db_navier_st_elements.h

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//LIC// Copyright (C) 2006-2022 Matthias Heil and Andrew Hazel
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//LIC//====================================================================
#ifndef DOUBLE_BUOYANT_NAVIER_STOKES_ELEMENTS_HEADER
#define DOUBLE_BUOYANT_NAVIER_STOKES_ELEMENTS_HEADER
 
//Oomph-lib headers, we require the generic, advection-diffusion-reaction,
//navier-stokes elements and fluid interface elements
#include "generic.h"
#include "advection_diffusion_reaction.h"
#include "navier_stokes.h"
 
namespace oomph
{
 
//======================class definition==============================
//=========================================================================
template<unsigned DIM>
class DoubleBuoyantQCrouzeixRaviartElement :
 public virtual QAdvectionDiffusionReactionElement<2,DIM,3>,
 public virtual QCrouzeixRaviartElement<DIM>
{
 
private:
 
 double* Ra_T_pt;
 
 double *Ra_S_pt;
 
 static double Default_Physical_Constant_Value;
 
public:
 
 DoubleBuoyantQCrouzeixRaviartElement() : 
  QAdvectionDiffusionReactionElement<2,DIM,3>(),
  QCrouzeixRaviartElement<DIM>() 
  {
   Ra_T_pt = &Default_Physical_Constant_Value;
   Ra_S_pt = &Default_Physical_Constant_Value;
  }
 
 void unfix_pressure(const unsigned &p_dof)
  {
   this->internal_data_pt(this->P_nst_internal_index)->unpin(p_dof);
  }
 
 
 unsigned required_nvalue(const unsigned &n) const
  {return (QAdvectionDiffusionReactionElement<2,DIM,3>::required_nvalue(n) +
           QCrouzeixRaviartElement<DIM>::required_nvalue(n));}
 
 const double &ra_t() const {return *Ra_T_pt;}
 
 double* &ra_t_pt() {return Ra_T_pt;}
 
 const double &ra_s() const {return *Ra_S_pt;}
 
 double* &ra_s_pt() {return Ra_S_pt;}
 
 void disable_ALE() 
  {
   //Disable ALE in both sets of equations
   NavierStokesEquations<DIM>::disable_ALE();
   AdvectionDiffusionReactionEquations<2,DIM>::disable_ALE();
  }
 
 void enable_ALE() 
  {
   //Enable ALE in both sets of equations
   NavierStokesEquations<DIM>::enable_ALE();
   AdvectionDiffusionReactionEquations<2,DIM>::enable_ALE();
  }
 
 
 void output(std::ostream &outfile) {FiniteElement::output(outfile);}
 
 // Start of output function
 void output(std::ostream &outfile, const unsigned &nplot)
  {
   //vector of local coordinates
   Vector<double> s(DIM);
   
   // Tecplot header info
   outfile << this->tecplot_zone_string(nplot);
   
   // Loop over plot points
   unsigned num_plot_points=this->nplot_points(nplot);
   for (unsigned iplot=0;iplot<num_plot_points;iplot++)
    {
     // Get local coordinates of plot point
     this->get_s_plot(iplot,nplot,s);
     
     // Output the position of the plot point
     for(unsigned i=0;i<DIM;i++) 
      {outfile << this->interpolated_x(s,i) << " ";}
     
     // Output the fluid velocities at the plot point
     for(unsigned i=0;i<DIM;i++) 
      {outfile << this->interpolated_u_nst(s,i) << " ";}
     
     // Output the fluid pressure at the plot point
     outfile << this->interpolated_p_nst(s)  << " ";
 
     //Output the temperature and the solute concentration
     for(unsigned i=0;i<2;i++)
      {
       outfile << this->interpolated_c_adv_diff_react(s,i) << " ";
      }
     outfile << "\n";
    }
   outfile << std::endl;
   
   // Write tecplot footer (e.g. FE connectivity lists)
   this->write_tecplot_zone_footer(outfile,nplot);
  } //End of output function
 
 
 void output(FILE* file_pt)
  {FiniteElement::output(file_pt);}
 
 void output(FILE* file_pt, const unsigned &n_plot)
  {FiniteElement::output(file_pt,n_plot);}
 
 void output_fct(std::ostream &outfile, const unsigned &Nplot,
                 FiniteElement::SteadyExactSolutionFctPt 
                 exact_soln_pt)
  {FiniteElement::output_fct(outfile,Nplot,exact_soln_pt);}
 
 
 void output_fct(std::ostream &outfile, const unsigned &Nplot,
                 const double& time,
                 FiniteElement::UnsteadyExactSolutionFctPt 
                 exact_soln_pt)
  {
   FiniteElement::
    output_fct(outfile,Nplot,time,exact_soln_pt);
  }
 
 // We choose to store them after the fluid velocities.
 inline unsigned c_index_adv_diff_react(const unsigned &i) const 
  {return DIM+i;}
 
 
  //Compute norm overload to NS version
  void compute_norm(double &norm)
  {QCrouzeixRaviartElement<DIM>::compute_norm(norm);}
 
 
 void compute_error(std::ostream &outfile,
                    FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt,
                    const double& time,
                    double& error, double& norm)
  {FiniteElement::compute_error(outfile,exact_soln_pt,
                                time,error,norm);}
 
 void compute_error(std::ostream &outfile,
                    FiniteElement::SteadyExactSolutionFctPt exact_soln_pt,
                    double& error, double& norm)
  {FiniteElement::compute_error(outfile,exact_soln_pt,error,norm);}
 
 void get_wind_adv_diff_react(const unsigned& ipt,
                              const Vector<double> &s, const Vector<double>& x,
                              Vector<double>& wind) const
 {
   //The wind function is simply the velocity at the points
   this->interpolated_u_nst(s,wind);
 }
 
 
 void get_body_force_nst(const double& time, const unsigned& ipt,
                         const Vector<double> &s, const Vector<double> &x,
                         Vector<double> &result)
  {
   // Get vector that indicates the direction of gravity from
   // the Navier-Stokes equations
   Vector<double> gravity(NavierStokesEquations<DIM>::g());
   
   //Get the indices at which the temp and concentration are stored
   unsigned c_index[2];
   for(unsigned r=0;r<2;r++) 
    {c_index[r] = this->c_index_adv_diff_react(r);}
 
   //Now get the shape function
   const unsigned n_node = this->nnode();
   Shape psi(n_node);
   //Get the shape functions
   this->shape(s,psi);
   //Storage for the local values of advected quantities
   Vector<double> interpolated_c(2,0.0);
   //Get the values
   for(unsigned l=0;l<n_node;l++)
    {
     for(unsigned r=0;r<2;r++)
      {
       interpolated_c[r] += this->raw_nodal_value(l,c_index[r])*psi(l);
      }
    }
 
   // Temperature and concentration-dependent body force:
   for(unsigned i=0;i<DIM;i++)
    {
                   
     result[i] = -gravity[i]*
      //Thermal contribution      //Concentration contribution
      (interpolated_c[0]*ra_t() + interpolated_c[1]*ra_s());
    }
  }
 
 void fill_in_contribution_to_residuals(Vector<double> &residuals)
  {
   //Fill in the residuals of the Navier-Stokes equations
   NavierStokesEquations<DIM>::fill_in_contribution_to_residuals(residuals);
 
   //Fill in the residuals of the advection-diffusion eqautions
   AdvectionDiffusionReactionEquations<2,DIM>::
    fill_in_contribution_to_residuals(residuals);
  }
 
 
#ifdef USE_FD_JACOBIAN_FOR_BUOYANT_Q_CROZIER_RAVIART_ELEMENT
 
 
 void fill_in_contribution_to_jacobian(Vector<double> &residuals,
                                   DenseMatrix<double> &jacobian)
  {
   // This function computes the Jacobian by finite-differencing
   FiniteElement::fill_in_contribution_to_jacobian(residuals,jacobian);
  }
 
#else
 
 void fill_in_off_diagonal_jacobian_blocks_by_fd(Vector<double> &residuals,
                                                 DenseMatrix<double> &jacobian)
  {
   //Local storage for the index in the nodes at which the
   //Navier-Stokes velocities are stored (we know that this should be 0,1,2)
   unsigned u_nodal_nst[DIM];
   for(unsigned i=0;i<DIM;i++) 
    {u_nodal_nst[i] = this->u_index_nst(i);}
 
   //Local storage for the  index at which the temperature and
   //solute are  stored
   unsigned C_nodal_adv_diff_react[2];
   for(unsigned r=0;r<2;r++)
    {C_nodal_adv_diff_react[r] = this->c_index_adv_diff_react(r);}
   
 
   //Find the total number of unknowns in the elements
   unsigned n_dof = this->ndof();
 
   //Temporary storage for residuals
   Vector<double> newres(n_dof);
 
   //Storage for local unknown and local equation
   int local_unknown =0, local_eqn = 0;
 
   //Set the finite difference step
   double fd_step = FiniteElement::Default_fd_jacobian_step;
 
   //Find the number of nodes
   unsigned n_node = this->nnode();
 
   //Calculate the contribution of the Navier--Stokes velocities to the
   //advection-diffusion equations
 
   //Loop over the nodes
   for(unsigned n=0;n<n_node;n++)
    {
     //There are DIM values of the  velocities
     for(unsigned i=0;i<DIM;i++)
      {
       //Get the local velocity equation number
       local_unknown = this->nodal_local_eqn(n,u_nodal_nst[i]);
 
       //If it's not pinned
       if(local_unknown >= 0)
        {
         //Get a pointer to the velocity value
         double *value_pt = this->node_pt(n)->value_pt(u_nodal_nst[i]); 
 
         //Save the old value
         double old_var = *value_pt;
 
         //Increment the value 
         *value_pt += fd_step;
 
         //Get the altered advection-diffusion residuals.
         //Do this using fill_in because get_residuals has never been 
         //overloaded, and will actually compute all residuals which
         //is slightly inefficient.
         for(unsigned m=0;m<n_dof;m++) {newres[m] = 0.0;}
         AdvectionDiffusionReactionEquations<2,DIM>::
          fill_in_contribution_to_residuals(newres);
 
         //Now fill in the Advection-Diffusion-Reaction sub-block
         //of the jacobian
         for(unsigned m=0;m<n_node;m++)
          {
           for(unsigned r=0;r<2;r++)
            {
             //Local equation for temperature or solute
             local_eqn = this->nodal_local_eqn(m,C_nodal_adv_diff_react[r]);
 
             //If it's not a boundary condition
             if(local_eqn >= 0)
              {
               double sum = (newres[local_eqn] - residuals[local_eqn])/fd_step;
               jacobian(local_eqn,local_unknown) = sum;
              }
            }
          }
         
         //Reset the nodal data
         *value_pt = old_var;
        }
      }
 
 
     //Calculate the contribution of the temperature to the Navier--Stokes
     //equations
     for(unsigned r=0;r<2;r++)
      {
       //Get the local equation number
       local_unknown = this->nodal_local_eqn(n,C_nodal_adv_diff_react[r]);
       
       //If it's not pinned
       if(local_unknown >= 0)
        {
         //Get a pointer to the concentration value
         double *value_pt = 
          this->node_pt(n)->value_pt(C_nodal_adv_diff_react[r]); 
         
         //Save the old value
         double old_var = *value_pt;
         
         //Increment the value (Really need access)
         *value_pt += fd_step;
         
         //Get the altered Navier--Stokes residuals
         //Do this using fill_in because get_residuals has never been 
         //overloaded, and will actually compute all residuals which
         //is slightly inefficient.
         for(unsigned m=0;m<n_dof;m++) {newres[m] = 0.0;}
         NavierStokesEquations<DIM>::fill_in_contribution_to_residuals(newres);
         
         //Now fill in the Navier-Stokes sub-block
         for(unsigned m=0;m<n_node;m++)
          {
           //Loop over the fluid velocities
           for(unsigned j=0;j<DIM;j++)
            {
             //Local fluid equation
             local_eqn = this->nodal_local_eqn(m,u_nodal_nst[j]);
             if(local_eqn >= 0)
              {
               double sum = (newres[local_eqn] - residuals[local_eqn])/fd_step;
               jacobian(local_eqn,local_unknown) = sum;
              }
            }
          }
         
         //Reset the nodal data
         *value_pt = old_var;
        }
      } //End of loop over reagents
     
    } //End of loop over nodes
  }
 
 void fill_in_contribution_to_jacobian(Vector<double> &residuals,
                                   DenseMatrix<double> &jacobian)
  {
 
   //Calculate the Navier-Stokes contributions (diagonal block and residuals)
   NavierStokesEquations<DIM>::
    fill_in_contribution_to_jacobian(residuals,jacobian);
 
   //Calculate the advection-diffusion contributions 
   //(diagonal block and residuals)
   AdvectionDiffusionReactionEquations<2,DIM>::
    fill_in_contribution_to_jacobian(residuals,jacobian);
 
   //Add in the off-diagonal blocks
   fill_in_off_diagonal_jacobian_blocks_by_fd(residuals,jacobian);
  } //End of jacobian calculation
 
#endif
 
 
 void fill_in_contribution_to_jacobian_and_mass_matrix(
  Vector<double> &residuals, DenseMatrix<double> &jacobian, 
  DenseMatrix<double> &mass_matrix)
  {
   NavierStokesEquations<DIM>::
    fill_in_contribution_to_jacobian_and_mass_matrix(
     residuals,jacobian,mass_matrix);
   
   AdvectionDiffusionReactionEquations<2,DIM>::
    fill_in_contribution_to_jacobian_and_mass_matrix(
     residuals,jacobian,mass_matrix);
 
   fill_in_off_diagonal_jacobian_blocks_by_fd(residuals,jacobian);
  }
 
 
};
 
//=========================================================================
//=========================================================================
template<>
double DoubleBuoyantQCrouzeixRaviartElement<2>::Default_Physical_Constant_Value=0.0;
 
 
//=======================================================================
//=======================================================================
template<unsigned int DIM>
class FaceGeometry<DoubleBuoyantQCrouzeixRaviartElement<DIM> >: 
public virtual QElement<DIM-1,3>
{
  public:
 FaceGeometry() : QElement<DIM-1,3>() {}
};
 
//=======================================================================
//=======================================================================
template<>
class FaceGeometry<FaceGeometry<DoubleBuoyantQCrouzeixRaviartElement<2> > >: 
public virtual PointElement
{
  public:
 FaceGeometry() : PointElement() {}
};
 
} //End of the oomph namespace
 
#endif