A class to represent a two-dimensional hyperbolic system of equations. More...

#include <TwoD_Hyperbolic_System.h>

Inheritance diagram for CppNoddy::TwoD_Hyperbolic_System:

Public Member Functions
	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 ()

Protected Attributes
const unsigned	ORDER_OF_SYSTEM
	The order of the system of equations. More...

Detailed Description

A class to represent a two-dimensional hyperbolic system of equations.

Definition at line 12 of file TwoD_Hyperbolic_System.h.

Constructor & Destructor Documentation

◆ TwoD_Hyperbolic_System()

CppNoddy::TwoD_Hyperbolic_System::TwoD_Hyperbolic_System ( const unsigned & order )

inlineexplicit

Parameters

order The order of the hyperbolic system

Definition at line 17 of file TwoD_Hyperbolic_System.h.

17 : ORDER_OF_SYSTEM(order)

18 {}

CppNoddy::TwoD_Hyperbolic_System::ORDER_OF_SYSTEM

const unsigned ORDER_OF_SYSTEM

The order of the system of equations.

Definition: TwoD_Hyperbolic_System.h:137

◆ ~TwoD_Hyperbolic_System()

virtual CppNoddy::TwoD_Hyperbolic_System::~TwoD_Hyperbolic_System ( )

inlinevirtual

An empty destructor, virtual since we have virtual methods.

Definition at line 21 of file TwoD_Hyperbolic_System.h.

22 {}

Member Function Documentation

◆ edge_slopes()

virtual void CppNoddy::TwoD_Hyperbolic_System::edge_slopes	(	const int &	face_index,
		const DenseVector< double > &	x,
		DenseVector< double > &	sigma_n
	)		const

inlinevirtual

Define the edge boundary condition slopes.

These default to zero unless otherwise over-ridden.

Parameters

face_index	An index for the face: 0,1,2,3 for S,E,N,W on the TwoD_TVDLF_Mesh
x	The global position vector
sigma_n	Specify the slope normal to the face

Definition at line 124 of file TwoD_Hyperbolic_System.h.

124 {

125 }

◆ edge_values()

virtual std::vector< bool > CppNoddy::TwoD_Hyperbolic_System::edge_values	(	const int &	face_index,
		const DenseVector< double > &	x,
		DenseVector< double > &	q
	)		const

inlinevirtual

Define the edge boundary conditions.

Parameters

face_index	An index for the face: 0,1,2,3 for S,E,N,W on the TwoD_TVDLF_Mesh
x	The global position vector
q	Specify the unknowns specified along the face

Returns: A vector that defines which components have been set as inflow

Reimplemented in CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, and CppNoddy::Example::Shallow_2d_source.

Definition at line 114 of file TwoD_Hyperbolic_System.h.

                                                                                                                           {
      return std::vector<bool>(ORDER_OF_SYSTEM, false);
    }

References ORDER_OF_SYSTEM.

◆ flux_fn_x()

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

inlinevirtual

A virtual flux function for the x-derivative.

Parameters

x	The vector position
q	The unknowns
f	The flux function

Reimplemented in CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::Shallow_2d_rad, and CppNoddy::Example::Shallow_2d_source.

Definition at line 28 of file TwoD_Hyperbolic_System.h.

                                                                                                                     {
      std::string problem;
      problem = "The Hyperbolic_Conservative_System::flux_fn_x method has not been implemented.\n";
      problem += "You have to implement this method to define the system.\n";
      throw ExceptionRuntime(problem);
    }

Referenced by Jac_flux_fn_x().

◆ flux_fn_y()

virtual void CppNoddy::TwoD_Hyperbolic_System::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 in CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::Shallow_2d_rad, and CppNoddy::Example::Shallow_2d_source.

Definition at line 39 of file TwoD_Hyperbolic_System.h.

                                                                                                                     {
      std::string problem;
      problem = "The Hyperbolic_Conservative_System::flux_fn_y method has not been implemented.\n";
      problem += "You have to implement this method to define the system.\n";
      throw ExceptionRuntime(problem);
    }

Referenced by Jac_flux_fn_y().

◆ get_order()

unsigned CppNoddy::TwoD_Hyperbolic_System::get_order ( )

inline

Definition at line 130 of file TwoD_Hyperbolic_System.h.

                         {
      return ORDER_OF_SYSTEM;
    }

References ORDER_OF_SYSTEM.

◆ Jac_flux_fn_x()

virtual void CppNoddy::TwoD_Hyperbolic_System::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 in CppNoddy::Example::Shallow_2d_rad, and CppNoddy::Example::Shallow_2d_source.

Definition at line 53 of file TwoD_Hyperbolic_System.h.

                                                                                                                         {
      /// cheap & nasty differencing
      const double delta(1.e-8);
      DenseVector<double> state(q);
      DenseVector<double> temp1(ORDER_OF_SYSTEM, 0.0);
      DenseVector<double> temp2(ORDER_OF_SYSTEM, 0.0);
      flux_fn_x(x, state, temp1);
      // default is to FD the Jacobian
      for(std::size_t i = 0; i < ORDER_OF_SYSTEM; ++i) {
        state[ i ] += delta;
        flux_fn_x(x, state, temp2);
        state[ i ] -= delta;
        J.set_col(i, (temp2 - temp1) / delta);
      }
    }

References flux_fn_x(), ORDER_OF_SYSTEM, and CppNoddy::DenseMatrix< _Type >::set_col().

◆ Jac_flux_fn_y()

virtual void CppNoddy::TwoD_Hyperbolic_System::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 in CppNoddy::Example::Shallow_2d_rad, and CppNoddy::Example::Shallow_2d_source.

Definition at line 76 of file TwoD_Hyperbolic_System.h.

                                                                                                                         {
      /// cheap & nasty differencing
      const double delta(1.e-8);
      DenseVector<double> state(q);
      DenseVector<double> temp1(ORDER_OF_SYSTEM, 0.0);
      DenseVector<double> temp2(ORDER_OF_SYSTEM, 0.0);
      flux_fn_y(x, state, temp1);
      // default is to FD the Jacobian
      for(std::size_t i = 0; i < ORDER_OF_SYSTEM; ++i) {
        state[ i ] += delta;
        flux_fn_y(x, state, temp2);
        state[ i ] -= delta;
        J.set_col(i, (temp2 - temp1) / delta);
      }
    }

References flux_fn_y(), ORDER_OF_SYSTEM, and CppNoddy::DenseMatrix< _Type >::set_col().

◆ max_charac_speed()

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

inlinevirtual

A virtual method that is used to bound the characteristic speed in both directions.

It determines the time step in order that the CFL constraint holds. It is sometimes required to specify a speed that is a function of position and to even specify the two-directional speeds. eg. your mesh may actually be w.r.t. a polar coordinate system in which the physical mesh size grows linearly with radius, so one of the speeds should be scaled accordingly.

Parameters

x	The global coordinate
q	The unknowns
c	The speed

Reimplemented in CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::NlinAdv, CppNoddy::Example::Shallow_2d_rad, and CppNoddy::Example::Shallow_2d_source.

Definition at line 101 of file TwoD_Hyperbolic_System.h.

                                                                                                                            {
      std::string problem;
      problem = "The Hyperbolic_Conservative_System::max_charac_speed method has not\n";
      problem += "been implemented. You have to implement this method to define the system.\n";
      throw ExceptionRuntime(problem);
    }

◆ source_fn()

virtual void CppNoddy::TwoD_Hyperbolic_System::source_fn	(	const DenseVector< double > &	x,
		const DenseVector< double > &	q,
		DenseVector< double > &	r
	)		const

inlinevirtual

Reimplemented in CppNoddy::Example::Shallow_2d_source.

Definition at line 127 of file TwoD_Hyperbolic_System.h.

127 {

128 }

Member Data Documentation

◆ ORDER_OF_SYSTEM

const unsigned CppNoddy::TwoD_Hyperbolic_System::ORDER_OF_SYSTEM

protected

The order of the system of equations.

Definition at line 137 of file TwoD_Hyperbolic_System.h.

Referenced by edge_values(), get_order(), Jac_flux_fn_x(), and Jac_flux_fn_y().

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

include/TwoD_Hyperbolic_System.h

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ TwoD_Hyperbolic_System()

◆ ~TwoD_Hyperbolic_System()

Member Function Documentation

◆ edge_slopes()

◆ edge_values()

◆ flux_fn_x()

◆ flux_fn_y()

◆ get_order()

◆ Jac_flux_fn_x()

◆ Jac_flux_fn_y()

◆ max_charac_speed()

◆ source_fn()

Member Data Documentation

◆ ORDER_OF_SYSTEM