#include <steady_axisym_advection_diffusion_elements.h>

Inheritance diagram for oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >:

Public Types
typedef void(*	SteadyAxisymAdvectionDiffusionPrescribedBetaFctPt) (const Vector< double > &x, double &beta)

typedef void(*	SteadyAxisymAdvectionDiffusionPrescribedAlphaFctPt) (const Vector< double > &x, double &alpha)

Public Types inherited from oomph::FiniteElement
typedef void(*	SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)

typedef void(*	UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)

Public Member Functions
	SteadyAxisymAdvectionDiffusionFluxElement (FiniteElement *const &bulk_el_pt, const int &face_index)

	SteadyAxisymAdvectionDiffusionFluxElement ()
	Broken empty constructor. More...

	SteadyAxisymAdvectionDiffusionFluxElement (const SteadyAxisymAdvectionDiffusionFluxElement &dummy)=delete
	Broken copy constructor. More...

SteadyAxisymAdvectionDiffusionPrescribedBetaFctPt &	beta_fct_pt ()
	Broken assignment operator. More...

SteadyAxisymAdvectionDiffusionPrescribedAlphaFctPt &	alpha_fct_pt ()
	Access function for the prescribed-alpha function pointer. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Add the element's contribution to its residual vector. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)

double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const

void	output (std::ostream &outfile)

void	output (std::ostream &outfile, const unsigned &nplot)

Public Member Functions inherited from oomph::FaceElement
	FaceElement ()
	Constructor: Initialise all appropriate member data. More...

virtual	~FaceElement ()
	Empty virtual destructor. More...

	FaceElement (const FaceElement &)=delete
	Broken copy constructor. More...

const unsigned &	boundary_number_in_bulk_mesh () const
	Broken assignment operator. More...

void	set_boundary_number_in_bulk_mesh (const unsigned &b)
	Set function for the boundary number in bulk mesh. More...

double	J_eulerian (const Vector< double > &s) const

double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

double	interpolated_x (const Vector< double > &s, const unsigned &i) const

double	interpolated_x (const unsigned &t, const Vector< double > &s, const unsigned &i) const

void	interpolated_x (const Vector< double > &s, Vector< double > &x) const

void	interpolated_x (const unsigned &t, const Vector< double > &s, Vector< double > &x) const

double	interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t)

void	interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt)

int &	normal_sign ()

int	normal_sign () const

int &	face_index ()

int	face_index () const

const Vector< double > *	tangent_direction_pt () const
	Public access function for the tangent direction pointer. More...

void	set_tangent_direction (Vector< double > *tangent_direction_pt)
	Set the tangent direction vector. More...

void	turn_on_warning_for_discontinuous_tangent ()

void	turn_off_warning_for_discontinuous_tangent ()

void	continuous_tangent_and_outer_unit_normal (const Vector< double > &s, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	continuous_tangent_and_outer_unit_normal (const unsigned &ipt, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	outer_unit_normal (const Vector< double > &s, Vector< double > &unit_normal) const
	Compute outer unit normal at the specified local coordinate. More...

void	outer_unit_normal (const unsigned &ipt, Vector< double > &unit_normal) const
	Compute outer unit normal at ipt-th integration point. More...

FiniteElement *&	bulk_element_pt ()
	Pointer to higher-dimensional "bulk" element. More...

FiniteElement *	bulk_element_pt () const
	Pointer to higher-dimensional "bulk" element (const version) More...

CoordinateMappingFctPt &	face_to_bulk_coordinate_fct_pt ()

CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt () const

BulkCoordinateDerivativesFctPt &	bulk_coordinate_derivatives_fct_pt ()

BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt () const

Vector< double >	local_coordinate_in_bulk (const Vector< double > &s) const

void	get_local_coordinate_in_bulk (const Vector< double > &s, Vector< double > &s_bulk) const

void	get_ds_bulk_ds_face (const Vector< double > &s, DenseMatrix< double > &dsbulk_dsface, unsigned &interior_direction) const

unsigned &	bulk_position_type (const unsigned &i)

const unsigned &	bulk_position_type (const unsigned &i) const

void	bulk_node_number_resize (const unsigned &i)
	Resize the storage for the bulk node numbers. More...

unsigned &	bulk_node_number (const unsigned &n)

const unsigned &	bulk_node_number (const unsigned &n) const

void	bulk_position_type_resize (const unsigned &i)
	Resize the storage for bulk_position_type to i entries. More...

unsigned &	nbulk_value (const unsigned &n)

unsigned	nbulk_value (const unsigned &n) const

void	nbulk_value_resize (const unsigned &i)

void	resize_nodes (Vector< unsigned > &nadditional_data_values)

void	output_zeta (std::ostream &outfile, const unsigned &nplot)
	Output boundary coordinate zeta. More...

Public Member Functions inherited from oomph::FiniteElement
void	set_dimension (const unsigned &dim)

void	set_nodal_dimension (const unsigned &nodal_dim)

void	set_nnodal_position_type (const unsigned &nposition_type)
	Set the number of types required to interpolate the coordinate. More...

void	set_n_node (const unsigned &n)

int	nodal_local_eqn (const unsigned &n, const unsigned &i) const

double	dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

	FiniteElement (const FiniteElement &)=delete
	Broken copy constructor. More...

virtual bool	local_coord_is_valid (const Vector< double > &s)
	Broken assignment operator. More...

virtual void	move_local_coord_back_into_element (Vector< double > &s) const

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const

virtual void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)

virtual double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

MacroElement *	macro_elem_pt ()
	Access function to pointer to macro element. More...

void	get_x (const Vector< double > &s, Vector< double > &x) const

void	get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x)

virtual void	get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const

virtual void	get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)

virtual void	set_integration_scheme (Integral *const &integral_pt)
	Set the spatial integration scheme. More...

Integral *const &	integral_pt () const
	Return the pointer to the integration scheme (const version) More...

virtual void	shape (const Vector< double > &s, Shape &psi) const =0

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const

virtual void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const

virtual void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const

virtual void	d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const

double	d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const

virtual double	d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	describe_local_dofs (std::ostream &out, const std::string &current_string) const

virtual void	describe_nodal_local_dofs (std::ostream &out, const std::string &current_string) const

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

Node *&	node_pt (const unsigned &n)
	Return a pointer to the local node n. More...

Node *const &	node_pt (const unsigned &n) const
	Return a pointer to the local node n (const version) More...

unsigned	nnode () const
	Return the number of nodes. More...

virtual unsigned	nnode_1d () const

double	raw_nodal_position (const unsigned &n, const unsigned &i) const

double	raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const

double	raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const

double	nodal_position (const unsigned &n, const unsigned &i) const

double	nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const

double	dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const

double	nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

double	nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const

double	dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const

double	dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

unsigned	nodal_dimension () const
	Return the required Eulerian dimension of the nodes in this element. More...

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

virtual Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)

virtual Node *	construct_boundary_node (const unsigned &n)

virtual Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)

int	get_node_number (Node *const &node_pt) const

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) const

double	raw_nodal_value (const unsigned &n, const unsigned &i) const

double	raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const

double	nodal_value (const unsigned &n, const unsigned &i) const

double	nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const

unsigned	dim () const

virtual ElementGeometry::ElementGeometry	element_geometry () const
	Return the geometry type of the element (either Q or T usually). More...

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

void	position (const Vector< double > &zeta, Vector< double > &r) const

void	position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const

void	dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt)

void	interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const

void	locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false)

virtual void	node_update ()

virtual void	identify_field_data_for_interactions (std::set< std::pair< Data *, unsigned >> &paired_field_data)

virtual void	identify_geometric_data (std::set< Data * > &geometric_data_pt)

virtual double	s_min () const
	Min value of local coordinate. More...

virtual double	s_max () const
	Max. value of local coordinate. More...

double	size () const

virtual double	compute_physical_size () const

virtual void	point_output_data (const Vector< double > &s, Vector< double > &data)

void	point_output (std::ostream &outfile, const Vector< double > &s)

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

void	output_paraview (std::ofstream &file_out, const unsigned &nplot) const

virtual void	write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const

virtual void	write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const

virtual void	write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const

virtual unsigned	nscalar_paraview () const

virtual void	scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const

virtual std::string	scalar_name_paraview (const unsigned &i) const

virtual void	output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const

virtual void	output (FILE *file_pt)

virtual void	output (FILE *file_pt, const unsigned &n_plot)

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output an exact solution over the element. More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
	Output a time-dependent exact solution over the element. More...

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, const SolutionFunctorBase &exact_soln) const
	Output a time-dependent exact solution over the element. More...

virtual void	get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const

virtual std::string	tecplot_zone_string (const unsigned &nplot) const

virtual void	write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const

virtual void	write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const

virtual unsigned	nplot_points (const unsigned &nplot) const

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)

virtual void	compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error)

void	integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
	Integrate Vector-valued function over element. More...

void	integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
	Integrate Vector-valued time-dep function over element. More...

virtual void	build_face_element (const int &face_index, FaceElement *face_element_pt)

virtual unsigned	self_test ()

virtual unsigned	get_bulk_node_number (const int &face_index, const unsigned &i) const

virtual int	face_outer_unit_normal_sign (const int &face_index) const
	Get the sign of the outer unit normal on the face given by face_index. More...

virtual unsigned	nnode_on_face () const

void	face_node_number_error_check (const unsigned &i) const
	Range check for face node numbers. More...

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

Public Member Functions inherited from oomph::GeneralisedElement
	GeneralisedElement ()
	Constructor: Initialise all pointers and all values to zero. More...

virtual	~GeneralisedElement ()
	Virtual destructor to clean up any memory allocated by the object. More...

	GeneralisedElement (const GeneralisedElement &)=delete
	Broken copy constructor. More...

void	operator= (const GeneralisedElement &)=delete
	Broken assignment operator. More...

Data *&	internal_data_pt (const unsigned &i)
	Return a pointer to i-th internal data object. More...

Data *const &	internal_data_pt (const unsigned &i) const
	Return a pointer to i-th internal data object (const version) More...

Data *&	external_data_pt (const unsigned &i)
	Return a pointer to i-th external data object. More...

Data *const &	external_data_pt (const unsigned &i) const
	Return a pointer to i-th external data object (const version) More...

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

void	flush_external_data ()
	Flush all external data. More...

void	flush_external_data (Data *const &data_pt)
	Flush the object addressed by data_pt from the external data array. More...

unsigned	ninternal_data () const
	Return the number of internal data objects. More...

unsigned	nexternal_data () const
	Return the number of external data objects. More...

unsigned	ndof () const
	Return the number of equations/dofs in the element. More...

void	dof_vector (const unsigned &t, Vector< double > &dof)
	Return the vector of dof values at time level t. More...

void	dof_pt_vector (Vector< double * > &dof_pt)
	Return the vector of pointers to dof values. More...

void	set_internal_data_time_stepper (const unsigned &i, TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data)

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)

void	describe_dofs (std::ostream &out, const std::string &current_string) const

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

virtual void	get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

virtual void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const

Public Member Functions inherited from oomph::GeomObject
	GeomObject ()
	Default constructor. More...

	GeomObject (const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)

	GeomObject (const GeomObject &dummy)=delete
	Broken copy constructor. More...

void	operator= (const GeomObject &)=delete
	Broken assignment operator. More...

virtual	~GeomObject ()
	(Empty) destructor More...

unsigned	nlagrangian () const
	Access function to # of Lagrangian coordinates. More...

unsigned	ndim () const
	Access function to # of Eulerian coordinates. More...

void	set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim)
	Set # of Lagrangian and Eulerian coordinates. More...

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

virtual void	position (const double &t, const Vector< double > &zeta, Vector< double > &r) const

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const

Protected Member Functions
double	shape_and_test (const Vector< double > &s, Shape &psi, Shape &test) const

double	shape_and_test_at_knot (const unsigned &ipt, Shape &psi, Shape &test) const

void	get_beta (const Vector< double > &x, double &beta)

void	get_alpha (const Vector< double > &x, double &alpha)

Protected Member Functions inherited from oomph::FaceElement
void	add_additional_values (const Vector< unsigned > &nadditional_values, const unsigned &id)

Protected Member Functions inherited from oomph::FiniteElement
virtual void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const

virtual void	assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const

virtual void	assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const

template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual double	invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const

virtual double	local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<unsigned DIM>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

virtual void	d_dshape_eulerian_dnodal_coordinates (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<unsigned DIM>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

void	transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

virtual void	transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<unsigned DIM>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<unsigned DIM>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

virtual void	fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Zero-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	One-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Two-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const

Protected Member Functions inherited from oomph::GeneralisedElement
unsigned	add_internal_data (Data *const &data_pt, const bool &fd=true)

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

int	internal_local_eqn (const unsigned &i, const unsigned &j) const

int	external_local_eqn (const unsigned &i, const unsigned &j)

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)

virtual void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

virtual void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)

virtual void	fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)

virtual void	fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)

virtual void	fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)

virtual void	fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)

Private Member Functions
void	fill_in_generic_residual_contribution_adv_diff_flux (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)

Private Attributes
SteadyAxisymAdvectionDiffusionPrescribedBetaFctPt	Beta_fct_pt
	Function pointer to the (global) prescribed-beta function. More...

SteadyAxisymAdvectionDiffusionPrescribedAlphaFctPt	Alpha_fct_pt
	Function pointer to the (global) prescribed-alpha function. More...

unsigned	U_index_adv_diff
	The index at which the unknown is stored at the nodes. More...

Additional Inherited Members
Static Public Attributes inherited from oomph::FiniteElement
static double	Tolerance_for_singular_jacobian = 1.0e-16
	Tolerance below which the jacobian is considered singular. More...

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_repeated_internal_data

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

Protected Attributes inherited from oomph::FaceElement
unsigned	Boundary_number_in_bulk_mesh
	The boundary number in the bulk mesh to which this element is attached. More...

FiniteElement *	Bulk_element_pt
	Pointer to the associated higher-dimensional "bulk" element. More...

Vector< unsigned >	Bulk_node_number

Vector< unsigned >	Nbulk_value

Vector< double > *	Tangent_direction_pt

Protected Attributes inherited from oomph::FiniteElement
MacroElement *	Macro_elem_pt
	Pointer to the element's macro element (NULL by default) More...

Protected Attributes inherited from oomph::GeomObject
unsigned	NLagrangian
	Number of Lagrangian (intrinsic) coordinates. More...

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default value for the number of values at a node. More...

static const double	Node_location_tolerance = 1.0e-14

static const unsigned	N2deriv [] = {0, 1, 3, 6}

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix

static std::deque< double * >	Dof_pt_deque

Detailed Description

template<class ELEMENT>
class oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >

///////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////// A class for elements that allow the imposition of an applied Robin boundary condition on the boundaries of Steady Axisymmnetric Advection Diffusion Flux elements.

\[ -\Delta u \cdot \mathbf{n} + \alpha(r,z) u = \beta(r,z) \]

The element geometry is obtained from the FaceGeometry<ELEMENT> policy class.

Member Typedef Documentation

◆ SteadyAxisymAdvectionDiffusionPrescribedAlphaFctPt

template<class ELEMENT >

typedef void(* oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::SteadyAxisymAdvectionDiffusionPrescribedAlphaFctPt) (const Vector< double > &x, double &alpha)

Function pointer to the prescribed-alpha function fct(x,alpha(x)) – x is a Vector!

◆ SteadyAxisymAdvectionDiffusionPrescribedBetaFctPt

template<class ELEMENT >

typedef void(* oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::SteadyAxisymAdvectionDiffusionPrescribedBetaFctPt) (const Vector< double > &x, double &beta)

Function pointer to the prescribed-beta function fct(x,beta(x)) – x is a Vector!

Constructor & Destructor Documentation

◆ SteadyAxisymAdvectionDiffusionFluxElement() [1/3]

template<class ELEMENT >

oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::SteadyAxisymAdvectionDiffusionFluxElement	(	FiniteElement *const &	bulk_el_pt,
		const int &	face_index
	)

Constructor, takes the pointer to the "bulk" element and the index of the face to be created

//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// Constructor, takes the pointer to the "bulk" element and the index of the face to be created

     : FaceGeometry<ELEMENT>(), FaceElement()
  
   {
     // Let the bulk element build the FaceElement, i.e. setup the pointers
     // to its nodes (by referring to the appropriate nodes in the bulk
     // element), etc.
     bulk_el_pt->build_face_element(face_index, this);
  
  
 #ifdef PARANOID
     {
       // Check that the element is not a refineable 3d element
       ELEMENT* elem_pt = dynamic_cast<ELEMENT*>(bulk_el_pt);
       // If it's three-d
       if (elem_pt->dim() == 3)
       {
         // Is it refineable
         RefineableElement* ref_el_pt =
           dynamic_cast<RefineableElement*>(elem_pt);
         if (ref_el_pt != 0)
         {
           if (this->has_hanging_nodes())
           {
             throw OomphLibError("This flux element will not work correctly if "
                                 "nodes are hanging\n",
                                 OOMPH_CURRENT_FUNCTION,
                                 OOMPH_EXCEPTION_LOCATION);
           }
         }
       }
     }
 #endif
  
     // Initialise the prescribed-beta function pointer to zero
     Beta_fct_pt = 0;
  
     // Set up U_index_adv_diff. Initialise to zero, which probably won't change
     // in most cases, oh well, the price we pay for generality
     U_index_adv_diff = 0;
  
     // Cast to the appropriate AdvectionDiffusionEquation so that we can
     // find the index at which the variable is stored
     // We assume that the dimension of the full problem is the same
     // as the dimension of the node, if this is not the case you will have
     // to write custom elements, sorry
     SteadyAxisymAdvectionDiffusionEquations* eqn_pt =
       dynamic_cast<SteadyAxisymAdvectionDiffusionEquations*>(bulk_el_pt);
  
     // If the cast has failed die
     if (eqn_pt == 0)
     {
       std::string error_string = "Bulk element must inherit from "
                                  "SteadyAxisymAdvectionDiffusionEquations.";
       error_string +=
         "Nodes are two dimensional, but cannot cast the bulk element to\n";
       error_string += "SteadyAxisymAdvectionDiffusionEquations<2>\n.";
       error_string +=
         "If you desire this functionality, you must implement it yourself\n";
  
       throw OomphLibError(
         error_string, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
     }
     else
     {
       // Read the index from the (cast) bulk element.
       U_index_adv_diff = eqn_pt->u_index_axisym_adv_diff();
     }
   }

References oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::Beta_fct_pt, oomph::FiniteElement::build_face_element(), oomph::FaceElement::face_index(), oomph::FiniteElement::has_hanging_nodes(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::Global_string_for_annotation::string(), oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::U_index_adv_diff, and oomph::SteadyAxisymAdvectionDiffusionEquations::u_index_axisym_adv_diff().

◆ SteadyAxisymAdvectionDiffusionFluxElement() [2/3]

template<class ELEMENT >

oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::SteadyAxisymAdvectionDiffusionFluxElement ( )

inline

Broken empty constructor.

     {
       throw OomphLibError("Don't call empty constructor for "
                           "SteadyAxisymAdvectionDiffusionFluxElement",
                           OOMPH_CURRENT_FUNCTION,
                           OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ SteadyAxisymAdvectionDiffusionFluxElement() [3/3]

template<class ELEMENT >

oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::SteadyAxisymAdvectionDiffusionFluxElement ( const SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT > & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ alpha_fct_pt()

template<class ELEMENT >

SteadyAxisymAdvectionDiffusionPrescribedAlphaFctPt& oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::alpha_fct_pt ( )

inline

Access function for the prescribed-alpha function pointer.

     {
       return Alpha_fct_pt;
     }

References oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::Alpha_fct_pt.

Referenced by AxisymFreeSurfaceNozzleAdvDiffRobinProblem< ELEMENT >::AxisymFreeSurfaceNozzleAdvDiffRobinProblem(), and Wind_fct_pt().

◆ beta_fct_pt()

template<class ELEMENT >

SteadyAxisymAdvectionDiffusionPrescribedBetaFctPt& oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::beta_fct_pt ( )

inline

Broken assignment operator.

Access function for the prescribed-beta function pointer

     {
       return Beta_fct_pt;
     }

References oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::Beta_fct_pt.

Referenced by AxisymFreeSurfaceNozzleAdvDiffRobinProblem< ELEMENT >::AxisymFreeSurfaceNozzleAdvDiffRobinProblem(), and Wind_fct_pt().

◆ fill_in_contribution_to_jacobian()

template<class ELEMENT >

void oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

Add the element's contribution to its residual vector and its Jacobian matrix

Reimplemented from oomph::FiniteElement.

     {
       // Call the generic routine with the flag set to 1
       fill_in_generic_residual_contribution_adv_diff_flux(
         residuals, jacobian, 1);
     }

References oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::fill_in_generic_residual_contribution_adv_diff_flux().

◆ fill_in_contribution_to_residuals()

template<class ELEMENT >

void oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

Add the element's contribution to its residual vector.

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the generic residuals function with flag set to 0
       // using a dummy matrix
       fill_in_generic_residual_contribution_adv_diff_flux(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::fill_in_generic_residual_contribution_adv_diff_flux().

◆ fill_in_generic_residual_contribution_adv_diff_flux()

template<class ELEMENT >

void oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::fill_in_generic_residual_contribution_adv_diff_flux	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		unsigned	flag
	)

private

Add the element's contribution to its residual vector. flag=1(or 0): do (or don't) compute the Jacobian as well.

Compute the element's residual vector and the (zero) Jacobian matrix for the Robin boundary condition:

\[ \Delta u \cdot \mathbf{n} + \alpha (\mathbf{x}) = \beta (\mathbf{x}) \]

   {
     // Find out how many nodes there are
     const unsigned n_node = nnode();
  
     // Locally cache the index at which the variable is stored
     const unsigned u_index_axisym_adv_diff = U_index_adv_diff;
  
     // Set up memory for the shape and test functions
     Shape psif(n_node), testf(n_node);
  
     // Set the value of n_intpt
     const unsigned n_intpt = integral_pt()->nweight();
  
     // Set the Vector to hold local coordinates
     Vector<double> s(1);
  
     // Integers used to store the local equation number and local unknown
     // indices for the residuals and jacobians
     int local_eqn = 0, local_unknown = 0;
  
     // Loop over the integration points
     //--------------------------------
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < 1; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Find the shape and test functions and return the Jacobian
       // of the mapping
       double J = shape_and_test(s, psif, testf);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Calculate local values of the solution and its derivatives
       // Allocate
       double interpolated_u = 0.0;
       Vector<double> interpolated_x(2, 0.0);
  
       // Calculate position
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the value at the node
         double u_value = raw_nodal_value(l, u_index_axisym_adv_diff);
         interpolated_u += u_value * psif(l);
         // Loop over coordinate direction
         for (unsigned i = 0; i < 2; i++)
         {
           interpolated_x[i] += nodal_position(l, i) * psif(l);
         }
       }
  
       // Get the imposed beta (beta=flux when alpha=0.0)
       double beta;
       get_beta(interpolated_x, beta);
  
       // Get the imposed alpha
       double alpha;
       get_alpha(interpolated_x, alpha);
  
       // r is the first position component
       double r = interpolated_x[0];
  
       // Now add to the appropriate equations
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Set the local equation number
         local_eqn = nodal_local_eqn(l, u_index_axisym_adv_diff);
         /*IF it's not a boundary condition*/
         if (local_eqn >= 0)
         {
           // Add the prescribed beta terms
           residuals[local_eqn] -=
             r * (beta - alpha * interpolated_u) * testf(l) * W;
  
           // Calculate the Jacobian
           //----------------------
           if ((flag) && (alpha != 0.0))
           {
             // Loop over the velocity shape functions again
             for (unsigned l2 = 0; l2 < n_node; l2++)
             {
               // Set the number of the unknown
               local_unknown = nodal_local_eqn(l2, u_index_axisym_adv_diff);
  
               // If at a non-zero degree of freedom add in the entry
               if (local_unknown >= 0)
               {
                 jacobian(local_eqn, local_unknown) +=
                   r * alpha * psif[l2] * testf[l] * W;
               }
             }
           }
         }
       } // end loop over test functions
  
     } // end loop over integration points
  
   } // end fill_in_generic_residual_contribution_adv_diff_flux

References alpha, beta, i, J, UniformPSDSelfTest::r, s, w, and oomph::QuadTreeNames::W.

Referenced by oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::fill_in_contribution_to_jacobian(), and oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::fill_in_contribution_to_residuals().

◆ get_alpha()

template<class ELEMENT >

void oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::get_alpha	(	const Vector< double > &	x,
		double &	alpha
	)

inlineprotected

Function to calculate the prescribed alpha at a given spatial position

     {
       // If the function pointer is zero return zero
       if (Alpha_fct_pt == 0)
       {
         alpha = 0.0;
       }
       // Otherwise call the function
       else
       {
         (*Alpha_fct_pt)(x, alpha);
       }
     }

References alpha, oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::Alpha_fct_pt, and plotDoE::x.

◆ get_beta()

template<class ELEMENT >

void oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::get_beta	(	const Vector< double > &	x,
		double &	beta
	)

inlineprotected

Function to calculate the prescribed beta at a given spatial position

     {
       // If the function pointer is zero return zero
       if (Beta_fct_pt == 0)
       {
         beta = 0.0;
       }
       // Otherwise call the function
       else
       {
         (*Beta_fct_pt)(x, beta);
       }
     }

References beta, oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::Beta_fct_pt, and plotDoE::x.

◆ output() [1/2]

template<class ELEMENT >

void oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::output ( std::ostream & outfile )

inlinevirtual

Output function – forward to broken version in FiniteElement until somebody decides what exactly they want to plot here...

Reimplemented from oomph::FiniteElement.

     {
       FiniteElement::output(outfile);
     }

References oomph::FiniteElement::output().

◆ output() [2/2]

template<class ELEMENT >

void oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

inlinevirtual

Output function – forward to broken version in FiniteElement until somebody decides what exactly they want to plot here...

Reimplemented from oomph::FiniteElement.

     {
       FiniteElement::output(outfile, nplot);
     }

References oomph::FiniteElement::output().

◆ shape_and_test()

template<class ELEMENT >

double oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::shape_and_test	(	const Vector< double > &	s,
		Shape &	psi,
		Shape &	test
	)		const

inlineprotected

Function to compute the shape and test functions and to return the Jacobian of mapping between local and global (Eulerian) coordinates

     {
       // Find number of nodes
       unsigned n_node = nnode();
  
       // Get the shape functions
       shape(s, psi);
  
       // Set the test functions to be the same as the shape functions
       for (unsigned i = 0; i < n_node; i++)
       {
         test[i] = psi[i];
       }
  
       // Return the value of the jacobian
       return J_eulerian(s);
     }

References i, oomph::FaceElement::J_eulerian(), oomph::FiniteElement::nnode(), s, and oomph::FiniteElement::shape().

◆ shape_and_test_at_knot()

template<class ELEMENT >

double oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::shape_and_test_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		Shape &	test
	)		const

inlineprotected

Function to compute the shape and test functions and to return the Jacobian of mapping between local and global (Eulerian) coordinates

     {
       // Find number of nodes
       unsigned n_node = nnode();
  
       // Get the shape functions
       shape_at_knot(ipt, psi);
  
       // Set the test functions to be the same as the shape functions
       for (unsigned i = 0; i < n_node; i++)
       {
         test[i] = psi[i];
       }
  
       // Return the value of the jacobian
       return J_eulerian_at_knot(ipt);
     }

References i, oomph::FaceElement::J_eulerian_at_knot(), oomph::FiniteElement::nnode(), and oomph::FiniteElement::shape_at_knot().

◆ zeta_nodal()

template<class ELEMENT >

double oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::zeta_nodal	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inlinevirtual

Specify the value of nodal zeta from the face geometry The "global" intrinsic coordinate of the element when viewed as part of a geometric object should be given by the FaceElement representation, by default (needed to break indeterminacy if bulk element is SolidElement)

Reimplemented from oomph::FaceElement.

     {
       return FaceElement::zeta_nodal(n, k, i);
     }

References i, k, n, and oomph::FaceElement::zeta_nodal().

Member Data Documentation

◆ Alpha_fct_pt

template<class ELEMENT >

SteadyAxisymAdvectionDiffusionPrescribedAlphaFctPt oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::Alpha_fct_pt

private

Function pointer to the (global) prescribed-alpha function.

Referenced by oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::alpha_fct_pt(), and oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::get_alpha().

◆ Beta_fct_pt

template<class ELEMENT >

SteadyAxisymAdvectionDiffusionPrescribedBetaFctPt oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::Beta_fct_pt

private

Function pointer to the (global) prescribed-beta function.

Referenced by oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::beta_fct_pt(), oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::get_beta(), and oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::SteadyAxisymAdvectionDiffusionFluxElement().

◆ U_index_adv_diff

template<class ELEMENT >

unsigned oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::U_index_adv_diff

private

The index at which the unknown is stored at the nodes.

Referenced by oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >::SteadyAxisymAdvectionDiffusionFluxElement().

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

steady_axisym_advection_diffusion_elements.h

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class ELEMENT> class oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >

Member Typedef Documentation

◆ SteadyAxisymAdvectionDiffusionPrescribedAlphaFctPt

◆ SteadyAxisymAdvectionDiffusionPrescribedBetaFctPt

Constructor & Destructor Documentation

◆ SteadyAxisymAdvectionDiffusionFluxElement() [1/3]

◆ SteadyAxisymAdvectionDiffusionFluxElement() [2/3]

◆ SteadyAxisymAdvectionDiffusionFluxElement() [3/3]

Member Function Documentation

◆ alpha_fct_pt()

◆ beta_fct_pt()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_adv_diff_flux()

◆ get_alpha()

◆ get_beta()

◆ output() [1/2]

◆ output() [2/2]

◆ shape_and_test()

◆ shape_and_test_at_knot()

◆ zeta_nodal()

Member Data Documentation

◆ Alpha_fct_pt

◆ Beta_fct_pt

◆ U_index_adv_diff

template<class ELEMENT>
class oomph::SteadyAxisymAdvectionDiffusionFluxElement< ELEMENT >