IBVPNonlinearAdvDiffusion.cpp File Reference

Solving the nonlinear advection diffusion equation. More...

#include <IBVP_bundle.h>

Go to the source code of this file.

Classes
class	CppNoddy::Example::Nlin_adv_equation
class	CppNoddy::Example::Nlin_adv_left_BC
class	CppNoddy::Example::Nlin_adv_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	{ U , Ud }

Functions
const double	CppNoddy::Example::eps (2.0)
double	CppNoddy::Example::source (const double &y, const double &t)
int	main ()

Detailed Description

Solving the nonlinear advection diffusion equation.

subject to and with initial condition and a source term

for some constant parameters and . This source term is chosen to allow an exact solution

against which the numerical computation is compared, by computing the maximum absolute deviation over all spatial and temporal nodes.

Definition in file IBVPNonlinearAdvDiffusion.cpp.

Enumeration Type Documentation

anonymous enum

anonymous enum

Enumerator
U
Ud

Definition at line 19 of file IBVPNonlinearAdvDiffusion.cpp.

{ U, Ud };

Function Documentation

main()

int main

(

)

Definition at line 107 of file IBVPNonlinearAdvDiffusion.cpp.

{
  cout << "\n";
  cout << "=== IBVP: Nonlinear advection diffusion =============\n";
  cout << "\n";
 
  // instantiate the problem
  Example::Nlin_adv_equation problem;
  Example::Nlin_adv_left_BC BC_left;
  Example::Nlin_adv_right_BC BC_right;
 
  // domain definition
  double left = 0.0;
  double right = 1.0;
  // number of (spatial) nodal points
  unsigned ny = 400;
  // number of time steps
  unsigned max_steps = 4000;
  // time step
  double dt = 1.0 / ( max_steps - 1 );
 
  // initial rotation frequency
  Example::Re = 1.0;
 
  // construct our IBVP
  PDE_IBVP<double> advection( &problem, Utility::uniform_node_vector( left, right, ny ), &BC_left, &BC_right );
 
  // initial conditions
  for ( unsigned i = 0; i < ny; ++i )
  {
    double y = advection.solution().coord( i );
    advection.solution()( i, U ) = 1.0 + y + Example::eps * y * ( 1 - y );
    advection.solution()( i, Ud ) = 1.0;
  }
 
  // set up output details
  std::string dirname("./DATA");
  mkdir( dirname.c_str(), S_IRWXU );
  TrackerFile my_file( "./DATA/IBVP_NlinAdvection.dat" );
  my_file.push_ptr( &advection.coord(), "time" );
  my_file.push_ptr( &advection.solution(), "Solution profile" );
  my_file.header();
 
  double max_err( 0.0 );
  // time step
  for ( unsigned i = 1; i < max_steps; ++i )
  {
    // take a time step
    try
    {
      advection.step2( dt );
    }
    catch ( const std::runtime_error &error )
    {
      cout << " \033[1;31;48m  * FAILED THROUGH EXCEPTION BEING RAISED \033[0m\n";
      return 1;
    }
    if ( i % 100 == 0 )
    {
      my_file.update();
      my_file.newline();
    }
    // generate the exact solution to compare to
    for ( unsigned i = 0; i < ny; ++i )
    {
      double y = advection.solution().coord( i );
      const double exact_solution = 1.0 + y + Example::eps * y * ( 1 - y ) * std::exp( -advection.coord() );
      max_err = std::max( max_err, std::abs( advection.solution()( i, 0 ) - exact_solution ) );
    }
  }
 
  if ( max_err > 1.e-6 )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout.precision( 14 );
    cout << 1. / ( ny - 1 ) << " " << dt << " " << max_err << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
}

References CppNoddy::PDE_IBVP< _Type >::coord(), CppNoddy::TrackerFile::header(), CppNoddy::TrackerFile::newline(), CppNoddy::TrackerFile::push_ptr(), CppNoddy::PDE_IBVP< _Type >::solution(), CppNoddy::PDE_IBVP< _Type >::step2(), U, Ud, CppNoddy::Utility::uniform_node_vector(), and CppNoddy::TrackerFile::update().