#include <polar_navier_stokes_elements.h>

Inheritance diagram for oomph::PolarTaylorHoodElement:

Public Member Functions
	PolarTaylorHoodElement ()
	Constructor, no internal data points. More...

virtual unsigned	required_nvalue (const unsigned &n) const

virtual int	p_nodal_index_pnst ()
	Which nodal value represents the pressure? More...

Node *	pressure_node_pt (const unsigned &n_p)
	Pointer to n_p-th pressure node. More...

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

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

double	p_pnst (const unsigned &n_p) const

unsigned	npres_pnst () const
	Return number of pressure values. More...

void	fix_pressure (const unsigned &p_dof, const double &p_value)
	Pin p_dof-th pressure dof and set it to value specified by p_value. More...

void	get_load_data (std::set< std::pair< Data *, unsigned >> &paired_load_data)

void	output (std::ostream &outfile)
	Redirect output to NavierStokesEquations output. More...

void	output (std::ostream &outfile, const unsigned &Nplot)
	Redirect output to NavierStokesEquations output. More...

void	output (FILE *file_pt)
	Redirect output to NavierStokesEquations output. More...

void	output (FILE *file_pt, const unsigned &Nplot)
	Redirect output to NavierStokesEquations output. More...

Public Member Functions inherited from oomph::PolarNavierStokesEquations
	PolarNavierStokesEquations ()
	Constructor: NULL the body force and source function. More...

const double &	re () const
	Reynolds number. More...

const double &	alpha () const
	Alpha. More...

const double &	re_st () const
	Product of Reynolds and Strouhal number (=Womersley number) More...

double *&	re_pt ()
	Pointer to Reynolds number. More...

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

double *&	re_st_pt ()
	Pointer to product of Reynolds and Strouhal number (=Womersley number) More...

const double &	viscosity_ratio () const

double *&	viscosity_ratio_pt ()
	Pointer to Viscosity Ratio. More...

const double &	density_ratio () const

double *&	density_ratio_pt ()
	Pointer to Density ratio. More...

const double &	re_invfr () const
	Global inverse Froude number. More...

double *&	re_invfr_pt ()
	Pointer to global inverse Froude number. More...

const Vector< double > &	g () const
	Vector of gravitational components. More...

Vector< double > *&	g_pt ()
	Pointer to Vector of gravitational components. More...

NavierStokesBodyForceFctPt &	body_force_fct_pt ()
	Access function for the body-force pointer. More...

NavierStokesBodyForceFctPt	body_force_fct_pt () const
	Access function for the body-force pointer. Const version. More...

NavierStokesSourceFctPt &	source_fct_pt ()
	Access function for the source-function pointer. More...

NavierStokesSourceFctPt	source_fct_pt () const
	Access function for the source-function pointer. Const version. More...

virtual unsigned	u_index_pnst (const unsigned &i) const

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

double	pressure_integral () const
	Integral of pressure over element. More...

double	dissipation () const
	Return integral of dissipation over element. More...

double	dissipation (const Vector< double > &s) const
	Return dissipation at local coordinate s. More...

double	kin_energy () const
	Get integral of kinetic energy over element. More...

void	strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate) const
	Strain-rate tensor: Now returns polar strain. More...

void	strain_rate_by_r (const Vector< double > &s, DenseMatrix< double > &strain_rate) const
	Function to return polar strain multiplied by r. More...

void	get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction)

void	get_load (const Vector< double > &s, const Vector< double > &xi, const Vector< double > &x, const Vector< double > &N, Vector< double > &load)

void	full_output (std::ostream &outfile)

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

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

void	output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)

void	output_fct (std::ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)

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

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

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Compute the element's residual Vector. More...

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

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

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

void	interpolated_u_pnst (const Vector< double > &s, Vector< double > &veloc) const
	Compute vector of FE interpolated velocity u at local coordinate s. More...

double	interpolated_u_pnst (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated velocity u[i] at local coordinate s. More...

double	interpolated_p_pnst (const Vector< double > &s) const
	Return FE interpolated pressure at local coordinate s. More...

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) 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 ()

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...

virtual double	interpolated_x (const Vector< double > &s, const unsigned &i) const
	Return FE interpolated coordinate x[i] at local coordinate s. More...

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

virtual void	interpolated_x (const Vector< double > &s, Vector< double > &x) const
	Return FE interpolated position x[] at local coordinate s as Vector. More...

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

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

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

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)

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

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_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, 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	dshape_and_dtest_eulerian_pnst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

double	dshape_and_dtest_eulerian_at_knot_pnst (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

void	pshape_pnst (const Vector< double > &s, Shape &psi) const
	Pressure shape functions at local coordinate s. More...

void	pshape_pnst (const Vector< double > &s, Shape &psi, Shape &test) const
	Pressure shape and test functions at local coordinte s. More...

int	p_local_eqn (const unsigned &n)
	Return the local equation numbers for the pressure values. More...

Protected Member Functions inherited from oomph::PolarNavierStokesEquations
void	get_body_force (double time, const Vector< double > &x, Vector< double > &result)
	Calculate the body force at a given time and Eulerian position. More...

double	get_source_fct (double time, const Vector< double > &x)

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)

Static Protected Attributes
static const unsigned	Pconv [] = {0, 2, 6, 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

Static Private Attributes
static const unsigned	Initial_Nvalue []
	Static array of ints to hold number of variables at node. More...

Additional Inherited Members
Public Types inherited from oomph::PolarNavierStokesEquations
typedef void(*	NavierStokesBodyForceFctPt) (const double &time, const Vector< double > &x, Vector< double > &body_force)

typedef double(*	NavierStokesSourceFctPt) (const double &time, const Vector< double > &x)

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::PolarNavierStokesEquations
static Vector< double >	Gamma
	Vector to decide whether the stress-divergence form is used or not. More...

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::PolarNavierStokesEquations
double *	Viscosity_Ratio_pt

double *	Density_Ratio_pt

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

double *	Re_pt
	Pointer to global Reynolds number. More...

double *	ReSt_pt
	Pointer to global Reynolds number x Strouhal number (=Womersley) More...

double *	ReInvFr_pt

Vector< double > *	G_pt
	Pointer to global gravity Vector. More...

NavierStokesBodyForceFctPt	Body_force_fct_pt
	Pointer to body force function. More...

NavierStokesSourceFctPt	Source_fct_pt
	Pointer to volumetric source function. More...

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

Detailed Description

///////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////// Taylor–Hood elements are Navier–Stokes elements with quadratic interpolation for velocities and positions and continous linear pressure interpolation

Constructor & Destructor Documentation

◆ PolarTaylorHoodElement()

oomph::PolarTaylorHoodElement::PolarTaylorHoodElement ( )

inline

Constructor, no internal data points.

1058 : QElement<2, 3>(), PolarNavierStokesEquations() {}

QElement

oomph::PolarNavierStokesEquations::PolarNavierStokesEquations

PolarNavierStokesEquations()

Constructor: NULL the body force and source function.

Definition: polar_navier_stokes_elements.h:245

Member Function Documentation

◆ dshape_and_dtest_eulerian_at_knot_pnst()

double oomph::PolarTaylorHoodElement::dshape_and_dtest_eulerian_at_knot_pnst	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlineprotectedvirtual

Velocity shape and test functions and their derivs w.r.t. to global coords at local coordinate s (taken from geometry) Return Jacobian of mapping between local and global coordinates.

2D : Derivatives of the shape functions and test functions w.r.t to global (Eulerian) coordinates. Return Jacobian of mapping between local and global coordinates.

Implements oomph::PolarNavierStokesEquations.

   {
     // Call the geometrical shape functions and derivatives
     double J = QElement<2, 3>::dshape_eulerian_at_knot(ipt, psi, dpsidx);
     // Loop over the test functions and derivatives and set them equal to the
     // shape functions
     for (unsigned i = 0; i < 9; i++)
     {
       test[i] = psi[i];
       dtestdx(i, 0) = dpsidx(i, 0);
       dtestdx(i, 1) = dpsidx(i, 1);
     }
     // Return the jacobian
     return J;
   }

References i, and J.

◆ dshape_and_dtest_eulerian_pnst()

double oomph::PolarTaylorHoodElement::dshape_and_dtest_eulerian_pnst	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlineprotectedvirtual

Velocity shape and test functions and their derivs w.r.t. to global coords at local coordinate s (taken from geometry) Return Jacobian of mapping between local and global coordinates.

2D : Derivatives of the shape functions and test functions w.r.t to global (Eulerian) coordinates. Return Jacobian of mapping between local and global coordinates.

Implements oomph::PolarNavierStokesEquations.

   {
     // Call the geometrical shape functions and derivatives
     double J = QElement<2, 3>::dshape_eulerian(s, psi, dpsidx);
     // Loop over the test functions and derivatives and set them equal to the
     // shape functions
     for (unsigned i = 0; i < 9; i++)
     {
       test[i] = psi[i];
       dtestdx(i, 0) = dpsidx(i, 0);
       dtestdx(i, 1) = dpsidx(i, 1);
     }
     // Return the jacobian
     return J;
   }

References i, J, and s.

◆ fix_pressure()

void oomph::PolarTaylorHoodElement::fix_pressure	(	const unsigned &	p_dof,
		const double &	p_value
	)

inlinevirtual

Pin p_dof-th pressure dof and set it to value specified by p_value.

Implements oomph::PolarNavierStokesEquations.

     {
       this->node_pt(Pconv[p_dof])->pin(this->p_nodal_index_pnst());
       *this->node_pt(Pconv[p_dof])->value_pt(this->p_nodal_index_pnst()) =
         p_value;
     }

References oomph::FiniteElement::node_pt(), p_nodal_index_pnst(), oomph::Data::pin(), and oomph::Data::value_pt().

◆ get_load_data()

void oomph::PolarTaylorHoodElement::get_load_data ( std::set< std::pair< Data *, unsigned >> & paired_load_data )

Add to the set paired_load_data pairs of pointers to data objects and unsigned integers that index the values in the data object that affect the load (traction), as specified in the get_load() function.

Add pointers to Data and the indices of the values that affect the potential load (traction) applied to the SolidElements to the set paired_load_data.

   {
     // Loop over the nodes
     unsigned n_node = this->nnode();
     for (unsigned n = 0; n < n_node; n++)
     {
       // Loop over the velocity components and add pointer to their data
       // and indices to the vectors
       for (unsigned i = 0; i < 2; i++)
       {
         paired_load_data.insert(std::make_pair(this->node_pt(n), i));
       }
     }
  
     // Loop over the pressure data
     unsigned n_pres = npres_pnst();
     for (unsigned l = 0; l < n_pres; l++)
     {
       // The 2th entry in each nodal data is the pressure, which
       // affects the traction
       paired_load_data.insert(std::make_pair(this->node_pt(Pconv[l]), 2));
     }
   }

References i, n, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), npres_pnst(), and Pconv.

◆ npres_pnst()

unsigned oomph::PolarTaylorHoodElement::npres_pnst ( ) const

inlinevirtual

Return number of pressure values.

Implements oomph::PolarNavierStokesEquations.

     {
       return 4;
     }

Referenced by get_load_data(), oomph::RefineablePolarTaylorHoodElement::insert_load_data(), and oomph::RefineablePolarTaylorHoodElement::pin_elemental_redundant_nodal_pressure_dofs().

◆ output() [1/4]

void oomph::PolarTaylorHoodElement::output ( FILE * file_pt )

inlinevirtual

Redirect output to NavierStokesEquations output.

Reimplemented from oomph::PolarNavierStokesEquations.

     {
       PolarNavierStokesEquations::output(file_pt);
     }

References oomph::PolarNavierStokesEquations::output().

◆ output() [2/4]

void oomph::PolarTaylorHoodElement::output	(	FILE *	file_pt,
		const unsigned &	Nplot
	)

inlinevirtual

Redirect output to NavierStokesEquations output.

Reimplemented from oomph::PolarNavierStokesEquations.

     {
       PolarNavierStokesEquations::output(file_pt, Nplot);
     }

References oomph::PolarNavierStokesEquations::output().

◆ output() [3/4]

void oomph::PolarTaylorHoodElement::output ( std::ostream & outfile )

inlinevirtual

Redirect output to NavierStokesEquations output.

Reimplemented from oomph::PolarNavierStokesEquations.

     {
       PolarNavierStokesEquations::output(outfile);
     }

References oomph::PolarNavierStokesEquations::output().

◆ output() [4/4]

void oomph::PolarTaylorHoodElement::output	(	std::ostream &	outfile,
		const unsigned &	Nplot
	)

inlinevirtual

Redirect output to NavierStokesEquations output.

Reimplemented from oomph::PolarNavierStokesEquations.

     {
       PolarNavierStokesEquations::output(outfile, Nplot);
     }

References oomph::PolarNavierStokesEquations::output().

◆ p_local_eqn()

int oomph::PolarTaylorHoodElement::p_local_eqn ( const unsigned & n )

inlineprotectedvirtual

Return the local equation numbers for the pressure values.

Implements oomph::PolarNavierStokesEquations.

     {
       return this->nodal_local_eqn(Pconv[n], p_nodal_index_pnst());
     }

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

◆ p_nodal_index_pnst()

virtual int oomph::PolarTaylorHoodElement::p_nodal_index_pnst ( )

inlinevirtual

Which nodal value represents the pressure?

Reimplemented from oomph::PolarNavierStokesEquations.

     {
       return 2;
     }

Referenced by fix_pressure(), oomph::RefineablePolarTaylorHoodElement::further_setup_hanging_nodes(), oomph::RefineablePolarTaylorHoodElement::insert_load_data(), p_local_eqn(), oomph::RefineablePolarTaylorHoodElement::pin_elemental_redundant_nodal_pressure_dofs(), and oomph::RefineablePolarTaylorHoodElement::unpin_elemental_pressure_dofs().

◆ p_pnst()

double oomph::PolarTaylorHoodElement::p_pnst ( const unsigned & n_p ) const

inlinevirtual

Access function for the pressure values at local pressure node n_p (const version)

Implements oomph::PolarNavierStokesEquations.

     {
       return this->nodal_value(Pconv[n_p], 2);
     }

References oomph::FiniteElement::nodal_value().

◆ pressure_node_pt()

Node* oomph::PolarTaylorHoodElement::pressure_node_pt ( const unsigned & n_p )

inlinevirtual

Pointer to n_p-th pressure node.

Reimplemented from oomph::PolarNavierStokesEquations.

Reimplemented in oomph::RefineablePolarTaylorHoodElement.

     {
       return this->node_pt(Pconv[n_p]);
     }

References oomph::FiniteElement::node_pt().

◆ pshape_pnst() [1/2]

void oomph::PolarTaylorHoodElement::pshape_pnst	(	const Vector< double > &	s,
		Shape &	psi
	)		const

inlineprotectedvirtual

Pressure shape functions at local coordinate s.

2D : Pressure shape functions

Implements oomph::PolarNavierStokesEquations.

   {
     // Call the OneDimensional Shape functions
     // Local storage
     double psi1[2], psi2[2];
     // Call the OneDimensional Shape functions
     OneDimLagrange::shape<2>(s[0], psi1);
     OneDimLagrange::shape<2>(s[1], psi2);
  
     // Now let's loop over the nodal points in the element
     // s1 is the "x" coordinate, s2 the "y"
     for (unsigned i = 0; i < 2; i++)
     {
       for (unsigned j = 0; j < 2; j++)
       {
         /*Multiply the two 1D functions together to get the 2D function*/
         psi[2 * i + j] = psi2[i] * psi1[j];
       }
     }
   }

References i, j, s, and oomph::OneDimLagrange::shape< 2 >().

Referenced by oomph::RefineablePolarTaylorHoodElement::interpolating_basis(), and pshape_pnst().

◆ pshape_pnst() [2/2]

void oomph::PolarTaylorHoodElement::pshape_pnst	(	const Vector< double > &	s,
		Shape &	psi,
		Shape &	test
	)		const

inlineprotectedvirtual

Pressure shape and test functions at local coordinte s.

2D : Pressure shape and test functions

Implements oomph::PolarNavierStokesEquations.

   {
     // Call the pressure shape functions
     pshape_pnst(s, psi);
     // Loop over the test functions and set them equal to the shape functions
     for (unsigned i = 0; i < 4; i++) test[i] = psi[i];
   }

References i, pshape_pnst(), and s.

◆ required_nvalue()

virtual unsigned oomph::PolarTaylorHoodElement::required_nvalue ( const unsigned & n ) const

inlinevirtual

Number of values (pinned or dofs) required at node n. Can be overwritten for hanging node version

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::RefineablePolarTaylorHoodElement.

     {
       return Initial_Nvalue[n];
     }

References Initial_Nvalue, and n.

◆ u_pnst() [1/2]

double oomph::PolarTaylorHoodElement::u_pnst	(	const unsigned &	n,
		const unsigned &	i
	)		const

inlinevirtual

Return the velocity component u[i] at local node n. Uses suitably interpolated value for hanging nodes.

Implements oomph::PolarNavierStokesEquations.

     {
       return this->nodal_value(n, i);
     }

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

◆ u_pnst() [2/2]

double oomph::PolarTaylorHoodElement::u_pnst	(	const unsigned &	t,
		const unsigned &	n,
		const unsigned &	i
	)		const

inlinevirtual

Return the velocity component u[i] at local node n at timestep t (t=0: present; t>0: previous timestep). Uses suitably interpolated value for hanging nodes.

Implements oomph::PolarNavierStokesEquations.

     {
       return this->nodal_value(t, n, i);
     }

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

Member Data Documentation

◆ Initial_Nvalue

const unsigned oomph::PolarTaylorHoodElement::Initial_Nvalue

staticprivate

Initial value:

= {

3, 2, 3, 2, 2, 2, 3, 2, 3}

Static array of ints to hold number of variables at node.

//////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////

Referenced by required_nvalue().

◆ Pconv

const unsigned oomph::PolarTaylorHoodElement::Pconv = {0, 2, 6, 8}

staticprotected

Static array of ints to hold conversion from pressure node numbers to actual node numbers

Referenced by get_load_data(), and oomph::RefineablePolarTaylorHoodElement::pressure_node_pt().

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

Public Member Functions

Protected Member Functions

Static Protected Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PolarTaylorHoodElement()

Member Function Documentation

◆ dshape_and_dtest_eulerian_at_knot_pnst()

◆ dshape_and_dtest_eulerian_pnst()

◆ fix_pressure()

◆ get_load_data()

◆ npres_pnst()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ p_local_eqn()

◆ p_nodal_index_pnst()

◆ p_pnst()

◆ pressure_node_pt()

◆ pshape_pnst() [1/2]

◆ pshape_pnst() [2/2]

◆ required_nvalue()

◆ u_pnst() [1/2]

◆ u_pnst() [2/2]

Member Data Documentation

◆ Initial_Nvalue

◆ Pconv