IBVPNonlinearFast.cpp File Reference

Solving the nonlinear problem. More...

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

Go to the source code of this file.

Classes
class	CppNoddy::Example::nonlinear
class	CppNoddy::Example::BC_lower
class	CppNoddy::Example::BC_upper

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::source (const double &x, const double &y, const double &t)
int	main ()

Detailed Description

Solving the nonlinear problem.

subject to , and , . The solution is computed over a range of for and the maximum deviation away from the exact solution is found. The test fails if this deviation is larger than a set tolerance . The example is solved using the PDE_double_IBVP for problems that are parabolic in 2 coordinates with a BVP in . This is the ‘fast’ version in which a number of default finite-differenced methods are overloaded with their analytic versions.

Definition in file IBVPNonlinearFast.cpp.

Enumeration Type Documentation

anonymous enum

anonymous enum

Enumerator
U
Ud

Definition at line 20 of file IBVPNonlinearFast.cpp.

{ U, Ud };

Function Documentation

main()

int main

(

)

Definition at line 123 of file IBVPNonlinearFast.cpp.

{
  cout << "\n";
  cout << "=== double_IBVP: non-constant mass matrix example ===\n";
  cout << "\n";
 
  // instantiate the problem
  Example::nonlinear problem;
  Example::BC_lower BC_bottom;
  Example::BC_upper BC_top;
 
  // domain definition
  double top = 1.0;
  double bottom = 0.0;
  double left = 0.0;
  double right = 10.0;
  // number of (spatial) nodal points
  unsigned ny = 11;
  unsigned nx = 1001;
  // time and time step
  double t_end = 1.;
  double dt = 0.01;
 
  // construct our IBVP
  PDE_double_IBVP<double> nlin( &problem,
                                Utility::uniform_node_vector( left, right, nx ),
                                Utility::uniform_node_vector( bottom, top, ny ),
                                &BC_bottom, &BC_top );
 
  // initial conditions
  for ( unsigned i = 0; i < nx; ++i )
  {
    for ( unsigned j = 0; j < ny; ++j )
    {
      nlin.solution()( i, j, U ) = 0.0;
      nlin.solution()( i, j, Ud ) = 0.0;
    }
  }
 
  double max_error( 0.0 );
  int counter( 0 );
  do
  {
    // inlet profile is time dependent, so we set it here for the next time level
    nlin.update_previous_solution();
    // now we can alter the solution stored in the double_IBVP class to define
    // the desired x=0 'initial' conditions at the next time step
    double t_next = nlin.t() + dt;
    for ( unsigned j = 0; j < ny; ++j )
    {
      double y = nlin.solution().coord( 0, j ).second;
      nlin.solution()( 0, j, U ) = t_next * y;
      nlin.solution()( 0, j, Ud ) = t_next;
    }
    nlin.step2( dt );
    for ( unsigned i = 0; i < nx; ++i )
    {
      for ( unsigned j = 0; j < ny; ++j )
      {
        double x = nlin.solution().coord( i, j ).first;
        double y = nlin.solution().coord( i, j ).second;
        double exact_u = y * nlin.t() * exp( - x );
        max_error = max( max_error, abs( exact_u - nlin.solution()( i, j, U ) ) );
      }
    }
    ++counter;
  }
  while ( nlin.t() < t_end );
 
  const double tol( 1.e-4 );
  // check the error from the exact solution
  if ( max_error > tol )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout << " Difference = " << max_error << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
 
}

References CppNoddy::PDE_double_IBVP< _Type >::solution(), CppNoddy::PDE_double_IBVP< _Type >::step2(), CppNoddy::PDE_double_IBVP< _Type >::t(), U, Ud, CppNoddy::Utility::uniform_node_vector(), and CppNoddy::PDE_double_IBVP< _Type >::update_previous_solution().