advection_diffusion_reaction_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,
//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
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//LIC// 
//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
//LIC// 
//LIC//====================================================================
//Non-inline functions for Advection Diffusion elements
#include "advection_diffusion_reaction_elements.h"

namespace oomph
{

///2D Advection Diffusion elements


/// Default value for Peclet number
template<unsigned NREAGENT, unsigned DIM>
Vector<double> AdvectionDiffusionReactionEquations<NREAGENT,DIM>::
Default_dimensionless_number(NREAGENT,1.0);

//======================================================================
/// \short Compute element residual Vector and/or element Jacobian matrix 
/// and/or the mass matrix
/// 
/// flag=2: compute Jacobian, residuals and mass matrix
/// flag=1: compute Jacobian and residuals
/// flag=0: compute only residual Vector
///
/// Pure version without hanging nodes
//======================================================================
template <unsigned NREAGENT, unsigned DIM>
void  AdvectionDiffusionReactionEquations<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
 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]= 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
 unsigned n_intpt = integral_pt()->nweight();
   
 //Set the Vector to hold local coordinates
 Vector<double> s(DIM);

 //Get diffusion coefficients
 Vector<double> D = diff();

 //Get the timescales
 Vector<double> T = 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;

 //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 = 
    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] += raw_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 = raw_nodal_value(l,c_nodal_index[r]);

       //Calculate the interpolated value
       interpolated_c[r] += c_value*psi(l);
       dcdt[r] += 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)
    {
     for(unsigned l=0;l<n_node;l++) 
      {
       for(unsigned j=0;j<DIM;j++)
        {
         mesh_velocity[j] += raw_dnodal_position_dt(l,j)*psi(l);
        }
      }
    }
   

   //Get source function
   Vector<double> source(NREAGENT);
   get_source_adv_diff_react(ipt,interpolated_x,source);


   //Get wind
   Vector<double> wind(DIM);
   get_wind_adv_diff_react(ipt,s,interpolated_x,wind);

   //Get reaction terms
   Vector<double> R(NREAGENT);
   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)
    {
     get_reaction_deriv_adv_diff_react(ipt,interpolated_c,dRdC);
    }
   

   // Assemble residuals and Jacobian
   //--------------------------------
   
   // Loop over the test functions
   for(unsigned l=0;l<n_node;l++)
    {
     //Loop over the reagents
     for(unsigned r=0;r<NREAGENT;r++)
      {
       //Set the local equation number
       local_eqn = nodal_local_eqn(l,c_nodal_index[r]);
       
       /*IF it's not a boundary condition*/
       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;
         
         // 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) {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;
          }
         
         // Calculate the jacobian
         //-----------------------
         if(flag)
          {
           //Loop over the velocity shape functions again
           for(unsigned l2=0;l2<n_node;l2++)
            { 
             //Loop over the reagents again
             for(unsigned r2=0;r2<NREAGENT;r2++)
              {
               //Set the number of the unknown
               local_unknown = nodal_local_eqn(l2,c_nodal_index[r2]);
               
               //If at a non-zero degree of freedom add in the entry
               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;
                   
                   //Add the mass matrix term
                   if(flag==2)
                    {
                     mass_matrix(local_eqn,local_unknown)
                      += T[r]*test(l)*psi(l2)*W;
                    }
                   
                   //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) 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;
                    }
                   
                  } //End of diagonal terms
               
                 //Now add the cross-reaction terms
                 jacobian(local_eqn,local_unknown) -= 
                  dRdC(r,r2)*psi(l2)*test(l)*W;
                }
              }
            } 
          } //End of jacobian 
        } 
      } //End of loop over reagents
    } //End of loop over nodes
  } // End of loop over integration points
} 




//======================================================================
/// Self-test:  Return 0 for OK
//======================================================================
template <unsigned NREAGENT, unsigned DIM>
unsigned  AdvectionDiffusionReactionEquations<NREAGENT,DIM>::self_test()
{

 bool passed=true;

 // Check lower-level stuff
 if (FiniteElement::self_test()!=0)
  {
   passed=false;
  }

 // Return verdict
 if (passed)
  {
   return 0;
  }
 else
  {
   return 1;
  }
   
}


//=========================================================================
/// Integrate the reagent concentrations over the element
//========================================================================
template <unsigned NREAGENT, unsigned DIM>
void AdvectionDiffusionReactionEquations<NREAGENT, DIM>::
integrate_reagents(Vector<double> &C) const
{
 //Find out how many nodes there are
 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]= c_index_adv_diff_react(r);}
   
 //Set up memory for the shape and test functions
 Shape psi(n_node);
 DShape dpsidx(n_node,DIM);
 
 //Set the value of n_intpt
 unsigned n_intpt = integral_pt()->nweight();

 //Loop over the integration points
 for(unsigned ipt=0;ipt<n_intpt;ipt++)
  {
   //Get the integral weight
   double w = integral_pt()->weight(ipt);

   //Call the derivatives of the shape and test functions
   double J = dshape_eulerian_at_knot(ipt,psi,dpsidx);
       
   //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);

   //Calculate function value and derivatives:
   // Loop over nodes
   for(unsigned l=0;l<n_node;l++) 
    {
     //Loop over the unknown reagents
     for(unsigned r=0;r<NREAGENT;r++)
      {
       //Get the value at the node
       const double c_value = raw_nodal_value(l,c_nodal_index[r]);

       //Calculate the interpolated value
       interpolated_c[r] += c_value*psi(l);
      }
    }
     
   for(unsigned r=0;r<NREAGENT;r++)
    {
     C[r] += interpolated_c[r]*W;
    }
  } //End of loop over integration points

}






//======================================================================
/// \short Output function:
///
///   x,y,u,w_x,w_y   or    x,y,z,u,w_x,w_y,w_z
///
/// nplot points in each coordinate direction
//======================================================================
template <unsigned NREAGENT, unsigned DIM>
void  AdvectionDiffusionReactionEquations<NREAGENT,DIM>::
output(std::ostream &outfile, const unsigned &nplot)
{ 
 //Vector of local coordinates
 Vector<double> s(DIM);

 
 // Tecplot header info
 outfile << tecplot_zone_string(nplot);
 
 // Loop over plot points
 unsigned num_plot_points=nplot_points(nplot);
 for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  {
   // Get local coordinates of plot point
   get_s_plot(iplot,nplot,s);
   
   // Get Eulerian coordinate of plot point
   Vector<double> x(DIM);
   interpolated_x(s,x);
   
   for(unsigned i=0;i<DIM;i++) 
    {
     outfile << x[i] << " ";
    }
   for(unsigned i=0;i<NREAGENT;i++)
    {
     outfile << interpolated_c_adv_diff_react(s,i) << " ";
    }

   // Get the wind
   Vector<double> wind(DIM);
   // Dummy integration point needed
   unsigned ipt=0;
   get_wind_adv_diff_react(ipt,s,x,wind);
   for(unsigned i=0;i<DIM;i++) 
    {
     outfile << wind[i] << " ";
    }
   outfile  << std::endl;
   
  }

 // Write tecplot footer (e.g. FE connectivity lists)
 write_tecplot_zone_footer(outfile,nplot);

}


//======================================================================
/// C-style output function:
///
///   x,y,u   or    x,y,z,u
///
/// nplot points in each coordinate direction
//======================================================================
template <unsigned NREAGENT,unsigned DIM>
void AdvectionDiffusionReactionEquations<NREAGENT,DIM>::
output(FILE* file_pt, const unsigned &nplot)
{
 //Vector of local coordinates
 Vector<double> s(DIM);
 
 // Tecplot header info
 fprintf(file_pt,"%s",tecplot_zone_string(nplot).c_str());

 // Loop over plot points
 unsigned num_plot_points=nplot_points(nplot);
 for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  {
   
   // Get local coordinates of plot point
   get_s_plot(iplot,nplot,s);
   
   for(unsigned i=0;i<DIM;i++) 
    {
     fprintf(file_pt,"%g ",interpolated_x(s,i));

    }
   for(unsigned i=0;i<NREAGENT;i++)
    {
     fprintf(file_pt,"%g \n",interpolated_c_adv_diff_react(s,i));
    }
  }

 // Write tecplot footer (e.g. FE connectivity lists)
 write_tecplot_zone_footer(file_pt,nplot);

}



//======================================================================
 /// \short  Output exact solution
 /// 
 /// Solution is provided via function pointer.
 /// Plot at a given number of plot points.
 ///
 ///   x,y,u_exact    or    x,y,z,u_exact
//======================================================================
template <unsigned NREAGENT,unsigned DIM>
void AdvectionDiffusionReactionEquations<NREAGENT,DIM>::
output_fct(std::ostream &outfile, 
           const unsigned &nplot, 
           FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
{
 
 //Vector of local coordinates
 Vector<double> s(DIM);
 
 // Vector for coordintes
 Vector<double> x(DIM);
 
 // Tecplot header info
 outfile << tecplot_zone_string(nplot);
 
 // Exact solution Vector (here a scalar)
 Vector<double> exact_soln(1);
 
 // Loop over plot points
 unsigned num_plot_points=nplot_points(nplot);
 for (unsigned iplot=0;iplot<num_plot_points;iplot++)
  {
   
   // Get local coordinates of plot point
   get_s_plot(iplot,nplot,s);
   
   // Get x position as Vector
   interpolated_x(s,x);
   
   // Get exact solution at this point
   (*exact_soln_pt)(x,exact_soln);
   
   //Output x,y,...,u_exact
   for(unsigned i=0;i<DIM;i++)
    {
     outfile << x[i] << " ";
    }
   outfile << exact_soln[0] << std::endl;  
  }
 
 // Write tecplot footer (e.g. FE connectivity lists)
 write_tecplot_zone_footer(outfile,nplot);
 
}




//======================================================================
 /// \short Validate against exact solution
 /// 
 /// Solution is provided via function pointer.
 /// Plot error at a given number of plot points.
 ///
//======================================================================
template <unsigned NREAGENT, unsigned DIM>
void AdvectionDiffusionReactionEquations<NREAGENT,DIM>::
compute_error(std::ostream &outfile, 
              FiniteElement::SteadyExactSolutionFctPt exact_soln_pt,
              double& error, double& norm)
{ 
 
 // Initialise
 error=0.0;
 norm=0.0;

 //Vector of local coordinates
 Vector<double> s(DIM);

 // Vector for coordintes
 Vector<double> x(DIM);

 //Find out how many nodes there are in the element
 unsigned n_node = nnode();

 Shape psi(n_node);

 //Set the value of n_intpt
 unsigned n_intpt = integral_pt()->nweight();
   
 // Tecplot header info
 outfile << "ZONE" << std::endl;
   
 // Exact solution Vector (here a scalar)
 Vector<double> exact_soln(1);

 //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);

   // Get jacobian of mapping
   double J=J_eulerian(s);

   //Premultiply the weights and the Jacobian
   double W = w*J;

   // Get x position as Vector
   interpolated_x(s,x);

   // Get FE function value
   double u_fe=interpolated_c_adv_diff_react(s,0);

   // Get exact solution at this point
   (*exact_soln_pt)(x,exact_soln);

   //Output x,y,...,error
   for(unsigned i=0;i<DIM;i++)
    {
     outfile << x[i] << " ";
    }
   outfile << exact_soln[0] << " " << exact_soln[0]-u_fe << std::endl;  

   // Add to error and norm
   norm+=exact_soln[0]*exact_soln[0]*W;
   error+=(exact_soln[0]-u_fe)*(exact_soln[0]-u_fe)*W;

  }
}

//====================================================================
// Force build of templates, only building binary reactions at present
//====================================================================
///One reagent only (!)
template class AdvectionDiffusionReactionEquations<1,1>;
template class AdvectionDiffusionReactionEquations<1,2>;
template class AdvectionDiffusionReactionEquations<1,3>;

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

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

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

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

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

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

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

}