BVPBerman.cpp File Reference

#include <BVP_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_left_BC
class	CppNoddy::Example::Berman_right_BC

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

Enumerations
enum	{ f , fd , fdd , fddd }

Functions
int	main ()

Enumeration Type Documentation

anonymous enum

anonymous enum

Enumerator
f
fd
fdd
fddd

Definition at line 15 of file BVPBerman.cpp.

{f, fd, fdd, fddd };

Function Documentation

main()

int main

(

)

Definition at line 79 of file BVPBerman.cpp.

{
  cout << "\n";
  cout << "=== BVP: finite-difference solution of Berman eqn ===\n";
  cout << "\n";
 
  Example::Berman_equation problem;
  Example::Berman_left_BC BC_left;
  Example::Berman_right_BC BC_right;
 
  // set the Reynolds number
  problem.Re = 1.0;
  // Reynolds number step
  double delta_Re = 0.1;
  // domain is -1 to 1
  double left = -1.0;
  double right = 1.0;
  // number of nodal points
  int N = 1401;
  // mesh
  DenseVector<double> nodes( Utility::uniform_node_vector( left, right, N ) );
  // Example tolerance
  const double tol = 1.e-4;
 
  // pass it to the ode
  ODE_BVP<double> ode( &problem, nodes, &BC_left, &BC_right );
 
  // our initial guess
  for ( int i = 0; i < N; ++i )
  {
    double y = ode.solution().coord( i );
    // set f(y)
    ode.solution()( i, f ) = 1.5 * ( y - y * y * y / 3 );
    // set f'(y)
    ode.solution()( i, fd ) = 1.5 * ( 1 - y * y );
    // set f''(y)
    ode.solution()( i, fdd ) = -3 * y;
    // set f''(y)
    ode.solution()( i, fddd ) = -3;
  }
 
  // zero-order continuation in Re
  do
  {
    // solve the problem using 2nd order finite-difference
    try
    {
      try
      {
        ode.solve2();
      }
      catch ( const std::runtime_error& error )
      {
        cout << " \033[1;31;48m  * FAILED THROUGH EXCEPTION BEING RAISED \033[0m\n";
        return 1;
      }
    }
    catch ( const ExceptionBifurcation& bifn )
    {
      cout << " Bifurcation detected between Re = " << problem.Re - delta_Re
           << " and Re = " << problem.Re << "\n";
      cout << " Continuing further.\n";
    }
    problem.Re += delta_Re;
 
  }
  while ( problem.Re < 10.0 + tol );
 
 
  // compare against the Shoot_Berman data at Re = 10
  // data to be compared is f''(y) at y = -1
  if ( std::abs( 5.99898 - ode.solution()( 0, fdd ) ) > tol )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout << std::abs( 5.99898 - ode.solution()( 0, fdd ) ) << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
}

References f, fd, fdd, fddd, CppNoddy::Example::Berman_equation::Re, CppNoddy::ODE_BVP< _Type, _Xtype >::solution(), CppNoddy::ODE_BVP< _Type, _Xtype >::solve2(), and CppNoddy::Utility::uniform_node_vector().