spherical_advection_diffusion_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//====================================================================
//Non-inline functions for Advection Diffusion elements in a spherical
//coordinate system
#include "spherical_advection_diffusion_elements.h"

namespace oomph
{

/// 2D Steady Axisymmetric Advection Diffusion elements

/// Default value for Peclet number
double SphericalAdvectionDiffusionEquations::
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
//======================================================================
void  SphericalAdvectionDiffusionEquations::
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
 const unsigned n_node = nnode();

 //Get the nodal index at which the unknown is stored
 const unsigned u_nodal_index = 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 Physical Variables from Element
 const double scaled_peclet = pe();

 //Get peclet number multiplied by Strouhal number
 const double scaled_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<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 = 
    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 solution and its derivatives
   //Allocate
   double interpolated_u = 0.0;
   double dudt = 0.0;
   Vector<double> interpolated_x(2,0.0);
   Vector<double> interpolated_dudx(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 = raw_nodal_value(l,u_nodal_index);
     interpolated_u += u_value*psi(l);
     dudt += du_dt_spherical_adv_diff(l)*psi(l);
     //Loop over the two coordinates directions
     for(unsigned j=0;j<2;j++)
      {
       interpolated_x[j] += raw_nodal_position(l,j)*psi(l);
       interpolated_dudx[j] += u_value*dpsidx(l,j);
      }
    }
     
   //Get source function
   //-------------------
   double source;
   get_source_spherical_adv_diff(ipt,interpolated_x,source);


   //Get wind
   //--------
   Vector<double> wind(3);
   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;

   //TEMPERATURE EQUATION (Neglected viscous dissipation) 
   //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
       residuals[local_eqn] -= (scaled_peclet_st*dudt + source)*dS*test(l)*W;
       
       //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;

       
       // 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) 
              -= scaled_peclet_st*test(l)*psi(l2)*
              node_pt(l2)->time_stepper_pt()->weight(1,0)*dS*W;
             
             //add the mass matrix term
             if(flag==2)
              {  
               mass_matrix(local_eqn,local_unknown)
                += scaled_peclet_st*test(l)*psi(l2)*dS*W;
              }

             //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;
            }
          }
        }
      }
    }


  } // End of loop over integration points
}   




//======================================================================
/// Self-test:  Return 0 for OK
//======================================================================
//template <unsigned DIM>
unsigned  SphericalAdvectionDiffusionEquations::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:
///
///   r,z,u,w_r,w_z
///
/// nplot points in each coordinate direction
//======================================================================
void SphericalAdvectionDiffusionEquations::output(std::ostream &outfile, 
                                                     const unsigned &nplot)
{ 
 //Vector of local coordinates
 Vector<double> s(2);
 
 //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(2);
   interpolated_x(s,x);
   
   for(unsigned i=0;i<2;i++) 
    {
     outfile << x[i] << " ";
    }

   //Convert to Cartesians
   outfile << x[0]*sin(x[1]) << " " << x[0]*cos(x[1]) << " ";
   //Output concentration
   outfile << this->interpolated_u_spherical_adv_diff(s) << " ";
   
   //Get the wind
   Vector<double> wind(2);
   //Dummy ipt argument needed... ?
   unsigned ipt = 0;
   get_wind_spherical_adv_diff(ipt,s,x,wind);
   for(unsigned i=0;i<2;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:
///
///   r,z,u
///
/// nplot points in each coordinate direction
//======================================================================
//template <unsigned DIM>
void SphericalAdvectionDiffusionEquations::output(FILE* file_pt,
                                                     const unsigned &nplot)
{
 //Vector of local coordinates
 Vector<double> s(2);
 
 //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<2;i++) 
    {
     fprintf(file_pt,"%g ",interpolated_x(s,i));

    }
   //Write Cartesian coordinates
   double r = interpolated_x(s,0); double theta = interpolated_x(s,1);
   fprintf(file_pt,"%g %g ",r*sin(theta),r*cos(theta));

   fprintf(file_pt,"%g \n",interpolated_u_spherical_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.
 ///
 ///   r,z,u_exact
//======================================================================
//template <unsigned DIM>
void SphericalAdvectionDiffusionEquations::output_fct(std::ostream &outfile, 
                                                         const unsigned &nplot, 
                                                         FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
  {

   //Vector of local coordinates
   Vector<double> s(2);

   //Vector for coordintes
   Vector<double> x(2);

   //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<2;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 SphericalAdvectionDiffusionEquations::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(2);

 //Vector for coordintes
 Vector<double> x(2);

 //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<2;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_spherical_adv_diff(s);

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

   //Output x,y,...,error
   for(unsigned i=0;i<2;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;

  }

}


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

//====================================================================
// Force build of templates
//====================================================================

template class QSphericalAdvectionDiffusionElement<2>;
template class QSphericalAdvectionDiffusionElement<3>;
template class QSphericalAdvectionDiffusionElement<4>;


}