refineable_advection_diffusion_reaction_elements.cc

Go to the documentation of this file.

//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,
//LIC// but WITHOUT ANY WARRANTY; without even the implied warranty of
//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
//LIC// License along with this library; if not, write to the Free Software
//LIC// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
//LIC// 02110-1301  USA.
//LIC// 
//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
//LIC// 
//LIC//====================================================================
#include "refineable_advection_diffusion_reaction_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.
//=========================================================================
template<unsigned NREAGENT,unsigned DIM>
void RefineableAdvectionDiffusionReactionEquations<NREAGENT,DIM>::
fill_in_generic_residual_contribution_adv_diff_react(
 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
 unsigned c_nodal_index[NREAGENT];
 for(unsigned r=0;r<NREAGENT;r++) 
  {c_nodal_index[r]= this->c_index_adv_diff_react(r);}
 
 //Set up memory for the shape and test functions
 Shape psi(n_node), test(n_node);
 DShape dpsidx(n_node,DIM), dtestdx(n_node,DIM);
 
 //Set the value of n_intpt
 const unsigned n_intpt = integral_pt()->nweight();
 
 //Set the Vector to hold local coordinates
 Vector<double> s(DIM);

 //Get diffusion coefficients
 Vector<double> D = this->diff();
 
 //Get the timescales
 Vector<double> T = this->tau();
 
 //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<DIM;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_adv_diff_react(ipt,psi,dpsidx,
                                                           test,dtestdx);
   
   //Premultiply the weights and the Jacobian
   double W = w*J;
   
   //Calculate local values of the solution and its derivatives
   //Allocate
   Vector<double> interpolated_c(NREAGENT,0.0);
   Vector<double> dcdt(NREAGENT,0.0);
   Vector<double> interpolated_x(DIM,0.0);
   DenseMatrix<double> interpolated_dcdx(NREAGENT,DIM,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++) 
    {
     // Loop over directions to calculate the position
     for(unsigned j=0;j<DIM;j++)
      {
       interpolated_x[j] += nodal_position(l,j)*psi(l);
      }
     
     //Loop over the unknown reagents
     for(unsigned r=0;r<NREAGENT;r++)
      {
       //Get the value at the node
       const double c_value = nodal_value(l,c_nodal_index[r]);
       
       //Calculate the interpolated value
       interpolated_c[r] += c_value*psi(l);
       dcdt[r] += this->dc_dt_adv_diff_react(l,r)*psi(l);
       
       // Loop over directions to calculate the derivatie
       for(unsigned j=0;j<DIM;j++)
        {
         interpolated_dcdx(r,j) += c_value*dpsidx(l,j);
        }
      }
    }
   
   // Mesh velocity?
   if (!ALE_is_disabled_flag)
    {
     for(unsigned l=0;l<n_node;l++) 
      {
       for(unsigned j=0;j<DIM;j++)
        {
         mesh_velocity[j] += dnodal_position_dt(l,j)*psi(l);
        }
      }
    }
   
   //Get source function
   Vector<double> source(NREAGENT);
   this->get_source_adv_diff_react(ipt,interpolated_x,source);
   
   
   //Get wind
   Vector<double> wind(DIM);
   this->get_wind_adv_diff_react(ipt,s,interpolated_x,wind);
   
   //Get reaction terms
   Vector<double> R(NREAGENT);
   this->get_reaction_adv_diff_react(ipt,interpolated_c,R);
   
   //If we are getting the jacobian the get the derivative terms
   DenseMatrix<double> dRdC(NREAGENT);
   if(flag)
    {
     this->get_reaction_deriv_adv_diff_react(ipt,interpolated_c,dRdC);
    }
   
   // 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++)
      {
       //Loop over the number of reagents
       for(unsigned r=0;r<NREAGENT;r++)
        {
         //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),
                                            c_nodal_index[r]);
           //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,c_nodal_index[r]);
           //The hang weight is one
           hang_weight = 1.0;
          }
         
         //If the nodal equation is not a boundary conditino
         if(local_eqn >= 0) 
          {
           // Add body force/source/reaction term and time derivative 
           residuals[local_eqn] -= 
            (T[r]*dcdt[r] + source[r] + R[r])*test(l)*W*hang_weight;
           
           // The Advection Diffusion bit itself
           for(unsigned k=0;k<DIM;k++)
            {
             //Terms that multiply the test function
             double tmp = wind[k];
             //If the mesh is moving need to subtract the mesh velocity
             if(!ALE_is_disabled_flag) {tmp -= T[r]*mesh_velocity[k];}
             //Now construct the contribution to the residuals
             residuals[local_eqn] -= 
              interpolated_dcdx(r,k)*(tmp*test(l) + 
                                      D[r]*dtestdx(l,k))*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++)
                {
                 //Loop over the reagents again
                 for(unsigned r2=0;r2<NREAGENT;r2++)
                  {
                   //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),
                                           c_nodal_index[r2]);
                     //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,c_nodal_index[r2]);
                     //The hang weight is one
                     hang_weight2 = 1.0;
                    }
                   
                   //If the unknown is not pinned
                   if(local_unknown >= 0)
                    {
                     //Diagonal terms (i.e. the basic equations)
                     if(r2==r)
                      {
                       //Mass matrix term
                       jacobian(local_eqn,local_unknown) 
                        -= T[r]*test(l)*psi(l2)*
                        node_pt(l2)->time_stepper_pt()->weight(1,0)*
                        W*hang_weight*hang_weight2;
                       
                       //Add the mass matrix term
                       if(flag==2)
                        {
                         mass_matrix(local_eqn,local_unknown)
                          += T[r]*test(l)*psi(l2)*W*hang_weight*hang_weight2;
                        }
                       
                       //Add contribution to Elemental Matrix
                       for(unsigned i=0;i<DIM;i++)
                        {
                         //Temporary term used in assembly
                         double tmp = wind[i];
                         if(!ALE_is_disabled_flag) 
                          {tmp -= T[r]*mesh_velocity[i];}
                         //Now assemble Jacobian term
                         jacobian(local_eqn,local_unknown) 
                          -= 
                          dpsidx(l2,i)*(tmp*test(l)+D[r]*dtestdx(l,i))*
                          W*hang_weight*hang_weight2;
                        }
                       
                      } //End of diagonal terms
                     
                     //Now add the cross-reaction terms
                     jacobian(local_eqn,local_unknown) -= 
                      dRdC(r,r2)*psi(l2)*test(l)*W*hang_weight*hang_weight2;
                    }
                  } //End of loop over reagents
                } //End of loop over master nodes
              } //End of loop over nodes
            } //End of Jacobian calculation
           
          } //End of non-zero equation
         
        } //End of loop over reagents
      } //End of loop over the master nodes for residual
    } //End of loop over nodes
   
  } // End of loop over integration points
}



//====================================================================
// Force build of templates
//====================================================================
///One reagent
template class RefineableQAdvectionDiffusionReactionElement<1,2,2>;
template class RefineableQAdvectionDiffusionReactionElement<1,2,3>;
template class RefineableQAdvectionDiffusionReactionElement<1,2,4>;

template class RefineableQAdvectionDiffusionReactionElement<1,3,2>;
template class RefineableQAdvectionDiffusionReactionElement<1,3,3>;
template class RefineableQAdvectionDiffusionReactionElement<1,3,4>;

//Two reagents
template class RefineableQAdvectionDiffusionReactionElement<2,1,2>;
template class RefineableQAdvectionDiffusionReactionElement<2,1,3>;
template class RefineableQAdvectionDiffusionReactionElement<2,1,4>;

template class RefineableQAdvectionDiffusionReactionElement<2,2,2>;
template class RefineableQAdvectionDiffusionReactionElement<2,2,3>;
template class RefineableQAdvectionDiffusionReactionElement<2,2,4>;

template class RefineableQAdvectionDiffusionReactionElement<2,3,2>;
template class RefineableQAdvectionDiffusionReactionElement<2,3,3>;
template class RefineableQAdvectionDiffusionReactionElement<2,3,4>;

}