BlasiusShooting.cpp File Reference

Solving the Blasius equation. More...

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

Go to the source code of this file.

Classes
class	CppNoddy::Example::Blasius_equation
	Define the Blasius equation by inheriting Equation base class. More...
class	CppNoddy::Example::Blasius_residual
	Define a residual function using the boundary conditions for the Blasius profile. 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 Blasius equation.

with and via Runge-Kutta and (scalar) Newton iteration.

Solving a BVP via local methods such as these is generally not a great way of doing things. Actually, in this case the BVP can formally be converted to an IVP and iteration can be avoided altogether. Here we check the iteration plus IVP approach by comparing it with the Cauchy problem formulation.

Definition in file BlasiusShooting.cpp.

Function Documentation

main()

int main

(

)

Definition at line 92 of file BlasiusShooting.cpp.

{
  cout << "\n";
  cout << "=== BVP_Shoot: scalar Newton solution of Blasius ====\n";
  cout << "\n";
 
  Example::Blasius_residual problem;
  // instantiate a scalar Newton class for the one Blasius residual
  Newton<double> Blasius( &problem );
 
  DenseVector<double> stress( 1, 0.0 );
  stress[ 0 ] = 1.0;
  try
  {
    Blasius.iterate( stress );
  }
  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/Blasius.dat" );
  my_file.push_ptr( &( problem.ode -> get_mesh() ) );
  my_file.update();
 
  // There is a rescaling that removes any need to iterate
  // c = f'(infty) when stress = 1 at the plate
  const double c = 1.65519036023e0;
  const double answer = 1. / pow( c, 3. / 2. );
 
  const double tol( 1.e-6 );          // A pass/fail tolerance
  if ( abs( stress[0] - answer ) > tol )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout.precision( 14 );
    cout << abs( stress[0] - answer ) << " > " << tol << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
}

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