IBVPDiffusionNonlinear.cpp File Reference

Solving the unstead diffusion problem: More...

#include <IBVP_bundle.h>

Go to the source code of this file.

Classes
class	CppNoddy::Example::Diffusion_equations
class	CppNoddy::Example::Diffusion_left_BC
	Define the boundary conditions. More...
class	CppNoddy::Example::Diffusion_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
double	CppNoddy::Example::A (10.0)
double	CppNoddy::Example::sigma (100.0)
int	main ()

Detailed Description

Solving the unstead diffusion problem:

with boundary conditions ; where . The initial condition is . The class constructs and solves the IBVP using 2nd order finite-differencing in both space and time over a non-uniform spatial mesh. The output is compared to the exact solution .

Definition in file IBVPDiffusionNonlinear.cpp.

Enumeration Type Documentation

anonymous enum

anonymous enum

Enumerator
U
Ud

Definition at line 14 of file IBVPDiffusionNonlinear.cpp.

{ U, Ud };

Function Documentation

main()

int main

(

)

Definition at line 100 of file IBVPDiffusionNonlinear.cpp.

{
  cout << "\n";
  cout << "=== IBVP: A nonlinear diffusion problem  ============\n";
  cout << "\n";
 
  // define the system
  Example::Diffusion_equations problem;
  // define the boundary conditions
  Example::Diffusion_left_BC BC_left;
  Example::Diffusion_right_BC BC_right;
 
  // domain definition
  double left = 0.0;
  double right = 1.0;
  // number of (spatial) nodal points
  unsigned ny = 400;
  // time step
  double dt = 0.005;
  // number of time steps
  unsigned max_steps = ( unsigned ) ( 2.0 / dt );
 
  // construct our IBVP with more nodes near the boundary
  PDE_IBVP<double> diffusion( &problem, Utility::power_node_vector( left, right, ny, 1.0 ), &BC_left, &BC_right );
  //
  for ( unsigned i = 0; i < ny; ++i )
  {
    double y( diffusion.solution().coord(i) );
    diffusion.solution()( i, U ) = (1+y) + Example::A*sin(M_PI*y);
    diffusion.solution()( i, Ud ) = 1 + Example::A*M_PI*cos(M_PI*y);
  }
 
  // set up output details
  std::string dirname("./DATA");
  mkdir( dirname.c_str(), S_IRWXU );
  TrackerFile metric( "./DATA/IBVP_diffusion_metric.dat" );
  metric.push_ptr( &diffusion.coord(), "time" );
  metric.push_ptr( &diffusion.solution()( 0, Ud ), "y=0 derivative" );
  metric.header();
  TrackerFile profs( "./DATA/IBVP_diffusion_profs.dat" );
  profs.push_ptr( &diffusion.coord(), "time" );
  profs.push_ptr( &diffusion.solution(), "solution" );
  profs.header();
 
  Timer timer;
  timer.start();
  //
  double max_error( 0.0 );
  // time step
  for ( unsigned i = 1; i < max_steps; ++i )
  {
    // take a time step
    try
    {
      diffusion.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 % 20 == 0 )
    {
      cout << diffusion.coord() << "\n";
      profs.update();
      profs.newline();
    }
    timer.counter()++;
    metric.update();
    //
    double yy( 0.5 );
    double Uexact = 1 + yy + Example::A*exp(-diffusion.coord())*sin(M_PI*yy);
    double error = diffusion.solution().get_interpolated_vars( 0.5 )[ U ] - Uexact;
    max_error = std::max( std::abs( error ), max_error );
    //
    // std::cout << " ****** " << diffusion.t() << " " << max_error << "\n";
  }
  timer.stop();
  timer.print();
  //
  const double tol( 1.e-4 );
  // check the BL transpiration vs the known solution
  if ( max_error > tol )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout << " Max difference over time steps = " << max_error << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
 
}

References CppNoddy::PDE_IBVP< _Type >::coord(), CppNoddy::Timer::counter(), CppNoddy::TrackerFile::header(), CppNoddy::TrackerFile::newline(), CppNoddy::Utility::power_node_vector(), CppNoddy::Timer::print(), CppNoddy::TrackerFile::push_ptr(), CppNoddy::PDE_IBVP< _Type >::solution(), CppNoddy::Timer::start(), CppNoddy::PDE_IBVP< _Type >::step2(), CppNoddy::Timer::stop(), U, Ud, and CppNoddy::TrackerFile::update().