#include <refineable_linearised_navier_stokes_elements.h>

Inheritance diagram for oomph::RefineableLinearisedQTaylorHoodElement:

Public Member Functions
	RefineableLinearisedQTaylorHoodElement ()
	Constructor: More...

unsigned	required_nvalue (const unsigned &n) const

unsigned	ncont_interpolated_values () const

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: empty. More...

unsigned	nrecovery_order ()

unsigned	nvertex_node () const
	Number of vertex nodes in the element. More...

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)

void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)

void	further_setup_hanging_nodes ()

Node *	interpolating_node_pt (const unsigned &n, const int &n_value)

double	local_one_d_fraction_of_interpolating_node (const unsigned &n1d, const unsigned &i, const int &n_value)

Node *	get_interpolating_node_at_local_coordinate (const Vector< double > &s, const int &n_value)

unsigned	ninterpolating_node_1d (const int &n_value)

unsigned	ninterpolating_node (const int &n_value)

void	interpolating_basis (const Vector< double > &s, Shape &psi, const int &n_value) const

Public Member Functions inherited from oomph::LinearisedQTaylorHoodElement
	LinearisedQTaylorHoodElement ()
	Constructor, no internal data points. More...

virtual int	p_index_linearised_nst (const unsigned &i) const

double	p_linearised_nst (const unsigned &n_p, const unsigned &i) const

void	pin_pressure_normalisation_dofs ()
	Pin the normalisation dofs. More...

virtual void	pin_real_or_imag (const unsigned &real)

virtual void	unpin_real_or_imag (const unsigned &real)

unsigned	npres_linearised_nst () const

void	fix_pressure (const unsigned &n_p, const double &pvalue)

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

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

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

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

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

unsigned	ndof_types () const

Public Member Functions inherited from oomph::LinearisedNavierStokesEquations
	LinearisedNavierStokesEquations ()

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

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

const double &	lambda () const

const double &	omega () const

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

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

double *&	lambda_pt ()
	Pointer to lambda. More...

double *&	omega_pt ()
	Pointer to frequency. More...

LinearisedNavierStokesEigenfunctionNormalisationElement *	normalisation_element_pt ()
	Pointer to normalisation element. More...

void	set_eigenfunction_normalisation_element (LinearisedNavierStokesEigenfunctionNormalisationElement *const &normalisation_el_pt)
	the boolean flag check_nodal_data is set to false. More...

const double &	viscosity_ratio () const

double *&	viscosity_ratio_pt ()
	Pointer to the viscosity ratio. More...

const double &	density_ratio () const

double *&	density_ratio_pt ()
	Pointer to the density ratio. More...

virtual unsigned	u_index_linearised_nst (const unsigned &i) const

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

void	disable_ALE ()

void	enable_ALE ()

void	strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate, const unsigned &real) const

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

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

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

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

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)

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	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	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

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 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 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_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, 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...

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 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 Member Functions inherited from oomph::RefineableLinearisedNavierStokesEquations
	RefineableLinearisedNavierStokesEquations ()
	Empty Constructor. More...

unsigned	num_Z2_flux_terms ()
	Number of 'flux' terms for Z2 error estimation. More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)

void	further_build ()
	Further build: pass the pointers down to the sons. More...

Public Member Functions inherited from oomph::RefineableElement
	RefineableElement ()

virtual	~RefineableElement ()
	Destructor, delete the allocated storage for the hanging equations. More...

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

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

Tree *	tree_pt ()
	Access function: Pointer to quadtree representation of this element. More...

void	set_tree_pt (Tree *my_tree_pt)
	Set pointer to quadtree representation of this element. More...

bool	refinement_is_enabled ()
	Flag to indicate suppression of any refinement. More...

void	disable_refinement ()
	Suppress of any refinement for this element. More...

void	enable_refinement ()
	Emnable refinement for this element. More...

template<class ELEMENT >
void	split (Vector< ELEMENT * > &son_pt) const

int	local_hang_eqn (Node *const &node_pt, const unsigned &i)

void	set_refinement_level (const int &refine_level)
	Set the refinement level. More...

unsigned	refinement_level () const
	Return the Refinement level. More...

void	select_for_refinement ()
	Select the element for refinement. More...

void	deselect_for_refinement ()
	Deselect the element for refinement. More...

void	select_sons_for_unrefinement ()
	Unrefinement will be performed by merging the four sons of this element. More...

void	deselect_sons_for_unrefinement ()

bool	to_be_refined ()
	Has the element been selected for refinement? More...

bool	sons_to_be_unrefined ()
	Has the element been selected for unrefinement? More...

virtual void	unbuild ()

virtual void	deactivate_element ()

virtual bool	nodes_built ()
	Return true if all the nodes have been built, false if not. More...

long	number () const
	Element number (for debugging/plotting) More...

void	set_number (const long &mynumber)
	Set element number (for debugging/plotting) More...

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

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

virtual RefineableElement *	root_element_pt ()

virtual RefineableElement *	father_element_pt () const
	Return a pointer to the father element. More...

void	get_father_at_refinement_level (unsigned &refinement_level, RefineableElement *&father_at_reflevel_pt)

virtual void	initial_setup (Tree *const &adopted_father_pt=0, const unsigned &initial_p_order=0)

virtual void	pre_build (Mesh &mesh_pt, Vector< Node > &new_node_pt)
	Pre-build the element. More...

void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

unsigned	nshape_controlling_nodes ()

std::map< Node *, unsigned >	shape_controlling_node_lookup ()

Public Member Functions inherited from oomph::ElementWithZ2ErrorEstimator
	ElementWithZ2ErrorEstimator ()
	Default empty constructor. More...

	ElementWithZ2ErrorEstimator (const ElementWithZ2ErrorEstimator &)=delete
	Broken copy constructor. More...

void	operator= (const ElementWithZ2ErrorEstimator &)=delete
	Broken assignment operator. More...

virtual unsigned	ncompound_fluxes ()

virtual void	compute_exact_Z2_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_flux_pt, double &error, double &norm)

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)

virtual double	geometric_jacobian (const Vector< double > &x)

Public Member Functions inherited from oomph::RefineableQElement< 2 >
	RefineableQElement ()
	Constructor: Pass refinement level (default 0 = root) More...

	RefineableQElement (const RefineableQElement< 2 > &dummy)=delete
	Broken copy constructor. More...

virtual	~RefineableQElement ()
	Broken assignment operator. More...

unsigned	required_nsons () const
	A refineable quad element has four sons. More...

virtual Node *	node_created_by_neighbour (const Vector< double > &s_fraction, bool &is_periodic)

virtual Node *	node_created_by_son_of_neighbour (const Vector< double > &s_fraction, bool &is_periodic)

virtual void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)

void	check_integrity (double &max_error)

void	output_corners (std::ostream &outfile, const std::string &colour) const
	Print corner nodes, use colour. More...

QuadTree *	quadtree_pt ()
	Pointer to quadtree representation of this element. More...

QuadTree *	quadtree_pt () const
	Pointer to quadtree representation of this element. More...

void	setup_hanging_nodes (Vector< std::ofstream * > &output_stream)

void	get_boundaries (const int &edge, std::set< unsigned > &boundaries) const

void	get_bcs (int bound, Vector< int > &bound_cons) const

void	interpolated_zeta_on_edge (const unsigned &boundary, const int &edge, const Vector< double > &s, Vector< double > &zeta)

Public Member Functions inherited from oomph::QuadElementBase
	QuadElementBase ()
	Constructor. Empty. More...

Public Member Functions inherited from oomph::QElementBase
	QElementBase ()
	Constructor: Initialise pointers to macro element reference coords. More...

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

virtual	~QElementBase ()
	Broken assignment operator. More...

bool	local_coord_is_valid (const Vector< double > &s)
	Check whether the local coordinate are valid or not. More...

void	move_local_coord_back_into_element (Vector< double > &s) const

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

double &	s_macro_ll (const unsigned &i)

double &	s_macro_ur (const unsigned &i)

double	s_macro_ll (const unsigned &i) const

double	s_macro_ur (const unsigned &i) const

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

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

unsigned	nnode_on_face () const

ElementGeometry::ElementGeometry	element_geometry () const
	It's a Q element! More...

Public Member Functions inherited from oomph::QElementGeometricBase
	QElementGeometricBase ()
	Empty default constructor. More...

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

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

void	unpin_elemental_pressure_dofs ()
	Unpin all pressure dofs. More...

void	pin_elemental_redundant_nodal_pressure_dofs ()
	Unpin the proper nodal pressure dofs. 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 > &)

Public Types inherited from oomph::RefineableQElement< 2 >
typedef void(RefineableQElement< 2 >::*	VoidMemberFctPt) ()

Static Public Member Functions inherited from oomph::RefineableLinearisedNavierStokesEquations
static void	pin_redundant_nodal_pressures (const Vector< GeneralisedElement * > &element_pt)

static void	unpin_all_pressure_dofs (const Vector< GeneralisedElement * > &element_pt)
	Unpin all pressure dofs in elements listed in Vector. More...

Static Public Member Functions inherited from oomph::RefineableElement
static double &	max_integrity_tolerance ()
	Max. allowed discrepancy in element integrity check. More...

Public Attributes inherited from oomph::LinearisedNavierStokesEquations
void(*&)(const double &time, const Vector< double > &x, Vector< double > &f)	base_flow_u_fct_pt ()
	Access function for the base flow solution pointer. More...

void(*&)(const double &time, const Vector< double > &x, DenseMatrix< double > &f)	base_flow_dudx_fct_pt ()

Static Public Attributes inherited from oomph::LinearisedNavierStokesEquations
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 Member Functions inherited from oomph::LinearisedQTaylorHoodElement
double	dshape_and_dtest_eulerian_linearised_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

void	pshape_linearised_nst (const Vector< double > &s, Shape &psi) const
	Compute the pressure shape functions at local coordinate s. More...

void	pshape_linearised_nst (const Vector< double > &s, Shape &psi, Shape &test) const
	Compute the pressure shape and test functions at local coordinte s. More...

Protected Member Functions inherited from oomph::LinearisedNavierStokesEquations
virtual void	get_base_flow_u (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &result) const

virtual void	get_base_flow_dudx (const double &time, const unsigned &ipt, const Vector< double > &x, DenseMatrix< double > &result) const

int	eigenvalue_local_eqn (const unsigned &i)

Protected Member Functions inherited from oomph::FiniteElement
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 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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

void	assign_hanging_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for hanging node variables. More...

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

Protected Member Functions inherited from oomph::RefineableQElement< 2 >
void	setup_father_bounds ()

void	get_edge_bcs (const int &edge, Vector< int > &bound_cons) const
	Determine Vector of boundary conditions along edge (N/S/W/E) More...

void	setup_hang_for_value (const int &value_id)

virtual void	quad_hang_helper (const int &value_id, const int &my_edge, std::ofstream &output_hangfile)

Static Protected Member Functions inherited from oomph::RefineableElement
static void	check_value_id (const int &n_continuously_interpolated_values, const int &value_id)

Protected Attributes inherited from oomph::LinearisedNavierStokesEquations
double *	Viscosity_Ratio_pt

double *	Density_Ratio_pt

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

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

double *	Lambda_pt
	Pointer to eigenvalue. More...

double *	Omega_pt
	Pointer to frequency. More...

LinearisedNavierStokesEigenfunctionNormalisationElement *	Normalisation_element_pt
	Pointer to the normalisation element. More...

unsigned	Data_number_of_eigenvalue
	Index of datum where eigenvalue is stored. More...

unsigned	Index_of_eigenvalue

void(*	Base_flow_u_fct_pt )(const double &time, const Vector< double > &x, Vector< double > &result)
	Pointer to base flow solution (velocity components) function. More...

void(*	Base_flow_dudx_fct_pt )(const double &time, const Vector< double > &x, DenseMatrix< double > &result)

bool	ALE_is_disabled

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

Protected Attributes inherited from oomph::RefineableElement
Tree *	Tree_pt
	A pointer to a general tree object. More...

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

bool	Refinement_is_enabled
	Flag to indicate suppression of any refinement. More...

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

long	Number
	Global element number – for plotting/validation purposes. More...

Static Protected Attributes inherited from oomph::LinearisedQTaylorHoodElement
static const unsigned	Pconv [] = {0, 2, 6, 8}
	Set the data for the pressure conversion array. More...

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 Protected Attributes inherited from oomph::RefineableElement
static double	Max_integrity_tolerance = 1.0e-8
	Max. allowed discrepancy in element integrity check. More...

Static Protected Attributes inherited from oomph::RefineableQElement< 2 >
static std::map< unsigned, DenseMatrix< int > >	Father_bound

Detailed Description

/////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////// Refineable version of linearised axisymmetric quadratic Taylor-Hood elements

Constructor & Destructor Documentation

◆ RefineableLinearisedQTaylorHoodElement()

oomph::RefineableLinearisedQTaylorHoodElement::RefineableLinearisedQTaylorHoodElement ( )

inline

Constructor:

       : RefineableElement(),
         RefineableLinearisedNavierStokesEquations(),
         RefineableQElement<2>(),
         LinearisedQTaylorHoodElement()
     {
     }

Member Function Documentation

◆ further_setup_hanging_nodes()

void oomph::RefineableLinearisedQTaylorHoodElement::further_setup_hanging_nodes ( )

inlinevirtual

Perform additional hanging node procedures for variables that are not interpolated by all nodes. The two pressure components are stored at the 6th and 7th location in each node

Implements oomph::RefineableQElement< 2 >.

     {
       for (unsigned i = 0; i < 2; i++)
       {
         this->setup_hang_for_value((2 * DIM) + i);
       }
     }

References DIM, i, and oomph::RefineableQElement< 2 >::setup_hang_for_value().

◆ get_interpolated_values() [1/2]

void oomph::RefineableLinearisedQTaylorHoodElement::get_interpolated_values	(	const unsigned &	t,
		const Vector< double > &	s,
		Vector< double > &	values
	)

inlinevirtual

Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here.

Implements oomph::RefineableElement.

     {
       // Set size of values Vector: U^C, U^S, W^C, W^S, V^C, V^S, P^C, P^S
       values.resize(2 * (DIM + 1));
  
       // Initialise all entries to zero
       for (unsigned i = 0; i < 2 * (DIM + 1); i++)
       {
         values[i] = 0.0;
       }
  
       // Determine number of nodes in element
       const unsigned n_node = nnode();
  
       // Shape functions
       Shape psif(n_node);
       shape(s, psif);
  
       // Calculate velocities: values[0],...
       for (unsigned i = 0; i < (2 * DIM); i++)
       {
         // Get the nodal coordinate of the velocity
         const unsigned u_nodal_index = u_index_linearised_nst(i);
         for (unsigned l = 0; l < n_node; l++)
         {
           values[i] += nodal_value(t, l, u_nodal_index) * psif[l];
         }
       }
  
       // Calculate pressure: values[DIM], values[DIM+1]
       // (no history is carried in the pressure)
       for (unsigned i = 0; i < 2; i++)
       {
         values[DIM + i] = interpolated_p_linearised_nst(s, i);
       }
     }

References DIM, i, oomph::LinearisedNavierStokesEquations::interpolated_p_linearised_nst(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), plotPSD::t, and oomph::LinearisedNavierStokesEquations::u_index_linearised_nst().

◆ get_interpolated_values() [2/2]

void oomph::RefineableLinearisedQTaylorHoodElement::get_interpolated_values	(	const Vector< double > &	s,
		Vector< double > &	values
	)

inlinevirtual

Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here.

Reimplemented from oomph::RefineableElement.

     {
       // Determine size of values Vector:
       // U^C, U^S, W^C, W^S, V^C, V^S, P^C, P^S
       const unsigned n_values = 2 * (DIM + 1);
  
       // Set size of values Vector and initialise to zero
       values.resize(n_values, 0.0);
  
       // Calculate velocities: values[0],...
       for (unsigned i = 0; i < (2 * DIM); i++)
       {
         values[i] = interpolated_u_linearised_nst(s, i);
       }
  
       // Calculate pressure: values[DIM], values[DIM+1]
       for (unsigned i = 0; i < 2; i++)
       {
         values[DIM + i] = interpolated_p_linearised_nst(s, i);
       }
     }

References DIM, i, oomph::LinearisedNavierStokesEquations::interpolated_p_linearised_nst(), oomph::LinearisedNavierStokesEquations::interpolated_u_linearised_nst(), and s.

◆ get_interpolating_node_at_local_coordinate()

Node* oomph::RefineableLinearisedQTaylorHoodElement::get_interpolating_node_at_local_coordinate	(	const Vector< double > &	s,
		const int &	n_value
	)

inlinevirtual

The velocity nodes are the same as the geometric nodes. The pressure nodes must be calculated by using the same methods as the geometric nodes, but by recalling that there are only two pressure nodes per edge.

Construct the general pressure index from the components.

Reimplemented from oomph::RefineableElement.

     {
       // If we are calculating pressure nodes
       if (n_value == static_cast<int>(2 * DIM) ||
           n_value == static_cast<int>((2 * DIM) + 1))
       {
         // Storage for the index of the pressure node
         unsigned total_index = 0;
         // The number of nodes along each 1d edge is 2.
         const unsigned NNODE_1D = 2;
         // Storage for the index along each boundary
         // Note that it's only a 2D spatial element
         Vector<int> index(2);
         // Loop over the coordinates
         for (unsigned i = 0; i < 2; i++)
         {
           // If we are at the lower limit, the index is zero
           if (s[i] == -1.0)
           {
             index[i] = 0;
           }
  
           // If we are at the upper limit, the index is the number of nodes
           // minus 1
           else if (s[i] == 1.0)
           {
             index[i] = NNODE_1D - 1;
           }
  
           // Otherwise, we have to calculate the index in general
           else
           {
             // For uniformly spaced nodes the 0th node number would be
             double float_index = 0.5 * (1.0 + s[i]) * (NNODE_1D - 1);
             index[i] = int(float_index);
             // What is the excess. This should be safe because the
             // taking the integer part rounds down
             double excess = float_index - index[i];
             // If the excess is bigger than our tolerance there is no node,
             // return null
             if ((excess > FiniteElement::Node_location_tolerance) &&
                 ((1.0 - excess) > FiniteElement::Node_location_tolerance))
             {
               return 0;
             }
           }
           total_index +=
             index[i] * static_cast<unsigned>(pow(static_cast<float>(NNODE_1D),
                                                  static_cast<int>(i)));
         }
         // If we've got here we have a node, so let's return a pointer to it
         return this->node_pt(this->Pconv[total_index]);
       }
       // Otherwise velocity nodes are the same as pressure nodes
       else
       {
         return this->get_node_at_local_coordinate(s);
       }
     }

References DIM, oomph::FiniteElement::get_node_at_local_coordinate(), i, int(), oomph::FiniteElement::Node_location_tolerance, oomph::FiniteElement::node_pt(), Eigen::bfloat16_impl::pow(), and s.

◆ interpolating_basis()

void oomph::RefineableLinearisedQTaylorHoodElement::interpolating_basis	(	const Vector< double > &	s,
		Shape &	psi,
		const int &	n_value
	)		const

inlinevirtual

The basis interpolating the pressure is given by pshape(). / The basis interpolating the velocity is shape().

Reimplemented from oomph::RefineableElement.

     {
       if (n_value == (2 * DIM) || n_value == ((2 * DIM) + 1))
       {
         return this->pshape_linearised_nst(s, psi);
       }
       else
       {
         return this->shape(s, psi);
       }
     }

References DIM, oomph::LinearisedQCrouzeixRaviartElement::pshape_linearised_nst(), and oomph::FiniteElement::shape().

◆ interpolating_node_pt()

Node* oomph::RefineableLinearisedQTaylorHoodElement::interpolating_node_pt	(	const unsigned &	n,
		const int &	n_value
	)

inlinevirtual

The velocities are isoparametric and so the "nodes" interpolating the velocities are the geometric nodes. The pressure "nodes" are a subset of the nodes, so when n_value==6 or 7, the n-th pressure node is returned.

Reimplemented from oomph::RefineableElement.

     {
       // The only different nodes are the pressure nodes
       if (n_value == (2 * DIM) || n_value == ((2 * DIM) + 1))
       {
         return this->node_pt(this->Pconv[n]);
       }
  
       // The other variables are interpolated via the usual nodes
       else
       {
         return this->node_pt(n);
       }
     }

References DIM, n, and oomph::FiniteElement::node_pt().

◆ local_one_d_fraction_of_interpolating_node()

double oomph::RefineableLinearisedQTaylorHoodElement::local_one_d_fraction_of_interpolating_node	(	const unsigned &	n1d,
		const unsigned &	i,
		const int &	n_value
	)

inlinevirtual

The pressure nodes are the corner nodes, so when n_value==6 or 7, the fraction is the same as the 1d node number, 0 or 1.

Reimplemented from oomph::RefineableElement.

     {
       if (n_value == (2 * DIM) || n_value == ((2 * DIM) + 1))
       {
         // The pressure nodes are just located on the boundaries at 0 or 1
         return double(n1d);
       }
       // Otherwise the velocity nodes are the same as the geometric ones
       else
       {
         return this->local_one_d_fraction_of_node(n1d, i);
       }
     }

References DIM, i, and oomph::FiniteElement::local_one_d_fraction_of_node().

◆ ncont_interpolated_values()

unsigned oomph::RefineableLinearisedQTaylorHoodElement::ncont_interpolated_values ( ) const

inlinevirtual

Number of continuously interpolated values: 8 (6 velocities + 2 pressures)

Implements oomph::RefineableElement.

     {
       return 8;
     }

◆ ninterpolating_node()

unsigned oomph::RefineableLinearisedQTaylorHoodElement::ninterpolating_node ( const int & n_value )

inlinevirtual

The number of pressure nodes is 4. The number of velocity nodes is the same as the number of geometric nodes.

Reimplemented from oomph::RefineableElement.

     {
       if (n_value == (2 * DIM) || n_value == ((2 * DIM) + 1))
       {
         return 4;
       }
       else
       {
         return this->nnode();
       }
     }

References DIM, and oomph::FiniteElement::nnode().

◆ ninterpolating_node_1d()

unsigned oomph::RefineableLinearisedQTaylorHoodElement::ninterpolating_node_1d ( const int & n_value )

inlinevirtual

The number of 1d pressure nodes is 2, the number of 1d velocity nodes is the same as the number of 1d geometric nodes.

Reimplemented from oomph::RefineableElement.

     {
       if (n_value == (2 * DIM) || n_value == ((2 * DIM) + 1))
       {
         return 2;
       }
       else
       {
         return this->nnode_1d();
       }
     }

References DIM, and oomph::FiniteElement::nnode_1d().

◆ nrecovery_order()

unsigned oomph::RefineableLinearisedQTaylorHoodElement::nrecovery_order ( )

inlinevirtual

Order of recovery shape functions for Z2 error estimation: Same order as shape functions.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return 2;
     }

◆ nvertex_node()

unsigned oomph::RefineableLinearisedQTaylorHoodElement::nvertex_node ( ) const

inlinevirtual

Number of vertex nodes in the element.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return LinearisedQTaylorHoodElement::nvertex_node();
     }

References oomph::FiniteElement::nvertex_node().

◆ pin_elemental_redundant_nodal_pressure_dofs()

void oomph::RefineableLinearisedQTaylorHoodElement::pin_elemental_redundant_nodal_pressure_dofs ( )

inlineprivatevirtual

Unpin the proper nodal pressure dofs.

Reimplemented from oomph::RefineableLinearisedNavierStokesEquations.

     {
       // Determine number of nodes in element
       const unsigned n_node = this->nnode();
  
       // Get nodal indeces of the two pressure components
       Vector<int> p_index(2);
       for (unsigned i = 0; i < 2; i++)
       {
         p_index[i] = this->p_index_linearised_nst(i);
       }
  
       // Loop over all nodes and pin all the nodal pressures
       for (unsigned n = 0; n < n_node; n++)
       {
         for (unsigned i = 0; i < 2; i++)
         {
           this->node_pt(n)->pin(p_index[i]);
         }
       }
  
       // Loop over all actual pressure nodes and unpin if they're not hanging
       const unsigned n_pres = this->npres_linearised_nst();
       for (unsigned l = 0; l < n_pres; l++)
       {
         Node* nod_pt = this->node_pt(this->Pconv[l]);
         for (unsigned i = 0; i < 2; i++)
         {
           if (!nod_pt->is_hanging(p_index[i]))
           {
             nod_pt->unpin(p_index[i]);
           }
         }
       }
     }

References i, oomph::Node::is_hanging(), n, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), oomph::LinearisedQCrouzeixRaviartElement::npres_linearised_nst(), oomph::LinearisedNavierStokesEquations::p_index_linearised_nst(), oomph::Data::pin(), and oomph::Data::unpin().

◆ pressure_node_pt()

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

inlineprivatevirtual

Pointer to n_p-th pressure node.

Reimplemented from oomph::RefineableLinearisedNavierStokesEquations.

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

References oomph::FiniteElement::node_pt().

◆ rebuild_from_sons()

void oomph::RefineableLinearisedQTaylorHoodElement::rebuild_from_sons ( Mesh *& mesh_pt )

inlinevirtual

Rebuild from sons: empty.

Implements oomph::RefineableElement.

703 {}

◆ required_nvalue()

unsigned oomph::RefineableLinearisedQTaylorHoodElement::required_nvalue ( const unsigned & n ) const

inlinevirtual

Number of values (pinned or dofs) required at node n. Bumped up to 8 so we don't have to worry if a hanging mid-side node gets shared by a corner node (which has extra degrees of freedom)

Reimplemented from oomph::LinearisedQTaylorHoodElement.

     {
       return 8;
     }

◆ unpin_elemental_pressure_dofs()

void oomph::RefineableLinearisedQTaylorHoodElement::unpin_elemental_pressure_dofs ( )

inlineprivatevirtual

Unpin all pressure dofs.

Implements oomph::RefineableLinearisedNavierStokesEquations.

     {
       // Determine number of nodes in element
       const unsigned n_node = this->nnode();
  
       // Get nodal indeces of the two pressure components
       Vector<int> p_index(2);
       for (unsigned i = 0; i < 2; i++)
       {
         p_index[i] = this->p_index_linearised_nst(i);
       }
  
       // Loop over nodes and unpin both pressure components
       for (unsigned n = 0; n < n_node; n++)
       {
         for (unsigned i = 0; i < 2; i++)
         {
           this->node_pt(n)->unpin(p_index[i]);
         }
       }
     }

References i, n, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), oomph::LinearisedNavierStokesEquations::p_index_linearised_nst(), and oomph::Data::unpin().

◆ vertex_node_pt()

Node* oomph::RefineableLinearisedQTaylorHoodElement::vertex_node_pt ( const unsigned & j ) const

inlinevirtual

Pointer to the j-th vertex node in the element.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return LinearisedQTaylorHoodElement::vertex_node_pt(j);
     }

References j, and oomph::FiniteElement::vertex_node_pt().

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

refineable_linearised_navier_stokes_elements.h

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RefineableLinearisedQTaylorHoodElement()

Member Function Documentation

◆ further_setup_hanging_nodes()

◆ get_interpolated_values() [1/2]

◆ get_interpolated_values() [2/2]

◆ get_interpolating_node_at_local_coordinate()

◆ interpolating_basis()

◆ interpolating_node_pt()

◆ local_one_d_fraction_of_interpolating_node()

◆ ncont_interpolated_values()

◆ ninterpolating_node()

◆ ninterpolating_node_1d()

◆ nrecovery_order()

◆ nvertex_node()

◆ pin_elemental_redundant_nodal_pressure_dofs()

◆ pressure_node_pt()

◆ rebuild_from_sons()

◆ required_nvalue()

◆ unpin_elemental_pressure_dofs()

◆ vertex_node_pt()