NonIsothermalAxisymmetricQCrouzeixRaviartElement Class Reference

#include <non_isothermal_axisym_nst_elements.h>

Inheritance diagram for NonIsothermalAxisymmetricQCrouzeixRaviartElement:

Public Types
typedef void(*	ViscosityRatioFctPt) (double &temperature, double &result)

Public Member Functions
	NonIsothermalAxisymmetricQCrouzeixRaviartElement ()
unsigned	required_nvalue (const unsigned &n) const
void	output (ostream &outfile)
	Overload the standard output function with the broken default. More...
void	output (ostream &outfile, const unsigned &nplot)
void	output (FILE *file_pt)
	C-style output function: Broken default. More...
void	output (FILE *file_pt, const unsigned &n_plot)
	C-style output function: Broken default. More...
void	output_fct (ostream &outfile, const unsigned &Nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output function for an exact solution: Broken default. More...
unsigned	u_index_axisym_adv_diff () const
void	compute_error (ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
ViscosityRatioFctPt &	viscosity_ratio_fct_pt ()
	Access function: Pointer to viscosity ratio function. More...
ViscosityRatioFctPt	viscosity_ratio_fct_pt () const
	Access function: Pointer to viscosity ratio function. Const version. More...
virtual void	get_viscosity_ratio_axisym_nst (const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, double &visco)
void	get_wind_axisym_adv_diff (const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &wind) const
void	fill_in_contribution_to_residuals (Vector< double > &residuals)
void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)

Private Attributes
ViscosityRatioFctPt	Viscosity_ratio_fct_pt

Detailed Description

A class that solves the nonisothermal melt spinning problem using the axisymmetric Navier–Stokes and energy equations by coupling two pre- existing classes. The QSteadyAxisymAdvectionDiffusionElement<Nnode1d> with bi-quadratic interpolation for the scalar variable (temperature) and QCrouzeixRaviartElement which solves the Navier–Stokes equations using bi-quadratic interpolation for the velocities and a discontinuous bi-linear interpolation for the pressure. Note that we are free to choose the order in which we store the variables at the nodes. In this case we choose to store the variables in the order fluid velocities followed by temperature. We must, therefore, overload the function AxisymAdvectionDiffusionEquations::u_index_axisym_adv_diff() to indicate that the temperature is stored at the 3-th position not the 0-th. We do not need to overload the corresponding function in the AxisymmetricNavierStokesEquations class because the velocities are stored first.

Member Typedef Documentation

ViscosityRatioFctPt

typedef void(* NonIsothermalAxisymmetricQCrouzeixRaviartElement::ViscosityRatioFctPt) (double &temperature, double &result)

Function pointer to the function that specifies the viscosity ratio as function of the temperature.

Constructor & Destructor Documentation

NonIsothermalAxisymmetricQCrouzeixRaviartElement()

NonIsothermalAxisymmetricQCrouzeixRaviartElement::NonIsothermalAxisymmetricQCrouzeixRaviartElement ( )

inline

Constructor: call the QSteadyAxisymAdvectionDiffusionElement and AxisymmetricQCrouzeixRaviartElement

                                                    :  
  QSteadyAxisymAdvectionDiffusionElement<3>(),
  AxisymmetricQCrouzeixRaviartElement(),
  Viscosity_ratio_fct_pt(0)
  {}

Member Function Documentation

compute_error()

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::compute_error ( ostream &  outfile, FiniteElement::SteadyExactSolutionFctPt  exact_soln_pt, double &  error, double &  norm  )

inline

Validate against exact solution. Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element Call the broken default

 {
  FiniteElement::compute_error(outfile,exact_soln_pt,error,norm);
 }

References oomph::compute_error(), and calibrate::error.

fill_in_contribution_to_jacobian()

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::fill_in_contribution_to_jacobian ( Vector< double > &  residuals, DenseMatrix< double > &  jacobian  )

inline

Compute the element's residual vector and the Jacobian matrix. Jacobian is computed by finite-differencing.

  {
   // This function computes the Jacobian by finite-differencing
   FiniteElement::fill_in_contribution_to_jacobian(residuals,jacobian);
  }

References oomph::fill_in_contribution_to_jacobian().

fill_in_contribution_to_residuals()

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::fill_in_contribution_to_residuals ( Vector< double > &  residuals )

inline

Calculate the element's contribution to the residual vector. Recall that fill_in_* functions MUST NOT initialise the entries in the vector to zero. This allows us to call the fill_in_* functions of the constituent single-physics elements sequentially, without wiping out any previously computed entries.

  {
   //Fill in the residuals of the Navier-Stokes equations
   AxisymmetricNavierStokesEquations::fill_in_contribution_to_residuals(residuals);
 
   //Fill in the residuals of the advection-diffusion eqautions
   SteadyAxisymAdvectionDiffusionEquations::fill_in_contribution_to_residuals(residuals);
  }

References oomph::fill_in_contribution_to_residuals().

get_viscosity_ratio_axisym_nst()

virtual void NonIsothermalAxisymmetricQCrouzeixRaviartElement::get_viscosity_ratio_axisym_nst ( const unsigned &  ipt, const Vector< double > &  s, const Vector< double > &  x, double &  visco  )

inlinevirtual

Overload the viscosity ratio in the Navier-Stokes equations This provides the coupling from axisymmetric advection-diffusion equations to the Axisymmetric Navier–Stokes equations.

  {
   //If the function pointer is zero return zero
   if (Viscosity_ratio_fct_pt == 0)
    {
     visco = *Viscosity_Ratio_pt;
    }
   //Otherwise call the function
   else
    {
     //Get the temperature
     double interpolated_t = this->interpolated_u_adv_diff(s);
 
     // Valuate viscosity ratio
     (*Viscosity_ratio_fct_pt)(interpolated_t,visco);
    }
 
/*    //Get the temperature */
/*    const double interpolated_t = this->interpolated_u_adv_diff(s); */
 
   
/*    // Parameters that modeling the viscosity */
/*    double G = 1.0; */
/*    double eta = 0.0; */
 
/*    visco = G*exp(eta*(1.0-interpolated_t)); */
 
  } // end of get_visco_axisym_nst

References s, and Viscosity_ratio_fct_pt.

get_wind_axisym_adv_diff()

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::get_wind_axisym_adv_diff ( const unsigned &  ipt, const Vector< double > &  s, const Vector< double > &  x, Vector< double > &  wind  ) const

inline

Overload the wind function in the advection-diffusion equations. This provides the coupling from the Navier–Stokes equations to the advection-diffusion equations because the wind is the fluid velocity.

 {
   //The wind function is simply the velocity at the points
   this->interpolated_u_axi_nst(s,wind);
 } // end of get_wind_axisym_adv_diff

References s.

output() [1/4]

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::output ( FILE *  file_pt )

inline

C-style output function: Broken default.

  {
   FiniteElement::output(file_pt);
  }

References output().

output() [2/4]

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::output ( FILE *  file_pt, const unsigned &  n_plot  )

inline

C-style output function: Broken default.

  {
   FiniteElement::output(file_pt,n_plot);
  }

References output().

output() [3/4]

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::output ( ostream &  outfile )

inline

Overload the standard output function with the broken default.

  {
   FiniteElement::output(outfile);
  }

References output().

output() [4/4]

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::output ( ostream &  outfile, const unsigned &  nplot  )

inline

Output function:
Output r, z, u, w, v, p, theta at Nplot^2 plot points

  {
   //vector of local coordinates
   Vector<double> s(2);
   
   // 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 (r,z) of the plot point
     for(unsigned i=0;i<2;i++) 
      {
       outfile << this->interpolated_x(s,i) << " ";
      }
     
     // Output the fluid velocities (u,w,v) at the plot point
     for(unsigned i=0;i<3;i++) 
      {
       outfile << this->interpolated_u_axi_nst(s,i) << " ";
      }
     
     // Output the fluid pressure at the plot point
     outfile << this->interpolated_p_axi_nst(s)  << " ";
  
     // Output the temperature (the advected variable) at the plot point
     outfile << this->interpolated_u_adv_diff(s) << std::endl;   
    }
   outfile << std::endl;
   
   // Write tecplot footer (e.g. FE connectivity lists)
   this->write_tecplot_zone_footer(outfile,nplot);
  } //End of output function

References i, and s.

output_fct()

void NonIsothermalAxisymmetricQCrouzeixRaviartElement::output_fct ( ostream &  outfile, const unsigned &  Nplot, FiniteElement::SteadyExactSolutionFctPt  exact_soln_pt  )

inline

Output function for an exact solution: Broken default.

  {
   FiniteElement::output_fct(outfile,Nplot,exact_soln_pt);
  }

References oomph::output_fct().

required_nvalue()

unsigned NonIsothermalAxisymmetricQCrouzeixRaviartElement::required_nvalue ( const unsigned &  n ) const

inline

The required number of values stored at the nodes is the sum of the required values of the two single-physics elements. Note that this step is generic for any multi-physics element of this type.

  {
   return ( QSteadyAxisymAdvectionDiffusionElement<3>::required_nvalue(n) +
            AxisymmetricQCrouzeixRaviartElement::required_nvalue(n) );
  }

References n.

u_index_axisym_adv_diff()

unsigned NonIsothermalAxisymmetricQCrouzeixRaviartElement::u_index_axisym_adv_diff ( ) const

inline

Overload the index at which the temperature variable is stored. We choose to store it after the fluid velocities.

  {
   return 3;
  }

viscosity_ratio_fct_pt() [1/2]

ViscosityRatioFctPt& NonIsothermalAxisymmetricQCrouzeixRaviartElement::viscosity_ratio_fct_pt ( )

inline

Access function: Pointer to viscosity ratio function.

{return Viscosity_ratio_fct_pt;}

References Viscosity_ratio_fct_pt.

viscosity_ratio_fct_pt() [2/2]

ViscosityRatioFctPt NonIsothermalAxisymmetricQCrouzeixRaviartElement::viscosity_ratio_fct_pt ( ) const

inline

Access function: Pointer to viscosity ratio function. Const version.

  {return Viscosity_ratio_fct_pt;}

References Viscosity_ratio_fct_pt.

Member Data Documentation

Viscosity_ratio_fct_pt

ViscosityRatioFctPt NonIsothermalAxisymmetricQCrouzeixRaviartElement::Viscosity_ratio_fct_pt

private

Function pointer to the function that specifies the viscosity ratio as a function of the temperature

Referenced by get_viscosity_ratio_axisym_nst(), and viscosity_ratio_fct_pt().

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The documentation for this class was generated from the following file:

• non_isothermal_axisym_nst_elements.h