored
 const unsigned u_nodal_index = this->u_index_spherical_adv_diff();

//Set up memory for the shape and test functions
 Shape psi(n_node), test(n_node);
 DShape dpsidx(n_node,2), dtestdx(n_node,2);

//Set the value of n_intpt
const unsigned n_intpt = integral_pt()->nweight();

//Set the Vector to hold local coordinates
Vector<double> s(2);

//Get Peclet number
const double scaled_peclet = this->pe();

//Get the Peclet number multiplied by the Strouhal number
const double scaled_peclet_st = this->pe_st();

//Integers used to store the local equation number and local unknown
//indices for the residuals and jacobians
int local_eqn=0, local_unknown=0;

// Local storage for pointers to hang_info objects
HangInfo *hang_info_pt=0, *hang_info2_pt=0;

//Local variable to determine the ALE stuff
// bool ALE_is_disabled_flag = this->ALE_is_disabled; 

//Loop over the integration points
for(unsigned ipt=0;ipt<n_intpt;ipt++)
 {
  
  //Assign values of s
  for(unsigned i=0;i<2;i++) s[i] = integral_pt()->knot(ipt,i);
  
  //Get the integral weight
  double w = integral_pt()->weight(ipt);
  
  //Call the derivatives of the shape and test functions
  double J = 
   this->dshape_and_dtest_eulerian_at_knot_spherical_adv_diff(ipt,psi,dpsidx,
                                                              test,dtestdx);
  
  //Premultiply the weights and the Jacobian
  double W = w*J;
  
  //Calculate local values of the function, initialise to zero
  double dudt=0.0;
  double interpolated_u=0.0;
  
  //These need to be a Vector to be ANSI C++, initialise to zero
  Vector<double> interpolated_x(2,0.0);
  Vector<double> interpolated_dudx(2,0.0);
  //Vector<double> mesh_velocity(DIM,0.0);
  
  //Calculate function value and derivatives:
  //-----------------------------------------
  
  // Loop over nodes
  for(unsigned l=0;l<n_node;l++) 
   {
    //Get the value at the node
    double u_value = this->nodal_value(l,u_nodal_index);
    interpolated_u += u_value*psi(l);
    dudt += this->du_dt_spherical_adv_diff(l)*psi(l);
    // Loop over directions
    for(unsigned j=0;j<2;j++)
     {
      interpolated_x[j] += nodal_position(l,j)*psi(l);
      interpolated_dudx[j] += u_value*dpsidx(l,j);
     }
   }
  
  //Get the mesh velocity, if required
/* if (!ALE_is_disabled_flag)
   {
   for(unsigned l=0;l<n_node;l++) 
   {
   // Loop over directions
   for(unsigned j=0;j<2;j++)
   {
   mesh_velocity[j] += dnodal_position_dt(l,j)*psi(l);
   }
   }
   }*/
  
  
  //Get body force
  double source;
  this->get_source_spherical_adv_diff(ipt,interpolated_x,source);
  
  
  //Get wind
  //--------
  Vector<double> wind(3);
  this->get_wind_spherical_adv_diff(ipt,s,interpolated_x,wind);
  
  //r is the first position component
  double r = interpolated_x[0];
  //theta is the second position component
  double sin_th = sin(interpolated_x[1]);
  //dS is the area weighting
  double dS = r*r*sin_th;
  
  
  // Assemble residuals and Jacobian
  //================================
  
  // Loop over the nodes for the test functions 
  for(unsigned l=0;l<n_node;l++)
   {
    //Local variables to store the number of master nodes and 
    //the weight associated with the shape function if the node is hanging
    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 number of master nodes
    for(unsigned m=0;m<n_master;m++)
     {
      //Get the local equation number and hang_weight
      //If the node is hanging
      if(is_node_hanging)
       {
        //Read out the local equation from the master node
        local_eqn = this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                         u_nodal_index);
        //Read out the weight from the master node
        hang_weight = hang_info_pt->master_weight(m);
       }
      //If the node is not hanging
      else
       {
        //The local equation number comes from the node itself
        local_eqn = this->nodal_local_eqn(l,u_nodal_index);
        //The hang weight is one
        hang_weight = 1.0;
       }
      
      //If the nodal equation is not a boundary conditino
      if(local_eqn >= 0) 
       {
        //Add du/dt and body force/source term here 
        residuals[local_eqn] -= 
         (scaled_peclet_st*dudt + source)*dS*test(l)*W*hang_weight;
       
       //The Advection Diffusion bit itself
       residuals[local_eqn] -= 
        //radial terms
        (dS*interpolated_dudx[0]*
         (scaled_peclet*wind[0]*test(l) + dtestdx(l,0)) +
         //azimuthal terms
         (sin_th*interpolated_dudx[1]*
          (r*scaled_peclet*wind[1]*test(l) + dtestdx(l,1))))*W*hang_weight;
       
       // Calculate the Jacobian
       if(flag)
        {
         //Local variables to store the number of master nodes
         //and the weights associated with each hanging node
         unsigned n_master2=1; double hang_weight2=1.0;
         //Loop over the nodes for the variables
         for(unsigned l2=0;l2<n_node;l2++)
          { 
           //Local bool (is the node hanging)
           bool is_node2_hanging = this->node_pt(l2)->is_hanging();
           //If the node is hanging, get the number of master nodes
           if(is_node2_hanging)
            {
             hang_info2_pt = this->node_pt(l2)->hanging_pt();
             n_master2 = hang_info2_pt->nmaster();
            }
           //Otherwise there is one master node, the node itself
           else
            {
             n_master2 = 1;
            }
           
           //Loop over the master nodes
           for(unsigned m2=0;m2<n_master2;m2++)
            {
             //Get the local unknown and weight
             //If the node is hanging
             if(is_node2_hanging)
              {
               //Read out the local unknown from the master node
               local_unknown = 
                this->local_hang_eqn(hang_info2_pt->master_node_pt(m2),
                                     u_nodal_index);
               //Read out the hanging weight from the master node
               hang_weight2 = hang_info2_pt->master_weight(m2);
              }
             //If the node is not hanging
             else
              {
               //The local unknown number comes from the node
               local_unknown = this->nodal_local_eqn(l2,u_nodal_index);
               //The hang weight is one
               hang_weight2 = 1.0;
              }
             
             //If the unknown is not pinned
             if(local_unknown >= 0)
              {
               //Add contribution to Elemental Matrix
               // Mass matrix du/dt term
               jacobian(local_eqn,local_unknown) 
                -= scaled_peclet_st*test(l)*psi(l2)*
                this->node_pt(l2)->time_stepper_pt()->weight(1,0)
                *dS*W*hang_weight*hang_weight2;
               
               //Add contribution to mass matrix
               if(flag==2)
                {
                 mass_matrix(local_eqn,local_unknown) +=
                  scaled_peclet_st*test(l)*psi(l2)*dS*
                  W*hang_weight*hang_weight2;
                }
               
               //Add contribution to Elemental Matrix
               //Assemble Jacobian term
               jacobian(local_eqn,local_unknown) -= 
                //radial terms
                (dS*dpsidx(l2,0)*
                 (scaled_peclet*wind[0]*test(l) + dtestdx(l,0)) +
                 //azimuthal terms
                 (sin_th*dpsidx(l2,1)*
                  (r*scaled_peclet*wind[1]*test(l) + dtestdx(l,1))))*W*
                hang_weight*hang_weight2;
              }
            } //End of loop over master nodes
          } //End of loop over nodes
        } //End of Jacobian calculation
       
      } //End of non-zero equation
     
    } //End of loop over the master nodes for residual
   } //End of loop over nodes
  
 } // End of loop over integration points
}



//====================================================================
// Force build of templates
//====================================================================
template class RefineableQSphericalAdvectionDiffusionElement<2>;
template class RefineableQSphericalAdvectionDiffusionElement<3>;
template class RefineableQSphericalAdvectionDiffusionElement<4>;

}