gen_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 $LastChangedRevision$
//LIC//
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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//====================================================================
//Non-inline functions for GeneralisedAdvection Diffusion elements
#include "gen_advection_diffusion_elements.h"

namespace oomph
{

///2D GeneralisedAdvection Diffusion elements


/// Default value for Peclet number
template<unsigned DIM>
double GeneralisedAdvectionDiffusionEquations<DIM>::Default_peclet_number=0.0;

//======================================================================
/// \short Compute element residual Vector and/or element Jacobian matrix 
/// 
/// flag=1: compute both
/// flag=0: compute only residual Vector
///
/// Pure version without hanging nodes
//======================================================================
template <unsigned DIM>
void  GeneralisedAdvectionDiffusionEquations<DIM>::
fill_in_generic_residual_contribution_cons_adv_diff(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
 const unsigned u_nodal_index = u_index_cons_adv_diff();
   
 //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 Peclet number
 const double peclet = pe();

 //Get the Peclet*Strouhal number
 const double peclet_st = 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;

 //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_cons_adv_diff(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
   double interpolated_u=0.0;
   double dudt=0.0;
   Vector<double> interpolated_x(DIM,0.0);
   Vector<double> interpolated_dudx(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++) 
    {
     //Get the value at the node
     double u_value = raw_nodal_value(l,u_nodal_index);
     interpolated_u += u_value*psi(l);
     dudt += du_dt_cons_adv_diff(l)*psi(l);
     // Loop over directions
     for(unsigned j=0;j<DIM;j++)
      {
       interpolated_x[j] += raw_nodal_position(l,j)*psi(l);
       interpolated_dudx[j] += u_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
   //-------------------
   double source;
   get_source_cons_adv_diff(ipt,interpolated_x,source);


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

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


   //Get diffusivity tensor
   DenseMatrix<double> D(DIM,DIM);
   get_diff_cons_adv_diff(ipt,s,interpolated_x,D);

   // Assemble residuals and Jacobian
   //--------------------------------
       
   // Loop over the test functions
   for(unsigned l=0;l<n_node;l++)
    {
     //Set the local equation number
     local_eqn = nodal_local_eqn(l,u_nodal_index);

     /*IF it's not a boundary condition*/
     if(local_eqn >= 0)
      {
       // Add body force/source term and time derivative 
       residuals[local_eqn] -= (peclet_st*dudt + source)*test(l)*W;
       
       // The Generalised Advection Diffusion bit itself
       for(unsigned k=0;k<DIM;k++)
        {
         //Terms that multiply the test function 
         //divergence-free wind
         double tmp = peclet*wind[k];
         //If the mesh is moving need to subtract the mesh velocity
         if(!ALE_is_disabled) {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 diuffusive term
         for(unsigned j=0;j<DIM;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))*W;
        }
       
       // Calculate the jacobian
       //-----------------------
       if(flag)
        {
         //Loop over the velocity shape functions again
         for(unsigned l2=0;l2<n_node;l2++)
          { 
           //Set the number of the unknown
           local_unknown = nodal_local_eqn(l2,u_nodal_index);
           
           //If at a non-zero degree of freedom add in the entry
           if(local_unknown >= 0)
            {
             //Mass matrix term
             jacobian(local_eqn,local_unknown) 
              -= peclet_st*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)
                += peclet_st*test(l)*psi(l2)*W;
              }

             //Add contribution to Elemental Matrix
             for(unsigned k=0;k<DIM;k++)
              {
               //Temporary term used in assembly
               double tmp = -peclet*wind[k];
               if(!ALE_is_disabled) 
                {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<DIM;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;
              }
            }
          }
        }
      }
    }


  } // End of loop over integration points
}



//======================================================================
/// Self-test:  Return 0 for OK
//======================================================================
template <unsigned DIM>
unsigned  GeneralisedAdvectionDiffusionEquations<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;
  }
   
}



//======================================================================
/// \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 DIM>
void  GeneralisedAdvectionDiffusionEquations<DIM>::output(std::ostream &outfile, 
                                               const unsigned &nplot)
{ 
 //Vector of local coordinates
 Vector<double> s(DIM);

 
 // Tecplot header info
 outfile << tecplot_zone_string(nplot);
 
 const unsigned n_node = this->nnode();
 Shape psi(n_node);
 DShape dpsidx(n_node,DIM);

 // 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] << " ";
    }
   outfile << interpolated_u_cons_adv_diff(s) << " ";
   
   //Get the gradients
   (void)this->dshape_eulerian(s,psi,dpsidx);
   Vector<double> interpolated_dudx(DIM,0.0);
   for(unsigned n=0;n<n_node;n++)
    {
     const double u_ = this->nodal_value(n,0);
     for(unsigned i=0;i<DIM;i++)
      {
       interpolated_dudx[i] += u_*dpsidx(n,i);
      }
    }

   for(unsigned i=0;i<DIM;i++)
    {
     outfile << interpolated_dudx[i]  << " ";
    }
    
   // Get the wind
   Vector<double> wind(DIM);
   // Dummy integration point variable needed
   unsigned ipt=0;
   get_wind_cons_adv_diff(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 DIM>
void GeneralisedAdvectionDiffusionEquations<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));

    }
   fprintf(file_pt,"%g \n",interpolated_u_cons_adv_diff(s));
  }

 // 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 DIM>
void GeneralisedAdvectionDiffusionEquations<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 DIM>
void GeneralisedAdvectionDiffusionEquations<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_u_cons_adv_diff(s);

   // 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;

  }

}

//======================================================================
/// \short Calculate the integrated value of the unknown over the element
///
//======================================================================
template <unsigned DIM>
double GeneralisedAdvectionDiffusionEquations<DIM>::integrate_u()
{ 

 // Initialise
 double sum = 0.0;

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

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

 //Find the index at which the concentration is stored
 const unsigned u_nodal_index = this->u_index_cons_adv_diff();

 //Allocate memory for the shape functions
 Shape psi(n_node);

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

 //Loop over the integration points
 for(unsigned ipt=0;ipt<n_intpt;ipt++)
  {
   //Get the integral weight
   const double w = integral_pt()->weight(ipt);
   
   //Get the shape functions
   this->shape_at_knot(ipt,psi);

   //Calculate the concentration
   double interpolated_u = 0.0;
   for(unsigned l=0;l<n_node;l++) 
    {interpolated_u += this->nodal_value(l,u_nodal_index)*psi(l);}

   // Get jacobian of mapping
   const double J=J_eulerian_at_knot(ipt);

   //Add the values to the sum
   sum += interpolated_u*w*J;
  }

 //return the sum
 return sum;
}


//======================================================================
// Set the data for the number of Variables at each node
//======================================================================
template<unsigned DIM, unsigned NNODE_1D>
const unsigned QGeneralisedAdvectionDiffusionElement<DIM,NNODE_1D>::Initial_Nvalue = 1;

//====================================================================
// Force build of templates
//====================================================================
template class GeneralisedAdvectionDiffusionEquations<1>;
template class GeneralisedAdvectionDiffusionEquations<2>;
template class GeneralisedAdvectionDiffusionEquations<3>;

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

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

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


}