#include <polar_fluid_traction_elements.h>

Inheritance diagram for oomph::PolarNavierStokesTractionElement< ELEMENT >:

Public Member Functions
const double &	alpha () const
	Alpha. More...

double *&	alpha_pt ()
	Pointer to Alpha. More...

void	set_external_pressure_data (Data *pext_data_pt)
	Function for setting up external pressure. More...

const int	boundary () const
	Boundary. More...

void	set_boundary (int bound)
	Function to set boundary. More...

const double	get_eta () const
	Eta. More...

void	set_eta (double eta)
	Function to set Eta. More...

	PolarNavierStokesTractionElement (FiniteElement *const &element_pt, const int &face_index)

	~PolarNavierStokesTractionElement ()
	Destructor should not delete anything. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	This function returns just the residuals. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	This function returns the residuals and the jacobian. More...

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

void	output (std::ostream &outfile)
	Overload the output function. More...

void	output (std::ostream &outfile, const unsigned &nplot)
	Output function: x,y,[z],u,v,[w],p in tecplot format. More...

double	u (const unsigned &l, const unsigned &i)
	local velocities More...

double	x (const unsigned &l, const unsigned &i)
	local position More...

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

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

Public Attributes
void(*&)(const double &t, const Vector< double > &x, Vector< double > &result)	traction_fct_pt ()

Protected Member Functions
virtual int	u_local_eqn (const unsigned &n, const unsigned &i)

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

void	get_traction (double time, const Vector< double > &x, Vector< double > &result)
	Function to calculate the traction applied to the fluid. More...

void	fill_in_generic_residual_contribution (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag)

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_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)

Protected Attributes
double *	Alpha_pt
	Pointer to the angle alpha. More...

Data *	Pext_data_pt
	Pointer to the Data item that stores the external pressure. More...

unsigned	External_data_number_of_Pext

int	Boundary

double	Eta

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

Private Attributes
void(*	Traction_fct_pt )(const double &time, const Vector< double > &x, Vector< double > &result)
	Pointer to an imposed traction function. More...

unsigned	Dim
	The highest dimension of the problem. More...

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

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

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

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::PolarNavierStokesTractionElement< ELEMENT >

A class for elements that allow the imposition of an applied traction to the Navier–Stokes equations The geometrical information can be read from the FaceGeometery<ELEMENT> class and and thus, we can be generic enough without the need to have a separate equations class

Constructor & Destructor Documentation

◆ PolarNavierStokesTractionElement()

template<class ELEMENT >

oomph::PolarNavierStokesTractionElement< ELEMENT >::PolarNavierStokesTractionElement	(	FiniteElement *const &	element_pt,
		const int &	face_index
	)

inline

Constructor, which takes a "bulk" element and the value of the index and its limit

       : FaceGeometry<ELEMENT>(), FaceElement()
     {
       // Attach the geometrical information to the element. N.B. This function
       // also assigns nbulk_value from the required_nvalue of the bulk element
       element_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*>(element_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
  
       // Set the body force function pointer to zero
       Traction_fct_pt = 0;
  
       // Set the external pressure pointer to be zero
       Pext_data_pt = 0;
  
       // Set the dimension from the dimension of the first node
       Dim = this->node_pt(0)->ndim();
  
       // Set Eta to one by default
       Eta = 1.0;
     }

References oomph::FiniteElement::build_face_element(), oomph::PolarNavierStokesTractionElement< ELEMENT >::Dim, oomph::FaceElement::face_index(), oomph::FiniteElement::has_hanging_nodes(), oomph::Node::ndim(), oomph::FiniteElement::node_pt(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::PolarNavierStokesTractionElement< ELEMENT >::Pext_data_pt, and oomph::PolarNavierStokesTractionElement< ELEMENT >::Traction_fct_pt.

◆ ~PolarNavierStokesTractionElement()

template<class ELEMENT >

oomph::PolarNavierStokesTractionElement< ELEMENT >::~PolarNavierStokesTractionElement ( )

inline

Destructor should not delete anything.

238 {}

Member Function Documentation

◆ alpha()

template<class ELEMENT >

const double& oomph::PolarNavierStokesTractionElement< ELEMENT >::alpha ( ) const

inline

Alpha.

     {
       return *Alpha_pt;
     }

References oomph::PolarNavierStokesTractionElement< ELEMENT >::Alpha_pt.

◆ alpha_pt()

template<class ELEMENT >

double*& oomph::PolarNavierStokesTractionElement< ELEMENT >::alpha_pt ( )

inline

Pointer to Alpha.

     {
       return Alpha_pt;
     }

References oomph::PolarNavierStokesTractionElement< ELEMENT >::Alpha_pt.

Referenced by oomph::jh_mesh< ELEMENT >::make_traction_elements().

◆ boundary()

template<class ELEMENT >

const int oomph::PolarNavierStokesTractionElement< ELEMENT >::boundary ( ) const

inline

Boundary.

     {
       return Boundary;
     }

References oomph::PolarNavierStokesTractionElement< ELEMENT >::Boundary.

◆ fill_in_contribution_to_jacobian()

template<class ELEMENT >

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

inlinevirtual

This function returns the residuals and the jacobian.

Reimplemented from oomph::FiniteElement.

     {
       // Call the generic routine with the flag set to 1
       fill_in_generic_residual_contribution(
         residuals, jacobian, GeneralisedElement::Dummy_matrix, 1);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::PolarNavierStokesTractionElement< ELEMENT >::fill_in_generic_residual_contribution().

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

template<class ELEMENT >

void oomph::PolarNavierStokesTractionElement< ELEMENT >::fill_in_contribution_to_jacobian_and_mass_matrix	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	mass_matrix
	)

inlinevirtual

Compute the element's residual Vector and the jacobian matrix Plus the mass matrix especially for eigenvalue problems

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the generic routine with the flag set to 2
       fill_in_generic_residual_contribution(
         residuals, jacobian, GeneralisedElement::Dummy_matrix, 2);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::PolarNavierStokesTractionElement< ELEMENT >::fill_in_generic_residual_contribution().

◆ fill_in_contribution_to_residuals()

template<class ELEMENT >

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

inlinevirtual

This function returns just the residuals.

Reimplemented from oomph::GeneralisedElement.

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

References oomph::GeneralisedElement::Dummy_matrix, and oomph::PolarNavierStokesTractionElement< ELEMENT >::fill_in_generic_residual_contribution().

◆ fill_in_generic_residual_contribution()

template<class ELEMENT >

void oomph::PolarNavierStokesTractionElement< ELEMENT >::fill_in_generic_residual_contribution	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	mass_matrix,
		unsigned	flag
	)

protected

This function returns the residuals for the traction function. flag=1(or 0): do (or don't) compute the Jacobian as well.

//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// Function that returns the residuals for the imposed traction Navier_Stokes equations

/////////////////////////////////////NEW//////////////////////////////////////////

The additional residual for the mass flux (ie. the extra equation for pext) This is an integral equation along the whole boundary It lies outside the loop over shape functions above

/////////////////////////////////////NEW//////////////////////////////////////////

   {
     // Find out how many nodes there are
     unsigned n_node = nnode();
  
     // Get continuous time from timestepper of first node
     double time = node_pt(0)->time_stepper_pt()->time_pt()->time();
  
     // Set up memory for the shape and test functions
     Shape psif(n_node), testf(n_node);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Get Alpha
     const double Alpha = alpha();
  
     // Storage for external pressure
     double pext = 0.0;
  
     // Get boundary multiplier
     // This is necessary because the sign of the traction is
     // dependent on the boundary
     const int multiplier = boundary();
  
     // Get the homotopy parameter (if necessary)
     const double eta = get_eta();
  
     // Integers to store local equation numbers
     int local_eqn = 0, local_unknown = 0, pext_local_eqn = 0,
         pext_local_unknown = 0;
  
  
     // Get local equation number of external pressure
     // Note that if we have not passed an external pressure pointer to this
     // element (and at the same time added it to the element's external data)
     // than this will be -1 to indicate that it is not a degree of freedom here
     if (Pext_data_pt == 0)
     {
       pext_local_eqn = -1;
     }
     else
     {
       // If at a non-zero degree of freedom add in the entry
       pext_local_eqn = external_local_eqn(External_data_number_of_Pext, 0);
  
       // Get external pressure
       pext = Pext_data_pt->value(0);
     }
  
     // The local unkown number of pext will be the same
     pext_local_unknown = pext_local_eqn;
  
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // 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_at_knot(ipt, psif, testf);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Need to find position to feed into Traction function
       Vector<double> interpolated_x(Dim);
       Vector<double> interpolated_u(Dim);
  
       // Initialise to zero
       for (unsigned i = 0; i < Dim; i++)
       {
         interpolated_x[i] = 0.0;
         interpolated_u[i] = 0.0;
       }
  
       // Calculate velocities and derivatives:
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over directions
         for (unsigned i = 0; i < Dim; i++)
         {
           // Get the nodal value
           interpolated_u[i] += this->nodal_value(l, i) * psif[l];
           interpolated_x[i] += this->nodal_position(l, i) * psif[l];
         }
       }
  
       // Get the user-defined traction terms
       Vector<double> traction(Dim);
       get_traction(time, interpolated_x, traction);
  
       // Now add to the appropriate equations
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Only alter u velocity component
         {
           unsigned i = 0;
           local_eqn = u_local_eqn(l, i);
           /*IF it's not a boundary condition*/
           if (local_eqn >= 0)
           {
             // Add the user-defined traction terms
             residuals[local_eqn] -= multiplier * eta * 3.0 *
                                     (interpolated_u[i] / interpolated_x[0]) *
                                     testf[l] * interpolated_x[0] * Alpha * W;
  
  
             // Plus additional external pressure contribution at inlet
             // This is zero if we haven't passed a Pext_data_pt to the element
             residuals[local_eqn] +=
               pext * testf[l] * interpolated_x[0] * Alpha * W;
  
  
             // CALCULATE THE JACOBIAN
             if (flag)
             {
               // Loop over the velocity shape functions again
               for (unsigned l2 = 0; l2 < n_node; l2++)
               {
                 // We only have an i2=0 contribution
                 unsigned i2 = 0;
                 {
                   // If at a non-zero degree of freedom add in the entry
                   local_unknown = u_local_eqn(l2, i2);
                   if (local_unknown >= 0)
                   {
                     // Add contribution to Elemental Matrix
                     jacobian(local_eqn, local_unknown) -=
                       multiplier * eta * 3.0 * (psif[l2] / interpolated_x[0]) *
                       testf[l] * interpolated_x[0] * Alpha * W;
  
                   } // End of (Jacobian's) if not boundary condition statement
                 } // End of i2=0 section
               } // End of l2 loop
  
               // Add pext's contribution to these residuals
               // This only needs to be done once hence why it is outside the l2
               // loop
               if (pext_local_unknown >= 0)
               {
                 // Add contribution to Elemental Matrix
                 jacobian(local_eqn, pext_local_unknown) +=
                   testf[l] * interpolated_x[0] * Alpha * W;
               }
  
             } /*End of Jacobian calculation*/
  
           } // end of if not boundary condition statement
         } // End of i=0 section
  
       } // End of loop over shape functions
  
  
       {
         /*IF it's not a boundary condition*/
         if (pext_local_eqn >= 0)
         {
           // Add the user-defined traction terms
           residuals[pext_local_eqn] +=
             interpolated_u[0] * interpolated_x[0] * Alpha * W;
  
           // No longer necessary due to my FluxCosntraint element
           // Now take off a fraction of the desired mass flux
           // Divided by number of elements and number of int points in each
           // HACK
           // residuals[pext_local_eqn] -= (1.0/(30.*3.));
           // HACK
  
           // CALCULATE THE JACOBIAN
           if (flag)
           {
             // Loop over the velocity shape functions again
             for (unsigned l2 = 0; l2 < n_node; l2++)
             {
               // We only have an i2=0 contribution
               unsigned i2 = 0;
               {
                 // If at a non-zero degree of freedom add in the entry
                 local_unknown = u_local_eqn(l2, i2);
                 if (local_unknown >= 0)
                 {
                   // Add contribution to Elemental Matrix
                   jacobian(pext_local_eqn, local_unknown) +=
                     psif[l2] * interpolated_x[0] * Alpha * W;
  
                 } // End of (Jacobian's) if not boundary condition statement
               } // End of i2=0 section
  
             } // End of l2 loop
           } /*End of Jacobian calculation*/
  
         } // end of if not boundary condition statement
       } // End of additional residual for the mass flux
  
  
     } // End of loop over integration points
  
   } // End of fill_in_generic_residual_contribution

References alpha, TanhSolnForAdvectionDiffusion::Alpha, Global_Variables::Dim, TestSoln::eta, i, J, Global_Physical_Variables::multiplier(), Global_Physical_Variables::Pext_data_pt, oomph::Data::value(), w, and oomph::QuadTreeNames::W.

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

◆ get_eta()

template<class ELEMENT >

const double oomph::PolarNavierStokesTractionElement< ELEMENT >::get_eta ( ) const

inline

Eta.

     {
       return Eta;
     }

References oomph::PolarNavierStokesTractionElement< ELEMENT >::Eta.

◆ get_traction()

template<class ELEMENT >

void oomph::PolarNavierStokesTractionElement< ELEMENT >::get_traction	(	double	time,
		const Vector< double > &	x,
		Vector< double > &	result
	)

inlineprotected

Function to calculate the traction applied to the fluid.

     {
       // If the function pointer is zero return zero
       if (Traction_fct_pt == 0)
       {
         // Loop over dimensions and set body forces to zero
         for (unsigned i = 0; i < Dim; i++)
         {
           result[i] = 0.0;
         }
       }
       // Otherwise call the function
       else
       {
         (*Traction_fct_pt)(time, x, result);
       }
     }

References oomph::PolarNavierStokesTractionElement< ELEMENT >::Dim, i, oomph::PolarNavierStokesTractionElement< ELEMENT >::Traction_fct_pt, and oomph::PolarNavierStokesTractionElement< ELEMENT >::x().

◆ output() [1/2]

template<class ELEMENT >

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

inlinevirtual

Overload the output function.

Reimplemented from oomph::FiniteElement.

     {
       FiniteElement::output(outfile);
     }

References oomph::FiniteElement::output().

◆ output() [2/2]

template<class ELEMENT >

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

inlinevirtual

Output function: x,y,[z],u,v,[w],p in tecplot format.

Reimplemented from oomph::FiniteElement.

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

References oomph::FiniteElement::output().

◆ set_boundary()

template<class ELEMENT >

void oomph::PolarNavierStokesTractionElement< ELEMENT >::set_boundary ( int bound )

inline

Function to set boundary.

     {
       Boundary = bound;
     }

References oomph::PolarNavierStokesTractionElement< ELEMENT >::Boundary.

Referenced by oomph::jh_mesh< ELEMENT >::make_traction_elements().

◆ set_eta()

template<class ELEMENT >

void oomph::PolarNavierStokesTractionElement< ELEMENT >::set_eta ( double eta )

inline

Function to set Eta.

     {
       Eta = eta;
     }

References TestSoln::eta, and oomph::PolarNavierStokesTractionElement< ELEMENT >::Eta.

Referenced by oomph::jh_mesh< ELEMENT >::make_traction_elements().

◆ set_external_pressure_data()

template<class ELEMENT >

void oomph::PolarNavierStokesTractionElement< ELEMENT >::set_external_pressure_data ( Data * pext_data_pt )

inline

Function for setting up external pressure.

     {
       // Set external pressure pointer
       Pext_data_pt = pext_data_pt;
  
       // Add to the element's external data so it gets included
       // in the black-box local equation numbering scheme
       External_data_number_of_Pext = this->add_external_data(pext_data_pt);
     }

References oomph::GeneralisedElement::add_external_data(), oomph::PolarNavierStokesTractionElement< ELEMENT >::External_data_number_of_Pext, and oomph::PolarNavierStokesTractionElement< ELEMENT >::Pext_data_pt.

◆ shape_and_test_at_knot()

template<class ELEMENT >

double oomph::PolarNavierStokesTractionElement< 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

     {
       // Find number of nodes
       unsigned n_node = nnode();
       // Calculate 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().

◆ u()

template<class ELEMENT >

double oomph::PolarNavierStokesTractionElement< ELEMENT >::u	(	const unsigned &	l,
		const unsigned &	i
	)

inline

local velocities

     {
       return nodal_value(l, i);
     }

References i, and oomph::FiniteElement::nodal_value().

◆ u_local_eqn()

template<class ELEMENT >

virtual int oomph::PolarNavierStokesTractionElement< ELEMENT >::u_local_eqn	(	const unsigned &	n,
		const unsigned &	i
	)

inlineprotectedvirtual

Access function that returns the local equation numbers for velocity components. u_local_eqn(n,i) = local equation number or < 0 if pinned. The default is to asssume that n is the local node number and the i-th velocity component is the i-th unknown stored at the node.

     {
       return nodal_local_eqn(n, i);
     }

References i, n, and oomph::FiniteElement::nodal_local_eqn().

◆ x()

template<class ELEMENT >

double oomph::PolarNavierStokesTractionElement< ELEMENT >::x	(	const unsigned &	l,
		const unsigned &	i
	)

inline

local position

     {
       return nodal_position(l, i);
     }

References i, and oomph::FiniteElement::nodal_position().

Referenced by oomph::PolarNavierStokesTractionElement< ELEMENT >::get_traction().

Member Data Documentation

◆ Alpha_pt

template<class ELEMENT >

double* oomph::PolarNavierStokesTractionElement< ELEMENT >::Alpha_pt

protected

Pointer to the angle alpha.

Referenced by oomph::PolarNavierStokesTractionElement< ELEMENT >::alpha(), and oomph::PolarNavierStokesTractionElement< ELEMENT >::alpha_pt().

◆ Boundary

template<class ELEMENT >

int oomph::PolarNavierStokesTractionElement< ELEMENT >::Boundary

protected

Referenced by oomph::PolarNavierStokesTractionElement< ELEMENT >::boundary(), and oomph::PolarNavierStokesTractionElement< ELEMENT >::set_boundary().

◆ Dim

template<class ELEMENT >

unsigned oomph::PolarNavierStokesTractionElement< ELEMENT >::Dim

private

The highest dimension of the problem.

Referenced by oomph::PolarNavierStokesTractionElement< ELEMENT >::get_traction(), and oomph::PolarNavierStokesTractionElement< ELEMENT >::PolarNavierStokesTractionElement().

◆ Eta

template<class ELEMENT >

double oomph::PolarNavierStokesTractionElement< ELEMENT >::Eta

protected

Referenced by oomph::PolarNavierStokesTractionElement< ELEMENT >::get_eta(), and oomph::PolarNavierStokesTractionElement< ELEMENT >::set_eta().

◆ External_data_number_of_Pext

template<class ELEMENT >

unsigned oomph::PolarNavierStokesTractionElement< ELEMENT >::External_data_number_of_Pext

protected

The Data that contains the traded pressure is stored as external Data for the element. Which external Data item is it?

Referenced by oomph::PolarNavierStokesTractionElement< ELEMENT >::set_external_pressure_data().

◆ Pext_data_pt

template<class ELEMENT >

Data* oomph::PolarNavierStokesTractionElement< ELEMENT >::Pext_data_pt

protected

Pointer to the Data item that stores the external pressure.

Referenced by oomph::PolarNavierStokesTractionElement< ELEMENT >::PolarNavierStokesTractionElement(), and oomph::PolarNavierStokesTractionElement< ELEMENT >::set_external_pressure_data().

◆ traction_fct_pt

template<class ELEMENT >

void(*&)(const double& t, const Vector<double>& x, Vector<double>& result) oomph::PolarNavierStokesTractionElement< ELEMENT >::traction_fct_pt()

inline

     {
       return Traction_fct_pt;
     }

Referenced by oomph::jh_mesh< ELEMENT >::make_traction_elements().

◆ Traction_fct_pt

template<class ELEMENT >

void(* oomph::PolarNavierStokesTractionElement< ELEMENT >::Traction_fct_pt) (const double &time, const Vector< double > &x, Vector< double > &result)

private

Pointer to an imposed traction function.

Referenced by oomph::PolarNavierStokesTractionElement< ELEMENT >::get_traction(), and oomph::PolarNavierStokesTractionElement< ELEMENT >::PolarNavierStokesTractionElement().

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

polar_fluid_traction_elements.h

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Attributes

Additional Inherited Members

Detailed Description

template<class ELEMENT> class oomph::PolarNavierStokesTractionElement< ELEMENT >

Constructor & Destructor Documentation

◆ PolarNavierStokesTractionElement()

◆ ~PolarNavierStokesTractionElement()

Member Function Documentation

◆ alpha()

◆ alpha_pt()

◆ boundary()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution()

◆ get_eta()

◆ get_traction()

◆ output() [1/2]

◆ output() [2/2]

◆ set_boundary()

◆ set_eta()

◆ set_external_pressure_data()

◆ shape_and_test_at_knot()

◆ u()

◆ u_local_eqn()

◆ x()

Member Data Documentation

◆ Alpha_pt

◆ Boundary

◆ Dim

◆ Eta

◆ External_data_number_of_Pext

◆ Pext_data_pt

◆ traction_fct_pt

◆ Traction_fct_pt

template<class ELEMENT>
class oomph::PolarNavierStokesTractionElement< ELEMENT >