refineable_gen_axisym_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 
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//LIC// 
//LIC//    Version 1.0; svn revision $LastChangedRevision$
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//LIC// $LastChangedDate$
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//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
//LIC// This library is free software; you can redistribute it and/or
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//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.
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//LIC//====================================================================
#include "refineable_gen_axisym_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 RefineableGeneralisedAxisymAdvectionDiffusionEquations::
fill_in_generic_residual_contribution_cons_axisym_adv_diff(
 Vector<double> &residuals, 
 DenseMatrix<double> &jacobian, 
 DenseMatrix<double> 
 &mass_matrix,
 unsigned flag)
{

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

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

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

//Get the Peclet multiplied by the Strouhal number
double 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_cons_axisym_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(2,0.0);

 //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_cons_axisym_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_cons_axisym_adv_diff(ipt,interpolated_x,source);
 
 
 //Get wind
 //--------
 Vector<double> wind(3);
 this->get_wind_cons_axisym_adv_diff(ipt,s,interpolated_x,wind);

 //Get the conserved wind (non-divergence free)
 Vector<double> conserved_wind(3);
 this->get_conserved_wind_cons_axisym_adv_diff(ipt,s,interpolated_x,
                                               conserved_wind);

 //Get diffusivity tensor
 DenseMatrix<double> D(3,3);
 this->get_diff_cons_axisym_adv_diff(ipt,s,interpolated_x,D);
 
 //r is the first component of position
 double r = interpolated_x[0];

 // 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] -= 
        (peclet_st*dudt + source)*test(l)*r*W*hang_weight;
       
       //The Mesh velocity and GeneralisedAxisymAdvection--Diffusion bit
       for(unsigned k=0;k<2;k++)
        {
         //Terms that multiply the test function 
         double tmp = peclet*wind[k];
         //If the mesh is moving need to subtract the mesh velocity
         if(!ALE_is_disabled_flag) 
          {tmp -= peclet_st*mesh_velocity[k];}
          tmp *= interpolated_dudx[k];

         //Terms that multiply the derivative of the test function
         //Advective term
         double tmp2 = - conserved_wind[k]*interpolated_u;
         //Now the diffusive term
         for(unsigned j=0;j<2;j++)
          {
           tmp2 += D(k,j)*interpolated_dudx[j];
          }
         //Now construct the contribution to the residuals
         residuals[local_eqn] -= (tmp*test(l) + tmp2*dtestdx(l,k))*r*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) 
                  -= peclet_st*test(l)*psi(l2)*
                  this->node_pt(l2)->time_stepper_pt()->weight(1,0)
                  *r*W*hang_weight*hang_weight2;
                 
                 //Add contribution to mass matrix
                 if(flag==2)
                  {
                   mass_matrix(local_eqn,local_unknown) +=
                    peclet_st*test(l)*psi(l2)*r*W*hang_weight*hang_weight2;
                  }

                 //Add contribution to Elemental Matrix
                 for(unsigned k=0;k<2;k++)
                  {
                   //Temporary term used in assembly
                   double tmp = peclet*wind[k];
                   if(!ALE_is_disabled_flag) 
                    {tmp -= peclet_st*mesh_velocity[k];}
                   tmp *= dpsidx(l2,k);
                   
                   double tmp2 = - conserved_wind[k]*psi(l2);
                   //Now the diffusive term
                   for(unsigned j=0;j<2;j++)
                    {
                     tmp2 += D(k,j)*dpsidx(l2,j);
                    }
                   
                   //Now assemble Jacobian term
                   jacobian(local_eqn,local_unknown) 
                    -= (tmp*test(l) + tmp2*dtestdx(l,k))*W*r*
                    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 RefineableQGeneralisedAxisymAdvectionDiffusionElement<2>;
template class RefineableQGeneralisedAxisymAdvectionDiffusionElement<3>;
template class RefineableQGeneralisedAxisymAdvectionDiffusionElement<4>;

}