CppNoddy::Example::Shallow_2d_rad Class Reference

Define the system. More...

Inheritance diagram for CppNoddy::Example::Shallow_2d_rad:

Public Member Functions
	Shallow_2d_rad ()
	One dimemsional constant coefft acoustic problem. More...
void	flux_fn_x (const DenseVector< double > &x, const DenseVector< double > &q, DenseVector< double > &f) const
	Define the vector flux. More...
void	flux_fn_y (const DenseVector< double > &x, const DenseVector< double > &q, DenseVector< double > &f) const
	A virtual flux function for the y-derivative. More...
void	Jac_flux_fn_x (const DenseVector< double > &x, const DenseVector< double > &q, DenseMatrix< double > &J) const
	A virtual function function to define the Jacobian of the x-flux function. More...
void	Jac_flux_fn_y (const DenseVector< double > &x, const DenseVector< double > &q, DenseMatrix< double > &J) const
	A virtual function function to define the Jacobian of the y-flux function. More...
void	max_charac_speed (const DenseVector< double > &x, const DenseVector< double > &q, DenseVector< double > &c) const
	Bound the wave speed. More...
Public Member Functions inherited from CppNoddy::TwoD_Hyperbolic_System
	TwoD_Hyperbolic_System (const unsigned &order)
virtual	~TwoD_Hyperbolic_System ()
	An empty destructor, virtual since we have virtual methods. More...
virtual void	flux_fn_x (const DenseVector< double > &x, const DenseVector< double > &q, DenseVector< double > &f) const
	A virtual flux function for the x-derivative. More...
virtual void	flux_fn_y (const DenseVector< double > &x, const DenseVector< double > &q, DenseVector< double > &f) const
	A virtual flux function for the y-derivative. More...
virtual void	Jac_flux_fn_x (const DenseVector< double > &x, const DenseVector< double > &q, DenseMatrix< double > &J) const
	A virtual function function to define the Jacobian of the x-flux function. More...
virtual void	Jac_flux_fn_y (const DenseVector< double > &x, const DenseVector< double > &q, DenseMatrix< double > &J) const
	A virtual function function to define the Jacobian of the y-flux function. More...
virtual void	max_charac_speed (const DenseVector< double > &x, const DenseVector< double > &q, DenseVector< double > &c) const
	A virtual method that is used to bound the characteristic speed in both directions. More...
virtual std::vector< bool >	edge_values (const int &face_index, const DenseVector< double > &x, DenseVector< double > &q) const
	Define the edge boundary conditions. More...
virtual void	edge_slopes (const int &face_index, const DenseVector< double > &x, DenseVector< double > &sigma_n) const
	Define the edge boundary condition slopes. More...
virtual void	source_fn (const DenseVector< double > &x, const DenseVector< double > &q, DenseVector< double > &r) const
unsigned	get_order ()

Additional Inherited Members
Protected Attributes inherited from CppNoddy::TwoD_Hyperbolic_System
const unsigned	ORDER_OF_SYSTEM
	The order of the system of equations. More...

Detailed Description

Define the system.

Definition at line 29 of file HYP2DRadialDamBreak.cpp.

Constructor & Destructor Documentation

Shallow_2d_rad()

CppNoddy::Example::Shallow_2d_rad::Shallow_2d_rad ( )

inline

One dimemsional constant coefft acoustic problem.

Definition at line 35 of file HYP2DRadialDamBreak.cpp.

                       : TwoD_Hyperbolic_System( 3 )
      {}

Member Function Documentation

flux_fn_x()

void CppNoddy::Example::Shallow_2d_rad::flux_fn_x ( const DenseVector< double > &  x, const DenseVector< double > &  q, DenseVector< double > &  f  ) const

inlinevirtual

Define the vector flux.

Reimplemented from CppNoddy::TwoD_Hyperbolic_System.

Definition at line 39 of file HYP2DRadialDamBreak.cpp.

      {
        f[ h ] = q[ hu ];
        f[ hu ] = q[ hu ] * q[ hu ] / q[ h ] + g * q[ h ] * q[ h ] / 2.;
        f[ hv ] = q[ hu ] * q[ hv ] / q[ h ];
      }

References f, CppNoddy::Example::g(), h, hu, and hv.

flux_fn_y()

void CppNoddy::Example::Shallow_2d_rad::flux_fn_y ( const DenseVector< double > &  x, const DenseVector< double > &  q, DenseVector< double > &  f  ) const

inlinevirtual

A virtual flux function for the y-derivative.

Parameters

x	The vector position
q	The unknowns
f	The flux function

Reimplemented from CppNoddy::TwoD_Hyperbolic_System.

Definition at line 46 of file HYP2DRadialDamBreak.cpp.

      {
        f[ h ] = q[ hv ];
        f[ hu ] = q[ hu ] * q[ hv ] / q[ h ];
        f[ hv ] = q[ hv ] * q[ hv ] / q[ h ] + g * q[ h ] * q[ h ] / 2.;
      }

References f, CppNoddy::Example::g(), h, hu, and hv.

Jac_flux_fn_x()

void CppNoddy::Example::Shallow_2d_rad::Jac_flux_fn_x ( const DenseVector< double > &  x, const DenseVector< double > &  q, DenseMatrix< double > &  J  ) const

inlinevirtual

A virtual function function to define the Jacobian of the x-flux function.

The default method uses first-order finite differencing to compute the Jacobian if not otherwise specified by the user.

Parameters

x	The vector position
q	The unknowns
J	The Jacobian of the flux function

cheap & nasty differencing

Reimplemented from CppNoddy::TwoD_Hyperbolic_System.

Definition at line 54 of file HYP2DRadialDamBreak.cpp.

      {
        J( 0, hu ) = 1;
        J( 1, h  ) = - q[ hu ] * q[ hu ] / ( q[ h ] * q[ h ] ) + g * q[ h ];
        J( 1, hu ) = 2 * q[ hu ] / q[ h ];
        J( 2, h  ) = - q[ hu ] * q[ hv ] / ( q[ h ] * q[ h ] );
        J( 2, hu ) = q[ hv ] / q[ h ];
        J( 2, hv ) = q[ hu ] / q[ h ];
      }

References CppNoddy::Example::g(), h, hu, and hv.

Jac_flux_fn_y()

void CppNoddy::Example::Shallow_2d_rad::Jac_flux_fn_y ( const DenseVector< double > &  x, const DenseVector< double > &  q, DenseMatrix< double > &  J  ) const

inlinevirtual

A virtual function function to define the Jacobian of the y-flux function.

The default method uses first-order finite differencing to compute the Jacobian if not otherwise specified by the user.

Parameters

x	The vector position
q	The unknowns
J	The Jacobian of the flux function

cheap & nasty differencing

Reimplemented from CppNoddy::TwoD_Hyperbolic_System.

Definition at line 64 of file HYP2DRadialDamBreak.cpp.

      {
        J( 0, hv ) = 1;
        J( 1, h  ) = - q[ hu ] * q[ hv ] / ( q[ h ] * q[ h ] );
        J( 1, hu ) = q[ hv ] / q[ h ];
        J( 1, hv ) = q[ hu ] / q[ h ];
        J( 2, h  ) = - q[ hv ] * q[ hv ] / ( q[ h ] * q[ h ] ) + g * q[ h ];
        J( 2, hv ) = 2 * q[ hv ] / q[ h ];
      }

References CppNoddy::Example::g(), h, hu, and hv.

max_charac_speed()

void CppNoddy::Example::Shallow_2d_rad::max_charac_speed ( const DenseVector< double > &  x, const DenseVector< double > &  q, DenseVector< double > &  c  ) const

inlinevirtual

Bound the wave speed.

Reimplemented from CppNoddy::TwoD_Hyperbolic_System.

Definition at line 75 of file HYP2DRadialDamBreak.cpp.

      {
        // wave speed
        double cc = sqrt( g * q[ h ] );
        // flow speed
        double U = q[ hu ] / q[ h ];
        double V = q[ hv ] / q[ h ];
        // maximum shock speed
        c[ 0 ] = std::max( std::abs( U + cc ), std::abs( U - cc ) );
        c[ 1 ] = std::max( std::abs( V + cc ), std::abs( V - cc ) );
      }

References CppNoddy::Example::g(), h, hu, hv, U, and V.

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The documentation for this class was generated from the following file:

• Tests/HYP_2D/HYP2DRadialDamBreak.cpp