HYP2DLinearAdvectionXY.cpp

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/// \file HYP2DLinearAdvectionXY.cpp
/// \ingroup Tests
/// \ingroup HYP_2D
/// Solving the 2D advection equation
/// \f[ Q_t + \left ( \frac{Q}{\sqrt{2}} \right )_x + \left ( \frac{Q}{\sqrt{2}} \right )_y= 0 \quad \mbox{where} \quad Q=Q(x,y,t) \f]
/// using a TVD Lax-Friedrichs scheme
/// for \f$ (x,y)\in[-1,1]\times[-1,1]\f$. The initial condition is a step.
 
#include <TwoD_HYP_bundle.h>
 
namespace CppNoddy
{
  namespace Example
  {
 
    /// Define the system
    class NlinAdv : public TwoD_Hyperbolic_System
    {
 
    public:
 
      /// Two dimemsional scalar linear advection problem
      NlinAdv() : TwoD_Hyperbolic_System( 1 )
      {}
 
      void flux_fn_x( const DenseVector<double>& x, const DenseVector<double> &q, DenseVector<double> &f ) const
      {
        f[ 0 ] = q[ 0 ] / sqrt( 2. );
      }
 
      void flux_fn_y( const DenseVector<double>& x, const DenseVector<double> &q, DenseVector<double> &f ) const
      {
        f[ 0 ] = q[ 0 ] / sqrt( 2. );
      }
 
      /// Bound the wave speed
      void max_charac_speed( const DenseVector<double> &x, const DenseVector<double> &q, DenseVector<double> &c ) const
      {
        // maximum wave speed
        c[ 0 ] = c[ 1 ] = 1.0;
      }
 
    };
 
    /// Set the initial state of the system
    void Q_init( const double &x, const double &y, DenseVector<double> &q )
    {
      if ( ( std::abs( x ) < 0.25 ) && ( std::abs( y ) < 0.25 ) )
      {
        q[ 0 ]  = 1.0;
      }
      else
      {
        q[ 0 ] = 0.0;
      }
    }
  } //end Example namespace
 
} //end CppNoddy namespace
 
 
using namespace CppNoddy;
using namespace std;
 
int main()
{
 
  cout << "\n";
  cout << "=== Hyperbolic: 2D linear advection at an angle =====\n";
  cout << "\n";
 
  // define the domain/mesh
  const double west =  1.0;
  const double east = -1.0;
  const double south =  -1.0;
  const double north = 1.0;
  const unsigned N = 51;
  DenseVector<double> faces_x = Utility::uniform_node_vector( east, west, N );
  DenseVector<double> faces_y = Utility::uniform_node_vector( south, north, N );
 
  Example::NlinAdv conservative_problem;
  TwoD_TVDLF_Mesh NlinAdv_mesh( faces_x, faces_y, &conservative_problem, Example::Q_init );
  NlinAdv_mesh.set_limiter( 1 );
 
  double asym( 0.0 );
  unsigned loop_counter( 0 );
  DenseVector<double> x1( 2, 0.0 );
  x1[ 0 ] = 0.2;
  x1[ 1 ] = 0.4;
  DenseVector<double> x2( 2, 0.0 );
  x2[ 0 ] = 0.4;
  x2[ 1 ] = 0.2;
  do
  {
    NlinAdv_mesh.update( 0.49 );
    asym = std::max( asym, std::abs( NlinAdv_mesh.get_point_values( x1 )[0] - NlinAdv_mesh.get_point_values( x2 )[0] ) );
    ++loop_counter;
  }
  while ( ( NlinAdv_mesh.get_time() < 1.0 ) && ( loop_counter < 20 ) );
 
  // problem should be antisymmetric about y = x
  if ( ( asym > 5.e-10 ) || ( loop_counter >= 1000 ) )
  {
    cout << "\033[1;31;48m  * FAILED \033[0m\n";
    cout << "asymmetry = " << asym << "\n";
    cout << "loop counter = " << loop_counter << "\n";
    return 1;
  }
  else
  {
    cout << "\033[1;32;48m  * PASSED \033[0m\n";
    return 0;
  }
 
} // end of main()