A Linear Element class. More...

#include <OneD_TVDLF_Elt.h>

Public Member Functions
	OneD_TVDLF_Elt (double a, double b, OneD_Hyperbolic_System *ptr, bool flag=false, int index=0)
	Construct a linear element. More...

	~OneD_TVDLF_Elt ()
	An empty destructor. More...

void	add_contribution (OneD_TVDLF_Elt *ptr, const DenseVector< double > &s_range, int index)
	Allow the connection of this element to another element. More...

void	clear_contributions ()
	Clear the record of contributions to this element. More...

DenseVector< double >	contributed_Q ()
	Find the integral contributions to this black/red element from the contributed red/black element. More...

void	contributed_flux_in_left (const double &dt, DenseVector< double > &flux_in_left, const double &current_time)
	Compute the flux into this element through the left face over a given time step. More...

void	contributed_flux_out_right (const double &dt, DenseVector< double > &flux_out_right, const double &current_time)
	Compute the flux out of this element through the right face over a given time step. More...

double	get_s (double x) const
	Convert a global coordinate into a local coordinate within this element If the global coordinate is outside the element, then we throw an exception. More...

double	get_x (double s) const
	Get the global position of the local coordinate. More...

double	get_dx () const
	Get the size of the element. More...

bool	get_external_flag () const
	Get the external flag. More...

void	set_external_flag (bool flag)
	Set the external flag. More...

int	get_external_face_i () const
	Get the exterior boundary number. More...

void	set_external_face_i (int i)
	Set the local coordinate of the external face. More...

DenseVector< double >	get_Q (double s) const
	Get the value of the 'concentration' stored in this element. More...

DenseVector< double >	get_int_Q (const double s0, const double s1)
	Get the integral of Q over a sub-element. More...

void	set_Q_mid (const DenseVector< double > value)
	Set the value of the 'concentration' stored in this element. More...

void	set_slope (const DenseVector< double > value)
	The concentration is approximated by a linear function in each element. More...

DenseVector< double >	get_slope () const
	The concentration is approximated by a linear function in each element. More...

DenseVector< double >	get_flux_fn (const double s) const
	Get the flux function evaluated for the concentration value stored in this elt. More...

DenseMatrix< double >	get_Jac_flux_fn (const double s) const
	Get the Jacobian of the flux function evaluated for the concentration value stored in this elt. More...

DenseVector< double >	get_source_fn (const double s) const
	Get the value of the source function term in this element at a given local coordinate. More...

double	get_max_dt () const
	Get the maximum allowable time step for this element by using information about the size of the element and the maximum wave speed set in the conservative system. More...

Public Attributes
OneD_Hyperbolic_System *	system_ptr

Detailed Description

A Linear Element class.

Definition at line 15 of file OneD_TVDLF_Elt.h.

Constructor & Destructor Documentation

◆ OneD_TVDLF_Elt()

CppNoddy::OneD_TVDLF_Elt::OneD_TVDLF_Elt	(	double	a,
		double	b,
		OneD_Hyperbolic_System *	ptr,
		bool	flag = `false`,
		int	index = `0`
	)

Construct a linear element.

Parameters

a	The left hand edge
b	The right hand edge
ptr	A pointer to the hyperbolic system for this element
flag	A boolean indicator to specify an elt with an external face
index	Index of the external face if flag=true

Definition at line 13 of file OneD_TVDLF_Elt.cpp.

                                                       {
#ifdef DEBUG
    std::cout << "DEBUG: Constructing a OneD_TVDLF_Elt object between "
              << a << " and " << b << "\n";
#endif
    system_ptr = ptr;
    LEFT = a;
    RIGHT = b;
    EXTERNAL = flag;
    EXTERNAL_FACE_I = index;
    SLOPE = DenseVector<double>(system_ptr -> get_order(), 0.0);
    Q = DenseVector<double>(system_ptr -> get_order(), 0.0);
  }

References system_ptr.

◆ ~OneD_TVDLF_Elt()

CppNoddy::OneD_TVDLF_Elt::~OneD_TVDLF_Elt ( )

An empty destructor.

Definition at line 29 of file OneD_TVDLF_Elt.cpp.

30 {}

Member Function Documentation

◆ add_contribution()

void CppNoddy::OneD_TVDLF_Elt::add_contribution	(	OneD_TVDLF_Elt *	ptr,
		const DenseVector< double > &	s_range,
		int	index
	)

Allow the connection of this element to another element.

Parameters

ptr	A pointer to another element of the same type
s_range	A vector range of local coordinates (s_min,s_max) in this 1D case.
index	An index to indicate which face of the current elt this contribution is associated with for flux computations -1=left, +1=right, 0=none

Definition at line 32 of file OneD_TVDLF_Elt.cpp.

                                                                                                          {
    contribution cont;
    cont.elt_ptr = ptr;
    cont.s = s_range;
    cont.face_index = index;
    // push the contribution data into a list
    CONT_LIST.push_back(cont);
  }

◆ clear_contributions()

void CppNoddy::OneD_TVDLF_Elt::clear_contributions ( )

inline

Clear the record of contributions to this element.

Definition at line 46 of file OneD_TVDLF_Elt.h.

                               {
      CONT_LIST.clear();
    }

◆ contributed_flux_in_left()

void CppNoddy::OneD_TVDLF_Elt::contributed_flux_in_left	(	const double &	dt,
		DenseVector< double > &	flux_in_left,
		const double &	current_time
	)

Compute the flux into this element through the left face over a given time step.

Parameters

dt	The time step to compute the flux over
flux_in_left	A vector to return the flux components in
current_time	The current mesh time level

Definition at line 54 of file OneD_TVDLF_Elt.cpp.

                                                                                                                               {
    std::list< contribution >::iterator c = CONT_LIST.begin();
    // loop over all contributing elements
    while(c != CONT_LIST.end()) {
      // find contributions to the left face
      if(c -> face_index == -1) {
        // which local coord in the contributing elt?
        const double s = c -> s[ 0 ];
        DenseVector<double> q_half_step(c -> elt_ptr -> get_Q(s));
        // add half step correction
        q_half_step += (c -> elt_ptr -> get_source_fn(s)
                        - c -> elt_ptr -> get_Jac_flux_fn(s).multiply(c -> elt_ptr -> SLOPE))
                       * 0.5 * dt;
        //DenseVector<double> x( 1, 0.0 ); x[ 0 ] = c -> elt_ptr -> get_x( s );
        double x(c -> elt_ptr -> get_x(s));
        // evaluate the flux at this Q value
        c -> elt_ptr -> system_ptr -> flux_fn(x, q_half_step, flux_in_left);
      }
      ++c;
    }
    // treat the user specified external faces separately
    if(EXTERNAL) {
      // we are in an external elt
      c = CONT_LIST.begin();
      while(c != CONT_LIST.end()) {
        // external faces are external for the current elt *and* its contributions
        if(c -> elt_ptr -> get_external_flag()) {
          if(EXTERNAL_FACE_I < 0) {
            // LH boundary
            DenseVector<double> q_left(c -> elt_ptr -> get_Q(-1.0));
            // convert x at boundary to a vector
            //DenseVector<double> x_left( 1, 0.0 ); x_left[ 0 ] = c -> elt_ptr -> get_x( -1.0 );
            double x_left(c -> elt_ptr -> get_x(-1.0));
            DenseVector<double> q_left_half_step(q_left);
            //compute flux at the half time step
            q_left_half_step += (c -> elt_ptr -> get_source_fn(-1.0)
                                 - c -> elt_ptr -> get_Jac_flux_fn(-1.0).multiply(c -> elt_ptr -> SLOPE))
                                * 0.5 * dt;
            // get the edge values
            system_ptr -> edge_values(-1, x_left, q_left_half_step, current_time + 0.5*dt);
            // get the flux
            system_ptr -> flux_fn(x_left, q_left_half_step, flux_in_left);
          }
        }
        ++c;
      }
    }
  }

References get_external_flag(), get_Jac_flux_fn(), get_Q(), get_source_fn(), get_x(), CppNoddy::DenseMatrix< _Type >::multiply(), and system_ptr.

◆ contributed_flux_out_right()

void CppNoddy::OneD_TVDLF_Elt::contributed_flux_out_right	(	const double &	dt,
		DenseVector< double > &	flux_out_right,
		const double &	current_time
	)

Compute the flux out of this element through the right face over a given time step.

Parameters

dt	The time step to compute the flux over
flux_out_right	A vector to return the flux components in
current_time	The current mesh time level

Definition at line 103 of file OneD_TVDLF_Elt.cpp.

                                                                                                                                   {
    std::list< contribution >::iterator c = CONT_LIST.begin();
    // loop over all contributing elements
    while(c != CONT_LIST.end()) {
      // find contributions to the right face
      if(c -> face_index == 1) {
        // which local coord in the contributing elt?
        const double s = c -> s[ 1 ];
        DenseVector<double> q_half_step(c -> elt_ptr -> get_Q(s));
        // add half step correction
        q_half_step += (c -> elt_ptr -> get_source_fn(s)
                        - c -> elt_ptr -> get_Jac_flux_fn(s).multiply(c -> elt_ptr -> SLOPE))
                       * 0.5 * dt;
        //DenseVector<double> x( 1, 0.0 ); x[ 0 ] = c -> elt_ptr -> get_x( s );
        double x(c -> elt_ptr -> get_x(s));
        // evaluate the flux at this Q value
        c -> elt_ptr -> system_ptr -> flux_fn(x, q_half_step, flux_out_right);
      }
      ++c;
    }
    // treat the user specified external faces separately
    if(EXTERNAL) {
      // we are in an external elt
      c = CONT_LIST.begin();
      while(c != CONT_LIST.end()) {
        // external faces are external for the current elt *and* its contributions
        if(c -> elt_ptr -> get_external_flag()) {
          if(EXTERNAL_FACE_I > 0) {
            // RH boundary
            DenseVector<double> q_right(c -> elt_ptr -> get_Q(1.0));
            // convert x at boundary to a vector
            //DenseVector<double> x_right( 1, 0.0 ); x_right[ 0 ] = c -> elt_ptr -> get_x( 1.0 );
            double x_right(c -> elt_ptr -> get_x(1.0));
            DenseVector<double> q_right_half_step(q_right);
            // compute flux at the half time step
            q_right_half_step += (c -> elt_ptr -> get_source_fn(1.0)
                                  - c -> elt_ptr -> get_Jac_flux_fn(1.0).multiply(c -> elt_ptr -> SLOPE))
                                 * 0.5 * dt;
            // get the edge values
            system_ptr -> edge_values(1, x_right, q_right_half_step, current_time + 0.5*dt);
            // get the flux
            system_ptr -> flux_fn(x_right, q_right_half_step, flux_out_right);
          }
        }
        ++c;
      }
    }
  }

References get_external_flag(), get_Jac_flux_fn(), get_Q(), get_source_fn(), get_x(), CppNoddy::DenseMatrix< _Type >::multiply(), and system_ptr.

◆ contributed_Q()

DenseVector< double > CppNoddy::OneD_TVDLF_Elt::contributed_Q ( )

Find the integral contributions to this black/red element from the contributed red/black element.

Returns: The integrated value of all components

Definition at line 41 of file OneD_TVDLF_Elt.cpp.

                                                    {
    std::list< contribution >::iterator c = CONT_LIST.begin();
    // start with zero
    DenseVector<double> sum(system_ptr -> get_order(), 0.0);
    // loop over contributions
    while(c != CONT_LIST.end()) {
      // get integral of each
      sum += c -> elt_ptr -> get_int_Q(c -> s[0], c -> s[1]);
      ++c;
    }
    return sum;
  }

References get_int_Q(), and system_ptr.

◆ get_dx()

double CppNoddy::OneD_TVDLF_Elt::get_dx ( ) const

inline

Get the size of the element.

Returns: The separation of the left and right faces

Definition at line 181 of file OneD_TVDLF_Elt.h.

                                             {
    return RIGHT - LEFT;
  }

Referenced by get_int_Q(), get_max_dt(), and get_x().

◆ get_external_face_i()

int CppNoddy::OneD_TVDLF_Elt::get_external_face_i ( ) const

inline

Get the exterior boundary number.

Returns: An integer boundary indicator +1 for right, -1 for left.

Definition at line 193 of file OneD_TVDLF_Elt.h.

                                                       {
    return EXTERNAL_FACE_I;
  }

◆ get_external_flag()

bool CppNoddy::OneD_TVDLF_Elt::get_external_flag ( ) const

inline

Get the external flag.

Returns: The value of the flag (true if this is an elt with an external face)

Definition at line 189 of file OneD_TVDLF_Elt.h.

                                                      {
    return EXTERNAL;
  }

Referenced by contributed_flux_in_left(), and contributed_flux_out_right().

◆ get_flux_fn()

DenseVector< double > CppNoddy::OneD_TVDLF_Elt::get_flux_fn ( const double s ) const

Get the flux function evaluated for the concentration value stored in this elt.

Parameters

s	The local coordinate at which to evaluate

Returns: The flux function vector

Definition at line 152 of file OneD_TVDLF_Elt.cpp.

                                                                      {
    DenseVector<double> f(system_ptr -> get_order(), 0.0);
    double x(get_x(s));
    system_ptr -> flux_fn(x, get_Q(s), f);
    return f;
  }

References f, get_Q(), get_x(), and system_ptr.

◆ get_int_Q()

DenseVector< double > CppNoddy::OneD_TVDLF_Elt::get_int_Q	(	const double	s0,
		const double	s1
	)

inline

Get the integral of Q over a sub-element.

Parameters

s0	The left local coordinate
s1	The right local coordinate

Returns: The integral of the concentration over the local range

Definition at line 201 of file OneD_TVDLF_Elt.h.

                                                                                       {
    // linear elt so integral is 0.5 * dx * ( f(s0) + f(s1) )
    return (get_Q(s0) + get_Q(s1)) * 0.5 * ((s1 - s0) * get_dx() / 2);
  }

References get_dx(), and get_Q().

Referenced by contributed_Q().

◆ get_Jac_flux_fn()

DenseMatrix< double > CppNoddy::OneD_TVDLF_Elt::get_Jac_flux_fn ( const double s ) const

Get the Jacobian of the flux function evaluated for the concentration value stored in this elt.

Parameters

s	The local coordinate at which to evaluate

Returns: The Jacobian matrix

Definition at line 159 of file OneD_TVDLF_Elt.cpp.

                                                                          {
    DenseMatrix<double> J(system_ptr -> get_order(), system_ptr -> get_order(), 0.0);
    double x(get_x(s));
    system_ptr -> Jac_flux_fn(x, get_Q(s), J);
    return J;
  }

References get_Q(), get_x(), and system_ptr.

Referenced by contributed_flux_in_left(), and contributed_flux_out_right().

◆ get_max_dt()

double CppNoddy::OneD_TVDLF_Elt::get_max_dt ( ) const

Get the maximum allowable time step for this element by using information about the size of the element and the maximum wave speed set in the conservative system.

The time step is guranteed to satisfy the CFL < 0.5 constraint.

Returns: The maximum time step.

Definition at line 173 of file OneD_TVDLF_Elt.cpp.

                                          {
    // left face & right face speeds
    return get_dx() / std::max(std::abs(system_ptr -> max_charac_speed(get_Q(-1.0))),
                               std::abs(system_ptr -> max_charac_speed(get_Q(1.0))));
  }

References get_dx(), get_Q(), and system_ptr.

◆ get_Q()

DenseVector< double > CppNoddy::OneD_TVDLF_Elt::get_Q ( double s ) const

inline

Get the value of the 'concentration' stored in this element.

Parameters

s	The local coordinate in the elt at which Q is requested

Returns: The concentration value of the elt for each component

Definition at line 197 of file OneD_TVDLF_Elt.h.

                                                                 {
    return Q + SLOPE * s * (RIGHT - LEFT) / 2;
  }

Referenced by contributed_flux_in_left(), contributed_flux_out_right(), get_flux_fn(), get_int_Q(), get_Jac_flux_fn(), get_max_dt(), and get_source_fn().

◆ get_s()

double CppNoddy::OneD_TVDLF_Elt::get_s ( double x ) const

inline

Convert a global coordinate into a local coordinate within this element If the global coordinate is outside the element, then we throw an exception.

Parameters

x	The global coordinate to convert

Definition at line 72 of file OneD_TVDLF_Elt.h.

                                 {
#ifdef PARANOID
      if((x < LEFT) || (x > RIGHT)) {
        std::string problem;
        problem = " The OneD_TVDLF_Elt::get_s method has been called for an element \n";
        problem += " whose range does not bracket the given global coordinate.\n";
        throw ExceptionRuntime(problem);
      }
#endif
      return -1.0 + 2 * (x - LEFT) / (RIGHT - LEFT);
    }

◆ get_slope()

DenseVector< double > CppNoddy::OneD_TVDLF_Elt::get_slope ( ) const

inline

The concentration is approximated by a linear function in each element.

The slope of this function is got through this method.

Returns: The value of the 'slope' member data

Definition at line 222 of file OneD_TVDLF_Elt.h.

                                                             {
    return SLOPE;
  }

Referenced by get_source_fn().

◆ get_source_fn()

DenseVector< double > CppNoddy::OneD_TVDLF_Elt::get_source_fn ( const double s ) const

Get the value of the source function term in this element at a given local coordinate.

Parameters

s	The local coordinate to evaluate at

Definition at line 166 of file OneD_TVDLF_Elt.cpp.

                                                                        {
    DenseVector<double> r(system_ptr -> get_order(), 0.0);
    double x(get_x(s));
    system_ptr -> source_fn(x, get_Q(s), get_slope(), r);
    return r;
  }

References get_Q(), get_slope(), get_x(), and system_ptr.

Referenced by contributed_flux_in_left(), and contributed_flux_out_right().

◆ get_x()

double CppNoddy::OneD_TVDLF_Elt::get_x ( double s ) const

inline

Get the global position of the local coordinate.

Parameters

s	The local coordinate

Returns: The global position

Definition at line 185 of file OneD_TVDLF_Elt.h.

                                                    {
    return (LEFT + RIGHT + s * get_dx()) / 2;
  }

References get_dx().

Referenced by contributed_flux_in_left(), contributed_flux_out_right(), get_flux_fn(), get_Jac_flux_fn(), and get_source_fn().

◆ set_external_face_i()

void CppNoddy::OneD_TVDLF_Elt::set_external_face_i ( int i )

inline

Set the local coordinate of the external face.

Only one face can be external.

Parameters

i	The index of the external face -1=left, +1=right

Definition at line 210 of file OneD_TVDLF_Elt.h.

                                                       {
    EXTERNAL_FACE_I = i;
  }

◆ set_external_flag()

void CppNoddy::OneD_TVDLF_Elt::set_external_flag ( bool flag )

inline

Set the external flag.

Parameters

flag	is the value to set

Definition at line 206 of file OneD_TVDLF_Elt.h.

                                                         {
    EXTERNAL = flag;
  }

◆ set_Q_mid()

void CppNoddy::OneD_TVDLF_Elt::set_Q_mid ( const DenseVector< double > value )

inline

Set the value of the 'concentration' stored in this element.

To second order, this is the value of the concentration at the mid-point of the element.

Parameters

value The value to be assigned to the concentration member data Q

Definition at line 214 of file OneD_TVDLF_Elt.h.

                                                                       {
    Q = value;
  }

◆ set_slope()

void CppNoddy::OneD_TVDLF_Elt::set_slope ( const DenseVector< double > value )

inline

The concentration is approximated by a linear function in each element.

The slope of this function is set through this method.

Parameters

value The value to be assigned to the member data 'slope'

Definition at line 218 of file OneD_TVDLF_Elt.h.

                                                                       {
    SLOPE = value;
  }

Member Data Documentation

◆ system_ptr

OneD_Hyperbolic_System* CppNoddy::OneD_TVDLF_Elt::system_ptr

Definition at line 165 of file OneD_TVDLF_Elt.h.

Referenced by contributed_flux_in_left(), contributed_flux_out_right(), contributed_Q(), get_flux_fn(), get_Jac_flux_fn(), get_max_dt(), get_source_fn(), and OneD_TVDLF_Elt().

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

include/OneD_TVDLF_Elt.h
src/OneD_TVDLF_Elt.cpp

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ OneD_TVDLF_Elt()

◆ ~OneD_TVDLF_Elt()

Member Function Documentation

◆ add_contribution()

◆ clear_contributions()

◆ contributed_flux_in_left()

◆ contributed_flux_out_right()

◆ contributed_Q()

◆ get_dx()

◆ get_external_face_i()

◆ get_external_flag()

◆ get_flux_fn()

◆ get_int_Q()

◆ get_Jac_flux_fn()

◆ get_max_dt()

◆ get_Q()

◆ get_s()

◆ get_slope()

◆ get_source_fn()

◆ get_x()

◆ set_external_face_i()

◆ set_external_flag()

◆ set_Q_mid()

◆ set_slope()

Member Data Documentation

◆ system_ptr