#include <refineable_linearised_axisym_navier_stokes_elements.h>

Inheritance diagram for oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement:

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

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 6 (velocities) More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: Reconstruct pressure from the (merged) sons. 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 ()

void	further_build ()

	RefineableLinearisedAxisymmetricQCrouzeixRaviartElement ()
	Constructor. More...

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 6 (velocities) More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: Reconstruct pressure from the (merged) sons. 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 ()

void	further_build ()

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

virtual unsigned	required_nvalue (const unsigned &n) const
	Return number of values (pinned or dofs) required at local node n. More...

double	p_linearised_axi_nst (const unsigned &i_internal, const unsigned &i) const

unsigned	npres_linearised_axi_nst () const

void	fix_pressure (const unsigned &p_dof, 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...

	LinearisedAxisymmetricQCrouzeixRaviartElement ()

virtual unsigned	required_nvalue (const unsigned &n) const
	Return number of values (pinned or dofs) required at local node n. More...

double	p_lin_axi_nst (const unsigned &i_internal, const unsigned &i) const

unsigned	npres_lin_axi_nst () const

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

void	fix_cosine_component_of_pressure (const unsigned &p_dof, const double &pvalue)

void	fix_sine_component_of_pressure (const unsigned &p_dof, 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

	LinearisedAxisymmetricQCrouzeixRaviartElement ()

virtual unsigned	required_nvalue (const unsigned &n) const
	Return number of values (pinned or dofs) required at local node n. More...

double	p_linearised_axi_nst (const unsigned &i_internal, const unsigned &i) const

unsigned	npres_linearised_axi_nst () const

void	fix_pressure (const unsigned &p_dof, 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::LinearisedAxisymmetricNavierStokesEquations
	LinearisedAxisymmetricNavierStokesEquations ()

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

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

const int &	azimuthal_mode_number () const
	Azimuthal mode number k in e^ik(theta) decomposition. More...

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

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

int *&	azimuthal_mode_number_pt ()
	Pointer to azimuthal mode number k in e^ik(theta) decomposition. 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_axi_nst (const unsigned &i) const

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

void	disable_ALE ()

void	enable_ALE ()

virtual int	p_index_linearised_axi_nst (const unsigned &i) const
	Which nodal value represents the pressure? More...

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

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)

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

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

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

	LinearisedAxisymmetricNavierStokesEquations ()

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

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

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

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

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

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

const double &	re_invro () const
	Global Reynolds number multiplied by inverse Rossby number. More...

double *&	re_invro_pt ()
	Pointer to global Reynolds number multiplied by inverse Rossby number. More...

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

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

const int &	azimuthal_mode_number () const
	Azimuthal mode number k in e^ik(theta) decomposition. More...

int *&	azimuthal_mode_number_pt ()
	Pointer to azimuthal mode number k in e^ik(theta) decomposition. 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 int	get_local_eqn_number_corresponding_to_geometric_dofs (const unsigned &n, const unsigned &i)=0

virtual unsigned	xhat_index_lin_axi_nst (const unsigned &i) const

virtual unsigned	u_index_lin_axi_nst (const unsigned &i) const

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

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

unsigned	nexternal_H_data ()
	Return the number of external perturbed spine "heights" data. More...

void	disable_ALE ()

void	enable_ALE ()

virtual int	p_index_lin_axi_nst (const unsigned &i) const
	Which nodal value represents the pressure? More...

void	dkin_energy_dt (double &dkin_en_dt, double &kin_en) const
	Get integral of kinetic energy over element plus deriv w.r.t. time. More...

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

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)

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

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

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

void	assign_additional_local_eqn_numbers ()
	Define the local equation numbering schemes. More...

	LinearisedAxisymmetricNavierStokesEquations ()

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

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

const int &	azimuthal_mode_number () const
	Azimuthal mode number k in e^ik(theta) decomposition. More...

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

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

int *&	azimuthal_mode_number_pt ()
	Pointer to azimuthal mode number k in e^ik(theta) decomposition. 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_axi_nst (const unsigned &i) const

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

void	disable_ALE ()

void	enable_ALE ()

virtual int	p_index_linearised_axi_nst (const unsigned &i) const
	Which nodal value represents the pressure? More...

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

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)

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

double	interpolated_p_linearised_axi_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::RefineableLinearisedAxisymmetricNavierStokesEquations
	RefineableLinearisedAxisymmetricNavierStokesEquations ()
	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)

double	geometric_jacobian (const Vector< double > &x)
	Fill in the geometric Jacobian, which in this case is r. More...

	RefineableLinearisedAxisymmetricNavierStokesEquations ()
	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)

double	geometric_jacobian (const Vector< double > &x)
	Fill in the geometric Jacobian, which in this case is r. 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...

virtual Node *	interpolating_node_pt (const unsigned &n, const int &value_id)

virtual double	local_one_d_fraction_of_interpolating_node (const unsigned &n1d, const unsigned &i, const int &value_id)

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

virtual unsigned	ninterpolating_node (const int &value_id)

virtual unsigned	ninterpolating_node_1d (const int &value_id)

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

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)

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
void	unpin_elemental_pressure_dofs ()
	Unpin all the internal pressure freedoms. More...

void	unpin_elemental_pressure_dofs ()
	Unpin all the internal pressure freedoms. 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::RefineableLinearisedAxisymmetricNavierStokesEquations
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 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::LinearisedAxisymmetricNavierStokesEquations
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 ()

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

void(*&)(const double &time, const Vector< double > &x, double &f)	base_flow_p_fct_pt ()
	Access function for the base flow pressure pointer. More...

void(*&)(const double &time, const Vector< double > &x, RankFourTensor< double > &f)	base_flow_d_dudx_dX_fct_pt ()

void(*&)(const double &time, const Vector< double > &x, Vector< double > &f)	body_force_fct_pt ()
	Access function for the body-force pointer. More...

double(*&)(const double &time, const Vector< double > &x)	source_fct_pt ()
	Access function for the source-function pointer. More...

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

Static Public Attributes inherited from oomph::LinearisedAxisymmetricNavierStokesEquations
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::LinearisedAxisymmetricQCrouzeixRaviartElement
double	dshape_and_dtest_eulerian_linearised_axi_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

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

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

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

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

double	dshape_and_dtest_eulerian_and_dnodal_coordinates_at_knot_lin_axi_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const

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

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

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

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

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

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

Protected Member Functions inherited from oomph::LinearisedAxisymmetricNavierStokesEquations
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

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

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

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

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

void	get_body_force_base_flow (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &result)

double	get_source_base_flow (const double &time, const unsigned &ipt, const Vector< double > &x)

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

void	get_source_gradient_base_flow (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &result)

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

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

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

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)

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)

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

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

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

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

Protected Member Functions inherited from oomph::RefineableLinearisedAxisymmetricNavierStokesEquations
virtual Node *	pressure_node_pt (const unsigned &n_p)

virtual void	pin_elemental_redundant_nodal_pressure_dofs ()

virtual Node *	pressure_node_pt (const unsigned &n_p)

virtual void	pin_elemental_redundant_nodal_pressure_dofs ()

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::LinearisedAxisymmetricQCrouzeixRaviartElement
Vector< unsigned >	P_linearised_axi_nst_internal_index

Vector< unsigned >	P_lin_axi_nst_internal_index

Protected Attributes inherited from oomph::LinearisedAxisymmetricNavierStokesEquations
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...

int *	Azimuthal_Mode_Number_pt
	Pointer to azimuthal mode number k in e^ik(theta) decomposition. More...

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

double *	ReInvFr_pt

double *	ReInvRo_pt

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

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

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

void(*	Base_flow_d_dudx_dX_fct_pt )(const double &time, const Vector< double > &x, RankFourTensor< double > &result)

void(*	Body_force_fct_pt )(const double &time, const Vector< double > &x, Vector< double > &result)
	Pointer to (base flow) body force function. More...

double(*	Source_fct_pt )(const double &time, const Vector< double > &x)
	Pointer to (base flow) volumetric source function. More...

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

Vector< int >	External_H_local_eqn

Vector< unsigned >	External_node

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::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 quad Crouzeix Raviart elements (note that unlike the cartesian version this is not scale-able to higher dimensions!)

/////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////// Refineable version of linearised axisymmetric quadratic Crouzeix-Raviart elements

Constructor & Destructor Documentation

◆ RefineableLinearisedAxisymmetricQCrouzeixRaviartElement() [1/2]

oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement ( )

inline

Constructor:

                                                            : 
   RefineableElement(),
   RefineableLinearisedAxisymmetricNavierStokesEquations(),
   RefineableQElement<2>(),  
   LinearisedAxisymmetricQCrouzeixRaviartElement() {}

◆ RefineableLinearisedAxisymmetricQCrouzeixRaviartElement() [2/2]

oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement ( )

inline

Constructor.

       : RefineableElement(),
         RefineableLinearisedAxisymmetricNavierStokesEquations(),
         RefineableQElement<2>(),
         LinearisedAxisymmetricQCrouzeixRaviartElement()
     {
     }

Member Function Documentation

◆ further_build() [1/2]

void oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::further_build ( )

inlinevirtual

Further build for Crouzeix_Raviart interpolates the internal pressure dofs from father element: Make sure pressure values and dp/ds agree between fathers and sons at the midpoints of the son elements.

Reimplemented from oomph::RefineableLinearisedAxisymmetricNavierStokesEquations.

   { 
    // Call the generic further build
    RefineableLinearisedAxisymmetricNavierStokesEquations::further_build();
    
    using namespace QuadTreeNames;
    
    // What type of son am I? Ask my quadtree representation...
    int son_type=quadtree_pt()->son_type();
    
    // Pointer to my father (in element impersonation)
    RefineableElement* father_el_pt=
     quadtree_pt()->father_pt()->object_pt();
    
    Vector<double> s_father(2);
    
    // Son midpoint is located at the following coordinates in father element:
    
    // South west son
    if(son_type==SW)
     {
      s_father[0]=-0.5;
      s_father[1]=-0.5;
     }
    // South east son
    else if(son_type==SE)
     {
      s_father[0]= 0.5;
      s_father[1]=-0.5;
     }
    // North east son
    else if(son_type==NE)
     {
      s_father[0]=0.5;
      s_father[1]=0.5;
     }
    
    // North west son
    else if(son_type==NW)
     {
      s_father[0]=-0.5;
      s_father[1]= 0.5;
     }
    
    // Pressure values in father element
    // ---------------------------------
  
    // Find pointer to father element
    RefineableLinearisedAxisymmetricQCrouzeixRaviartElement* cast_father_el_pt=
     dynamic_cast<RefineableLinearisedAxisymmetricQCrouzeixRaviartElement*>
     (father_el_pt);
  
    // Set up storage for pressure in father element
    Vector<double> press(2,0.0);
    
    // Loop over pressure components
    for(unsigned i=0;i<2;i++)
     {
      // Get pressure from father element
      press[i]
       = cast_father_el_pt->interpolated_p_linearised_axi_nst(s_father,i);
    
      // Pressure value gets copied straight into internal dof:
      internal_data_pt(P_linearised_axi_nst_internal_index[i])->
       set_value(0,press[i]);
    
      // The slopes get copied from father
      internal_data_pt(P_linearised_axi_nst_internal_index[i])->
       set_value(1,0.5*cast_father_el_pt
                 ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                 ->value(1));
      
      internal_data_pt(P_linearised_axi_nst_internal_index[i])->
       set_value(2,0.5*cast_father_el_pt
                 ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                 ->value(2));
     } // End of loop over pressure components
   }

References oomph::Tree::father_pt(), oomph::RefineableLinearisedAxisymmetricNavierStokesEquations::further_build(), i, oomph::GeneralisedElement::internal_data_pt(), oomph::LinearisedAxisymmetricNavierStokesEquations::interpolated_p_linearised_axi_nst(), oomph::QuadTreeNames::NE, oomph::QuadTreeNames::NW, oomph::Tree::object_pt(), oomph::LinearisedAxisymmetricQCrouzeixRaviartElement::P_linearised_axi_nst_internal_index, oomph::RefineableQElement< 2 >::quadtree_pt(), oomph::QuadTreeNames::SE, oomph::Tree::son_type(), oomph::QuadTreeNames::SW, and Eigen::value.

◆ further_build() [2/2]

void oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::further_build ( )

inlinevirtual

Further build for Crouzeix_Raviart interpolates the internal pressure dofs from father element: Make sure pressure values and dp/ds agree between fathers and sons at the midpoints of the son elements.

Reimplemented from oomph::RefineableLinearisedAxisymmetricNavierStokesEquations.

     {
       // Call the generic further build
       RefineableLinearisedAxisymmetricNavierStokesEquations::further_build();
  
       using namespace QuadTreeNames;
  
       // What type of son am I? Ask my quadtree representation...
       int son_type = quadtree_pt()->son_type();
  
       // Pointer to my father (in element impersonation)
       RefineableElement* father_el_pt = quadtree_pt()->father_pt()->object_pt();
  
       Vector<double> s_father(2);
  
       // Son midpoint is located at the following coordinates in father element:
  
       // South west son
       if (son_type == SW)
       {
         s_father[0] = -0.5;
         s_father[1] = -0.5;
       }
       // South east son
       else if (son_type == SE)
       {
         s_father[0] = 0.5;
         s_father[1] = -0.5;
       }
       // North east son
       else if (son_type == NE)
       {
         s_father[0] = 0.5;
         s_father[1] = 0.5;
       }
  
       // North west son
       else if (son_type == NW)
       {
         s_father[0] = -0.5;
         s_father[1] = 0.5;
       }
  
       // Pressure values in father element
       // ---------------------------------
  
       // Find pointer to father element
       RefineableLinearisedAxisymmetricQCrouzeixRaviartElement*
         cast_father_el_pt = dynamic_cast<
           RefineableLinearisedAxisymmetricQCrouzeixRaviartElement*>(
           father_el_pt);
  
       // Set up storage for pressure in father element
       Vector<double> press(2, 0.0);
  
       // Loop over pressure components
       for (unsigned i = 0; i < 2; i++)
       {
         // Get pressure from father element
         press[i] =
           cast_father_el_pt->interpolated_p_linearised_axi_nst(s_father, i);
  
         // Pressure value gets copied straight into internal dof:
         internal_data_pt(P_linearised_axi_nst_internal_index[i])
           ->set_value(0, press[i]);
  
         // The slopes get copied from father
         internal_data_pt(P_linearised_axi_nst_internal_index[i])
           ->set_value(
             1,
             0.5 * cast_father_el_pt
                     ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                     ->value(1));
  
         internal_data_pt(P_linearised_axi_nst_internal_index[i])
           ->set_value(
             2,
             0.5 * cast_father_el_pt
                     ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                     ->value(2));
       } // End of loop over pressure components
     }

References oomph::Tree::father_pt(), oomph::RefineableLinearisedAxisymmetricNavierStokesEquations::further_build(), i, oomph::GeneralisedElement::internal_data_pt(), oomph::LinearisedAxisymmetricNavierStokesEquations::interpolated_p_linearised_axi_nst(), oomph::QuadTreeNames::NE, oomph::QuadTreeNames::NW, oomph::Tree::object_pt(), oomph::LinearisedAxisymmetricQCrouzeixRaviartElement::P_linearised_axi_nst_internal_index, oomph::RefineableQElement< 2 >::quadtree_pt(), oomph::QuadTreeNames::SE, oomph::Data::set_value(), oomph::Tree::son_type(), oomph::QuadTreeNames::SW, and Eigen::value.

◆ further_setup_hanging_nodes() [1/2]

void oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::further_setup_hanging_nodes ( )

inlinevirtual

Perform additional hanging node procedures for variables that are not interpolated by all nodes. Empty

Implements oomph::RefineableQElement< 2 >.

786 {}

◆ further_setup_hanging_nodes() [2/2]

void oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::further_setup_hanging_nodes ( )

inlinevirtual

Perform additional hanging node procedures for variables that are not interpolated by all nodes. Empty

Implements oomph::RefineableQElement< 2 >.

465 {}

◆ get_interpolated_values() [1/4]

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

inlinevirtual

Get all function values [U^C,U^S,...,P^S] at previous timestep t (t=0: present; t>0: previous timestep).
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.
Note: No pressure history is kept, so pressure is always the current value.

Implements oomph::RefineableElement.

  {
   const unsigned DIM=3;
   
   // Set size of Vector: U^C, U^S, W^C, W^S, V^C, V^S
   values.resize(2*DIM);
    
   // Initialise to zero
   for(unsigned i=0;i<2*DIM;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 local index at which the i-th velocity is stored
     const unsigned u_local_index = u_index_linearised_axi_nst(i);
     for(unsigned l=0;l<n_node;l++) 
      {
       values[i] += nodal_value(t,l,u_local_index)*psif[l];
      } 
    }
  }

References DIM, i, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), plotPSD::t, and oomph::LinearisedAxisymmetricNavierStokesEquations::u_index_linearised_axi_nst().

◆ get_interpolated_values() [2/4]

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

inlinevirtual

Get all function values [U^C,U^S,...,P^S] at previous timestep t (t=0: present; t>0: previous timestep).
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.
Note: No pressure history is kept, so pressure is always the current value.

Implements oomph::RefineableElement.

     {
       const unsigned DIM = 3;
  
       // Set size of Vector: U^C, U^S, W^C, W^S, V^C, V^S
       values.resize(2 * DIM);
  
       // Initialise to zero
       for (unsigned i = 0; i < 2 * DIM; 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 local index at which the i-th velocity is stored
         const unsigned u_local_index = u_index_linearised_axi_nst(i);
         for (unsigned l = 0; l < n_node; l++)
         {
           values[i] += nodal_value(t, l, u_local_index) * psif[l];
         }
       }
     }

References DIM, i, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), plotPSD::t, and oomph::LinearisedAxisymmetricNavierStokesEquations::u_index_linearised_axi_nst().

◆ get_interpolated_values() [3/4]

void oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::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.

   {
   // Set the velocity dimension of the element
    const unsigned DIM=3;
  
    // Determine size of values Vector: U^C, U^S, W^C, W^S, V^C, V^S
    const unsigned n_values = 2*DIM;
    
    // Set size of values Vector and initialise to zero
    values.resize(n_values,0.0);
    
    // Calculate velocities: values[0],...
    for(unsigned i=0;i<n_values;i++)
     {
      values[i] = interpolated_u_linearised_axi_nst(s,i);
     }
   }

References DIM, i, oomph::LinearisedAxisymmetricNavierStokesEquations::interpolated_u_linearised_axi_nst(), and s.

◆ get_interpolated_values() [4/4]

void oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::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.

     {
       // Set the velocity dimension of the element
       const unsigned DIM = 3;
  
       // Determine size of values Vector: U^C, U^S, W^C, W^S, V^C, V^S
       const unsigned n_values = 2 * DIM;
  
       // Set size of values Vector and initialise to zero
       values.resize(n_values, 0.0);
  
       // Calculate velocities: values[0],...
       for (unsigned i = 0; i < n_values; i++)
       {
         values[i] = interpolated_u_linearised_axi_nst(s, i);
       }
     }

References DIM, i, oomph::LinearisedAxisymmetricNavierStokesEquations::interpolated_u_linearised_axi_nst(), and s.

◆ ncont_interpolated_values() [1/2]

unsigned oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::ncont_interpolated_values ( ) const

inlinevirtual

Number of continuously interpolated values: 6 (velocities)

Implements oomph::RefineableElement.

622 { return 6; }

◆ ncont_interpolated_values() [2/2]

unsigned oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::ncont_interpolated_values ( ) const

inlinevirtual

Number of continuously interpolated values: 6 (velocities)

Implements oomph::RefineableElement.

     {
       return 6;
     }

◆ nrecovery_order() [1/2]

unsigned oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::nrecovery_order ( )

inlinevirtual

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

Implements oomph::ElementWithZ2ErrorEstimator.

   {
    return 2;
   }

◆ nrecovery_order() [2/2]

unsigned oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::nrecovery_order ( )

inlinevirtual

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

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return 2;
     }

◆ nvertex_node() [1/2]

unsigned oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::nvertex_node ( ) const

inlinevirtual

Number of vertex nodes in the element.

Implements oomph::ElementWithZ2ErrorEstimator.

717 { return LinearisedAxisymmetricQCrouzeixRaviartElement::nvertex_node(); }

oomph::FiniteElement::nvertex_node

virtual unsigned nvertex_node() const

Definition: elements.h:2491

References oomph::FiniteElement::nvertex_node().

◆ nvertex_node() [2/2]

unsigned oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::nvertex_node ( ) const

inlinevirtual

Number of vertex nodes in the element.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return LinearisedAxisymmetricQCrouzeixRaviartElement::nvertex_node();
     }

References oomph::FiniteElement::nvertex_node().

◆ rebuild_from_sons() [1/2]

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

inlinevirtual

Rebuild from sons: Reconstruct pressure from the (merged) sons.

Implements oomph::RefineableElement.

   {
    using namespace QuadTreeNames;
    
    // Central pressure value:
    // -----------------------
     
    // Use average of the sons central pressure values
    // Other options: Take average of the four (discontinuous)
    // pressure values at the father's midpoint]
    
    Vector<double> av_press(2,0.0);
    
    // Loop over the sons
    for(unsigned ison=0;ison<4;ison++)
     {
      // Loop over the two pressure components
      for(unsigned i=0;i<2;i++)
       {
        // Add the sons midnode pressure
        av_press[i] += quadtree_pt()->son_pt(ison)->object_pt()->
         internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0);
       }
     }
    
    // Use the average
    for(unsigned i=0;i<2;i++)
     {
      internal_data_pt(P_linearised_axi_nst_internal_index[i])
       ->set_value(0,0.25*av_press[i]);
     }
  
    Vector<double> slope1(2,0.0), slope2(2,0.0);
  
    // Loop over pressure components
    for(unsigned i=0;i<2;i++)
     {
      // Slope in s_0 direction
      // ----------------------
      
      // Use average of the 2 FD approximations based on the 
      // elements central pressure values
      // [Other options: Take average of the four 
      // pressure derivatives]
      
      slope1[i] = quadtree_pt()->son_pt(SE)->object_pt()->
       internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0) -
       quadtree_pt()->son_pt(SW)->object_pt()->
       internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0);
      
      slope2[i] = quadtree_pt()->son_pt(NE)->object_pt()->
       internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0) -
       quadtree_pt()->son_pt(NW)->object_pt()->
       internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0);
      
      // Use the average
      internal_data_pt(P_linearised_axi_nst_internal_index[i])->
       set_value(1,0.5*(slope1[i]+slope2[i]));
      
      // Slope in s_1 direction
      // ----------------------
      
      // Use average of the 2 FD approximations based on the 
      // elements central pressure values
      // [Other options: Take average of the four 
      // pressure derivatives]
      
      slope1[i] = quadtree_pt()->son_pt(NE)->object_pt()->
       internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0) -
       quadtree_pt()->son_pt(SE)->object_pt()->
       internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0);
      
      slope2[i] = quadtree_pt()->son_pt(NW)->object_pt()->
       internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0) -
       quadtree_pt()->son_pt(SW)->object_pt()->
       internal_data_pt(P_linearised_axi_nst_internal_index[i])->value(0);
      
      // Use the average
      internal_data_pt(P_linearised_axi_nst_internal_index[i])->
       set_value(2,0.5*(slope1[i]+slope2[i]));
     } // End of loop over pressure components
   }

References i, oomph::GeneralisedElement::internal_data_pt(), oomph::QuadTreeNames::NE, oomph::QuadTreeNames::NW, oomph::Tree::object_pt(), oomph::LinearisedAxisymmetricQCrouzeixRaviartElement::P_linearised_axi_nst_internal_index, oomph::RefineableQElement< 2 >::quadtree_pt(), oomph::QuadTreeNames::SE, oomph::Data::set_value(), oomph::Tree::son_pt(), oomph::QuadTreeNames::SW, and oomph::Data::value().

◆ rebuild_from_sons() [2/2]

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

inlinevirtual

Rebuild from sons: Reconstruct pressure from the (merged) sons.

Implements oomph::RefineableElement.

     {
       using namespace QuadTreeNames;
  
       // Central pressure value:
       // -----------------------
  
       // Use average of the sons central pressure values
       // Other options: Take average of the four (discontinuous)
       // pressure values at the father's midpoint]
  
       Vector<double> av_press(2, 0.0);
  
       // Loop over the sons
       for (unsigned ison = 0; ison < 4; ison++)
       {
         // Loop over the two pressure components
         for (unsigned i = 0; i < 2; i++)
         {
           // Add the sons midnode pressure
           av_press[i] +=
             quadtree_pt()
               ->son_pt(ison)
               ->object_pt()
               ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
               ->value(0);
         }
       }
  
       // Use the average
       for (unsigned i = 0; i < 2; i++)
       {
         internal_data_pt(P_linearised_axi_nst_internal_index[i])
           ->set_value(0, 0.25 * av_press[i]);
       }
  
       Vector<double> slope1(2, 0.0), slope2(2, 0.0);
  
       // Loop over pressure components
       for (unsigned i = 0; i < 2; i++)
       {
         // Slope in s_0 direction
         // ----------------------
  
         // Use average of the 2 FD approximations based on the
         // elements central pressure values
         // [Other options: Take average of the four
         // pressure derivatives]
  
         slope1[i] = quadtree_pt()
                       ->son_pt(SE)
                       ->object_pt()
                       ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                       ->value(0) -
                     quadtree_pt()
                       ->son_pt(SW)
                       ->object_pt()
                       ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                       ->value(0);
  
         slope2[i] = quadtree_pt()
                       ->son_pt(NE)
                       ->object_pt()
                       ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                       ->value(0) -
                     quadtree_pt()
                       ->son_pt(NW)
                       ->object_pt()
                       ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                       ->value(0);
  
         // Use the average
         internal_data_pt(P_linearised_axi_nst_internal_index[i])
           ->set_value(1, 0.5 * (slope1[i] + slope2[i]));
  
         // Slope in s_1 direction
         // ----------------------
  
         // Use average of the 2 FD approximations based on the
         // elements central pressure values
         // [Other options: Take average of the four
         // pressure derivatives]
  
         slope1[i] = quadtree_pt()
                       ->son_pt(NE)
                       ->object_pt()
                       ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                       ->value(0) -
                     quadtree_pt()
                       ->son_pt(SE)
                       ->object_pt()
                       ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                       ->value(0);
  
         slope2[i] = quadtree_pt()
                       ->son_pt(NW)
                       ->object_pt()
                       ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                       ->value(0) -
                     quadtree_pt()
                       ->son_pt(SW)
                       ->object_pt()
                       ->internal_data_pt(P_linearised_axi_nst_internal_index[i])
                       ->value(0);
  
         // Use the average
         internal_data_pt(P_linearised_axi_nst_internal_index[i])
           ->set_value(2, 0.5 * (slope1[i] + slope2[i]));
       } // End of loop over pressure components
     }

References i, oomph::GeneralisedElement::internal_data_pt(), oomph::QuadTreeNames::NE, oomph::QuadTreeNames::NW, oomph::Tree::object_pt(), oomph::LinearisedAxisymmetricQCrouzeixRaviartElement::P_linearised_axi_nst_internal_index, oomph::RefineableQElement< 2 >::quadtree_pt(), oomph::QuadTreeNames::SE, oomph::Data::set_value(), oomph::Tree::son_pt(), oomph::QuadTreeNames::SW, and oomph::Data::value().

◆ unpin_elemental_pressure_dofs() [1/2]

void oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::unpin_elemental_pressure_dofs ( )

inlineprivatevirtual

Unpin all the internal pressure freedoms.

Implements oomph::RefineableLinearisedAxisymmetricNavierStokesEquations.

  {
   const unsigned n_pres = this->npres_linearised_axi_nst();
   // Loop over pressure dofs and unpin
   for(unsigned l=0;l<n_pres;l++) 
    {
     // There are two pressure components
     for(unsigned i=0;i<2;i++)
      {
       this->internal_data_pt(P_linearised_axi_nst_internal_index[i])->unpin(l);
      }
    }
  }

References i, oomph::GeneralisedElement::internal_data_pt(), oomph::LinearisedAxisymmetricQCrouzeixRaviartElement::npres_linearised_axi_nst(), oomph::LinearisedAxisymmetricQCrouzeixRaviartElement::P_linearised_axi_nst_internal_index, and oomph::Data::unpin().

◆ unpin_elemental_pressure_dofs() [2/2]

void oomph::RefineableLinearisedAxisymmetricQCrouzeixRaviartElement::unpin_elemental_pressure_dofs ( )

inlineprivatevirtual

Unpin all the internal pressure freedoms.

Implements oomph::RefineableLinearisedAxisymmetricNavierStokesEquations.

     {
       const unsigned n_pres = this->npres_linearised_axi_nst();
       // Loop over pressure dofs and unpin
       for (unsigned l = 0; l < n_pres; l++)
       {
         // There are two pressure components
         for (unsigned i = 0; i < 2; i++)
         {
           this->internal_data_pt(P_linearised_axi_nst_internal_index[i])
             ->unpin(l);
         }
       }
     }

References i, oomph::GeneralisedElement::internal_data_pt(), oomph::LinearisedAxisymmetricQCrouzeixRaviartElement::npres_linearised_axi_nst(), oomph::LinearisedAxisymmetricQCrouzeixRaviartElement::P_linearised_axi_nst_internal_index, and oomph::Data::unpin().

◆ vertex_node_pt() [1/2]

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

inlinevirtual

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

Implements oomph::ElementWithZ2ErrorEstimator.

721 { return LinearisedAxisymmetricQCrouzeixRaviartElement::vertex_node_pt(j); }

oomph::FiniteElement::vertex_node_pt

virtual Node * vertex_node_pt(const unsigned &j) const

Definition: elements.h:2500

j

std::ptrdiff_t j

Definition: tut_arithmetic_redux_minmax.cpp:2

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

◆ vertex_node_pt() [2/2]

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

inlinevirtual

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

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return LinearisedAxisymmetricQCrouzeixRaviartElement::vertex_node_pt(j);
     }

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

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

demo_drivers/axisym_navier_stokes/counter_rotating_disks/refineable_linearised_axisym_navier_stokes_elements.h

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RefineableLinearisedAxisymmetricQCrouzeixRaviartElement() [1/2]

◆ RefineableLinearisedAxisymmetricQCrouzeixRaviartElement() [2/2]

Member Function Documentation

◆ further_build() [1/2]

◆ further_build() [2/2]

◆ further_setup_hanging_nodes() [1/2]

◆ further_setup_hanging_nodes() [2/2]

◆ get_interpolated_values() [1/4]

◆ get_interpolated_values() [2/4]

◆ get_interpolated_values() [3/4]

◆ get_interpolated_values() [4/4]

◆ ncont_interpolated_values() [1/2]

◆ ncont_interpolated_values() [2/2]

◆ nrecovery_order() [1/2]

◆ nrecovery_order() [2/2]

◆ nvertex_node() [1/2]

◆ nvertex_node() [2/2]

◆ rebuild_from_sons() [1/2]

◆ rebuild_from_sons() [2/2]

◆ unpin_elemental_pressure_dofs() [1/2]

◆ unpin_elemental_pressure_dofs() [2/2]

◆ vertex_node_pt() [1/2]

◆ vertex_node_pt() [2/2]