BermanShooting.cpp File Reference

Solving the fourth-order Berman (porous channel) similarity equation. More...

#include <IVP_bundle.h>
#include "../Utils_Fill.h"

Go to the source code of this file.

Classes
class	CppNoddy::Example::Berman_equation
	Define the Berman equation by inheriting Equation base class. More...
class	CppNoddy::Example::Berman_residual
	Define a residual function using the boundary conditions for the Berman equation. More...

Namespaces
namespace	CppNoddy
	A collection of OO numerical routines aimed at simple (typical) applied problems in continuum mechanics.
namespace	CppNoddy::Example

Functions
int	main ()

Detailed Description

Solving the fourth-order Berman (porous channel) similarity equation.

where and is a pressure constant and is the Reynolds number based on the channel half-height and the wall suction. The boundary conditions are that and . This BVP is solved via Runge-Kutta and (vector) Newton iteration. This similarity form is an exact reduction of the Navier-Stokes equations.

Solving a BVP by converting it to an IVP like this is generally not a smart move!

Definition in file BermanShooting.cpp.

Function Documentation

main()

int main

(

)

Definition at line 100 of file BermanShooting.cpp.

{
 
  cout << "\n";
  cout << "=== BVP_Shoot: vector Newton solution of Berman eqn =\n";
  cout << "\n";
 
  Example::Berman_residual problem;
  // instantiate a Vector Newton class for the Biharmonic
  Newton<double> Berman( &problem );
 
  DenseVector<double> guess( 2, 0.0 );
  guess[ 0 ] = -2.0;
  guess[ 1 ] = 1.0;
 
  try
  {
    Berman.iterate( guess );
  }
  catch ( const std::runtime_error &error )
  {
    cout << " \033[1;31;48m  * FAILED THROUGH EXCEPTION BEING RAISED \033[0m\n";
    return 1;
  }
 
  // output the data
  std::string dirname("./DATA");
  mkdir( dirname.c_str(), S_IRWXU );
  TrackerFile my_file( "./DATA/Berman.dat" );
  my_file.push_ptr( &( problem.ode -> get_mesh() ) );
  my_file.update();
 
  // check against the known pressure constant K for Re=1.
  if ( std::abs( guess[ 1 ] - 0.70457 ) > 1.e-5 )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout.precision( 14 );
    cout << guess[ 0 ] << " " << guess[ 1 ] << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
 
 
}

References CppNoddy::Newton< _Type >::iterate(), CppNoddy::Example::Berman_residual::ode, CppNoddy::TrackerFile::push_ptr(), and CppNoddy::TrackerFile::update().