#include <refineable_navier_stokes_elements.h>

Inheritance diagram for oomph::RefineableQTaylorHoodElement< DIM >:

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

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

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

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

unsigned	ninterpolating_node_1d (const int &value_id)

unsigned	ninterpolating_node (const int &value_id)

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

void	build_fp_press_adv_diff_robin_bc_element (const unsigned &face_index)

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

Public Member Functions inherited from oomph::QTaylorHoodElement< DIM >
	QTaylorHoodElement ()
	Constructor, no internal data points. More...

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

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

virtual int	p_nodal_index_nst () const
	Set the value at which the pressure is stored in the nodes. More...

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

double	p_nst (const unsigned &n_p) const

double	p_nst (const unsigned &t, const unsigned &n_p) const

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

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

bool	is_pressure_node (const unsigned &n) const
	Deduce whether or not the provided node is a pressure node. More...

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

void	identify_pressure_data (std::set< std::pair< Data *, unsigned >> &paired_pressure_data)

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

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

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

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

unsigned	ndof_types () const

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

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

void	pshape_nst (const Vector< double > &s, Shape &psi) const

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

void	pshape_nst (const Vector< double > &s, Shape &psi) const

Public Member Functions inherited from oomph::NavierStokesEquations< DIM >
	NavierStokesEquations ()

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

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

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

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

const double &	viscosity_ratio () const

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

const double &	density_ratio () const

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

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

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

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

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

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

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

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

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

NavierStokesPressureAdvDiffSourceFctPt &	source_fct_for_pressure_adv_diff ()

NavierStokesPressureAdvDiffSourceFctPt	source_fct_for_pressure_adv_diff () const

int &	pinned_fp_pressure_eqn ()

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

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

virtual unsigned	u_index_nst (const unsigned &i) const

unsigned	n_u_nst () const

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

void	disable_ALE ()

void	enable_ALE ()

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

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

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

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
	Compute the vorticity vector at local coordinate s. More...

void	get_vorticity (const Vector< double > &s, double &vorticity) const
	Compute the scalar vorticity at local coordinate s (2D) More...

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

double	d_kin_energy_dt () const
	Get integral of time derivative of kinetic energy over element. More...

void	strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate) const
	Strain-rate tensor: 1/2 (du_i/dx_j + du_j/dx_i) More...

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

void	get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction_p, Vector< double > &traction_visc_n, Vector< double > &traction_visc_t)

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

unsigned	nscalar_paraview () const

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

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

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

void	full_output (std::ostream &outfile)

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

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

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

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

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

void	compute_norm (double &norm)
	Compute norm of solution: square of the L2 norm of the velocities. More...

void	compute_norm (Vector< double > &norm)
	Compute the vector norm of the FEM solution. More...

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

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

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

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

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

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

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

void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Compute the element's residual Vector. More...

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

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)

void	fill_in_pressure_advection_diffusion_residuals (Vector< double > &residuals)

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

void	pin_all_non_pressure_dofs (std::map< Data *, std::vector< int >> &eqn_number_backup)
	Pin all non-pressure dofs and backup eqn numbers. More...

void	output_pressure_advection_diffusion_robin_elements (std::ostream &outfile)

void	delete_pressure_advection_diffusion_robin_elements ()

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

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

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

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

double	interpolated_p_nst (const unsigned &t, const Vector< double > &s) const
	Return FE interpolated pressure at local coordinate s at time level t. More...

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

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

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const

void	get_vorticity (const Vector< double > &s, double &vorticity) const

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
	Compute 3D vorticity vector at local coordinate s. More...

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

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

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

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

virtual void	identify_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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

virtual unsigned	self_test ()

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

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::TemplateFreeNavierStokesEquationsBase
	TemplateFreeNavierStokesEquationsBase ()
	Constructor (empty) More...

virtual	~TemplateFreeNavierStokesEquationsBase ()
	Virtual destructor (empty) More...

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

virtual	~NavierStokesElementWithDiagonalMassMatrices ()
	Virtual destructor. More...

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

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

Public Member Functions inherited from oomph::RefineableNavierStokesEquations< DIM >
	RefineableNavierStokesEquations ()
	Constructor. More...

void	get_pressure_and_velocity_mass_matrix_diagonal (Vector< double > &press_mass_diag, Vector< double > &veloc_mass_diag, const unsigned &which_one=0)

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...

void	dinterpolated_u_nst_ddata (const Vector< double > &s, const unsigned &i, Vector< double > &du_ddata, Vector< unsigned > &global_eqn_number)

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...

virtual unsigned	required_nsons () const

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)

virtual void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)=0

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 void	check_integrity (double &max_error)=0

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...

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

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< DIM >
	RefineableQElement ()
	Empty constuctor. More...

Private Member Functions
void	unpin_elemental_pressure_dofs ()
	Unpin all pressure dofs. More...

void	pin_elemental_redundant_nodal_pressure_dofs ()
	Pin all nodal pressure dofs that are not required. More...

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

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

typedef double(*	NavierStokesPressureAdvDiffSourceFctPt) (const Vector< double > &x)

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

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

Static Public Member Functions inherited from oomph::RefineableNavierStokesEquations< DIM >
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...

Static Public Attributes inherited from oomph::NavierStokesEquations< DIM >
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::QTaylorHoodElement< DIM >
double	dshape_and_dtest_eulerian_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

double	dshape_and_dtest_eulerian_at_knot_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

const unsigned	Pconv [4]

const unsigned	Pconv [8]

double	dshape_and_dtest_eulerian_at_knot_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

double	dshape_and_dtest_eulerian_at_knot_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

Protected Member Functions inherited from oomph::NavierStokesEquations< DIM >
virtual void	get_body_force_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &result)

virtual void	get_body_force_gradient_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, DenseMatrix< double > &d_body_force_dx)

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

virtual void	get_source_gradient_nst (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &gradient)

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

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

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)

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_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::RefineableNavierStokesEquations< DIM >
void	fill_in_generic_residual_contribution_nst (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag)

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

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)

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::NavierStokesEquations< DIM >
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 *	ReInvFr_pt

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

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

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

NavierStokesPressureAdvDiffSourceFctPt	Press_adv_diff_source_fct_pt

bool	ALE_is_disabled

Vector< FpPressureAdvDiffRobinBCElementBase * >	Pressure_advection_diffusion_robin_element_pt

int	Pinned_fp_pressure_eqn

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::QTaylorHoodElement< DIM >
static const unsigned	Pconv []

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...

Detailed Description

template<unsigned DIM>
class oomph::RefineableQTaylorHoodElement< DIM >

Refineable version of Taylor Hood elements. These classes can be written in total generality.

Constructor & Destructor Documentation

◆ RefineableQTaylorHoodElement()

template<unsigned DIM>

oomph::RefineableQTaylorHoodElement< DIM >::RefineableQTaylorHoodElement ( )

inline

Constructor.

       : RefineableElement(),
         RefineableNavierStokesEquations<DIM>(),
         RefineableQElement<DIM>(),
         QTaylorHoodElement<DIM>()
     {
     }

Member Function Documentation

◆ build_fp_press_adv_diff_robin_bc_element()

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::build_fp_press_adv_diff_robin_bc_element ( const unsigned & face_index )

inlinevirtual

Build FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner

Reimplemented from oomph::QTaylorHoodElement< DIM >.

     {
       this->Pressure_advection_diffusion_robin_element_pt.push_back(
         new RefineableFpPressureAdvDiffRobinBCElement<
           RefineableQTaylorHoodElement<DIM>>(this, face_index));
     }

References oomph::NavierStokesEquations< DIM >::Pressure_advection_diffusion_robin_element_pt.

◆ further_setup_hanging_nodes()

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::further_setup_hanging_nodes ( )

inlinevirtual

Perform additional hanging node procedures for variables that are not interpolated by all nodes. The pressures are stored at the p_nodal_index_nst-th location in each node

Reimplemented from oomph::RefineableElement.

     {
       this->setup_hang_for_value(this->p_nodal_index_nst());
     }

References oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst().

◆ get_interpolated_values() [1/2]

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::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 Vector: u,v,p
       values.resize(DIM + 1);
  
       // Initialise
       for (unsigned i = 0; i < DIM + 1; i++)
       {
         values[i] = 0.0;
       }
  
       // Find out how many nodes there are
       unsigned n_node = this->nnode();
  
       // Shape functions
       Shape psif(n_node);
       this->shape(s, psif);
  
       // Calculate velocities: values[0],...
       for (unsigned i = 0; i < DIM; i++)
       {
         // Get the index at which the i-th velocity is stored
         unsigned u_nodal_index = this->u_index_nst(i);
         for (unsigned l = 0; l < n_node; l++)
         {
           values[i] += this->nodal_value(t, l, u_nodal_index) * psif[l];
         }
       }
  
       // Calculate pressure: values[DIM]
       //(no history is carried in the pressure)
       values[DIM] = this->interpolated_p_nst(s);
     }

References DIM, i, oomph::NavierStokesEquations< DIM >::interpolated_p_nst(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), oomph::FiniteElement::shape(), and oomph::NavierStokesEquations< DIM >::u_index_nst().

◆ get_interpolated_values() [2/2]

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::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 size of Vector: u,v,p and initialise to zero
       values.resize(DIM + 1, 0.0);
  
       // Calculate velocities: values[0],...
       for (unsigned i = 0; i < DIM; i++)
       {
         values[i] = this->interpolated_u_nst(s, i);
       }
  
       // Calculate pressure: values[DIM]
       values[DIM] = this->interpolated_p_nst(s);
     }

References DIM, i, oomph::NavierStokesEquations< DIM >::interpolated_p_nst(), and oomph::NavierStokesEquations< DIM >::interpolated_u_nst().

◆ get_interpolating_node_at_local_coordinate()

template<unsigned DIM>

Node* oomph::RefineableQTaylorHoodElement< DIM >::get_interpolating_node_at_local_coordinate	(	const Vector< double > &	s,
		const int &	value_id
	)

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 (value_id == DIM)
       {
         // Storage for the index of the pressure node
         unsigned total_index = 0;
         // The number of nodes along each 1d edge is 2.
         unsigned NNODE_1D = 2;
         // Storage for the index along each boundary
         Vector<int> index(DIM);
         // Loop over the coordinates
         for (unsigned i = 0; i < DIM; 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->pressure_node_pt(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, Eigen::bfloat16_impl::pow(), oomph::RefineableQTaylorHoodElement< DIM >::pressure_node_pt(), and s.

◆ identify_load_data()

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::identify_load_data ( std::set< std::pair< Data *, unsigned >> & paired_load_data )

inlinevirtual

Add to the set paired_load_data pairs containing

the pointer to a Data object and
the index of the value in that Data object

for all values (pressures, velocities) that affect the load computed in the get_load(...) function. (Overloads non-refineable version and takes hanging nodes into account)

Reimplemented from oomph::QTaylorHoodElement< DIM >.

     {
       // Get the nodal indices at which the velocities are stored
       unsigned u_index[DIM];
       for (unsigned i = 0; i < DIM; i++)
       {
         u_index[i] = this->u_index_nst(i);
       }
  
       // Loop over the nodes
       unsigned n_node = this->nnode();
       for (unsigned n = 0; n < n_node; n++)
       {
         // Pointer to current node
         Node* nod_pt = this->node_pt(n);
  
         // Check if it's hanging:
         if (nod_pt->is_hanging())
         {
           // It's hanging -- get number of master nodes
           unsigned nmaster = nod_pt->hanging_pt()->nmaster();
  
           // Loop over masters
           for (unsigned j = 0; j < nmaster; j++)
           {
             Node* master_nod_pt = nod_pt->hanging_pt()->master_node_pt(j);
  
             // Loop over the velocity components and add pointer to their data
             // and indices to the vectors
             for (unsigned i = 0; i < DIM; i++)
             {
               paired_load_data.insert(
                 std::make_pair(master_nod_pt, u_index[i]));
             }
           }
         }
         // Not hanging
         else
         {
           // Loop over the velocity components and add pointer to their data
           // and indices to the vectors
           for (unsigned i = 0; i < DIM; i++)
           {
             paired_load_data.insert(
               std::make_pair(this->node_pt(n), u_index[i]));
           }
         }
       }
  
       // Get the nodal index at which the pressure is stored
       int p_index = this->p_nodal_index_nst();
  
       // Loop over the pressure data
       unsigned n_pres = this->npres_nst();
       for (unsigned l = 0; l < n_pres; l++)
       {
         // Get the pointer to the nodal pressure
         Node* pres_node_pt = this->pressure_node_pt(l);
         // Check if the pressure dof is hanging
         if (pres_node_pt->is_hanging(p_index))
         {
           // Get the pointer to the hang info object
           // (pressure is stored as p_index--th nodal dof).
           HangInfo* hang_info_pt = pres_node_pt->hanging_pt(p_index);
  
           // Get number of pressure master nodes (pressure is stored
           unsigned nmaster = hang_info_pt->nmaster();
  
           // Loop over pressure master nodes
           for (unsigned m = 0; m < nmaster; m++)
           {
             // The p_index-th entry in each nodal data is the pressure, which
             // affects the traction
             paired_load_data.insert(
               std::make_pair(hang_info_pt->master_node_pt(m), p_index));
           }
         }
         // It's not hanging
         else
         {
           // The p_index-th entry in each nodal data is the pressure, which
           // affects the traction
           paired_load_data.insert(std::make_pair(pres_node_pt, p_index));
         }
       }
     }

References DIM, oomph::Node::hanging_pt(), i, oomph::Node::is_hanging(), j, m, oomph::HangInfo::master_node_pt(), n, oomph::HangInfo::nmaster(), oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), oomph::QTaylorHoodElement< DIM >::npres_nst(), oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst(), oomph::RefineableQTaylorHoodElement< DIM >::pressure_node_pt(), and oomph::NavierStokesEquations< DIM >::u_index_nst().

◆ interpolating_basis()

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::interpolating_basis	(	const Vector< double > &	s,
		Shape &	psi,
		const int &	value_id
	)		const

inlinevirtual

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

Reimplemented from oomph::RefineableElement.

     {
       if (value_id == DIM)
       {
         return this->pshape_nst(s, psi);
       }
       else
       {
         return this->shape(s, psi);
       }
     }

References DIM, oomph::QTaylorHoodElement< DIM >::pshape_nst(), and oomph::FiniteElement::shape().

◆ interpolating_node_pt()

template<unsigned DIM>

Node* oomph::RefineableQTaylorHoodElement< DIM >::interpolating_node_pt	(	const unsigned &	n,
		const int &	value_id
	)

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 value_id==DIM, the n-th pressure node is returned.

Reimplemented from oomph::RefineableElement.

     {
       // The only different nodes are the pressure nodes
       if (value_id == DIM)
       {
         return this->pressure_node_pt(n);
       }
       // The other variables are interpolated via the usual nodes
       else
       {
         return this->node_pt(n);
       }
     }

References DIM, oomph::FiniteElement::node_pt(), and oomph::RefineableQTaylorHoodElement< DIM >::pressure_node_pt().

◆ local_one_d_fraction_of_interpolating_node()

template<unsigned DIM>

double oomph::RefineableQTaylorHoodElement< DIM >::local_one_d_fraction_of_interpolating_node	(	const unsigned &	n1d,
		const unsigned &	i,
		const int &	value_id
	)

inlinevirtual

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

Reimplemented from oomph::RefineableElement.

     {
       if (value_id == DIM)
       {
         // 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()

template<unsigned DIM>

unsigned oomph::RefineableQTaylorHoodElement< DIM >::ncont_interpolated_values ( ) const

inlinevirtual

Number of continuously interpolated values: (DIM velocities + 1 pressure)

Implements oomph::RefineableElement.

     {
       return DIM + 1;
     }

References DIM.

◆ ninterpolating_node()

template<unsigned DIM>

unsigned oomph::RefineableQTaylorHoodElement< DIM >::ninterpolating_node ( const int & value_id )

inlinevirtual

The number of pressure nodes is 2^DIM. The number of velocity nodes is the same as the number of geometric nodes.

Reimplemented from oomph::RefineableElement.

     {
       if (value_id == DIM)
       {
         return static_cast<unsigned>(pow(2.0, static_cast<int>(DIM)));
       }
       else
       {
         return this->nnode();
       }
     }

References DIM, oomph::FiniteElement::nnode(), and Eigen::bfloat16_impl::pow().

◆ ninterpolating_node_1d()

template<unsigned DIM>

unsigned oomph::RefineableQTaylorHoodElement< DIM >::ninterpolating_node_1d ( const int & value_id )

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 (value_id == DIM)
       {
         return 2;
       }
       else
       {
         return this->nnode_1d();
       }
     }

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

◆ nrecovery_order()

template<unsigned DIM>

unsigned oomph::RefineableQTaylorHoodElement< DIM >::nrecovery_order ( )

inlinevirtual

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

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return 2;
     }

◆ nvertex_node()

template<unsigned DIM>

unsigned oomph::RefineableQTaylorHoodElement< DIM >::nvertex_node ( ) const

inlinevirtual

Number of vertex nodes in the element.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return QTaylorHoodElement<DIM>::nvertex_node();
     }

References oomph::FiniteElement::nvertex_node().

◆ pin_elemental_redundant_nodal_pressure_dofs()

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::pin_elemental_redundant_nodal_pressure_dofs ( )

inlineprivatevirtual

Pin all nodal pressure dofs that are not required.

Reimplemented from oomph::RefineableNavierStokesEquations< DIM >.

     {
       // Find the pressure index
       int p_index = this->p_nodal_index_nst();
       // Loop over all nodes
       unsigned n_node = this->nnode();
       // loop over all nodes and pin all  the nodal pressures
       for (unsigned n = 0; n < n_node; n++)
       {
         this->node_pt(n)->pin(p_index);
       }
  
       // Loop over all actual pressure nodes and unpin if they're not hanging
       unsigned n_pres = this->npres_nst();
       for (unsigned l = 0; l < n_pres; l++)
       {
         Node* nod_pt = this->pressure_node_pt(l);
         if (!nod_pt->is_hanging(p_index))
         {
           nod_pt->unpin(p_index);
         }
       }
     }

References oomph::Node::is_hanging(), n, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), oomph::QTaylorHoodElement< DIM >::npres_nst(), oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst(), oomph::Data::pin(), oomph::RefineableQTaylorHoodElement< DIM >::pressure_node_pt(), and oomph::Data::unpin().

◆ pressure_node_pt()

template<unsigned DIM>

Node* oomph::RefineableQTaylorHoodElement< DIM >::pressure_node_pt ( const unsigned & n_p )

inlinevirtual

Pointer to n_p-th pressure node.

Reimplemented from oomph::RefineableNavierStokesEquations< DIM >.

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

References oomph::FiniteElement::node_pt(), and oomph::QTaylorHoodElement< DIM >::Pconv.

Referenced by oomph::RefineableQTaylorHoodElement< DIM >::get_interpolating_node_at_local_coordinate(), oomph::RefineableQTaylorHoodElement< DIM >::identify_load_data(), oomph::RefineableQTaylorHoodElement< DIM >::interpolating_node_pt(), and oomph::RefineableQTaylorHoodElement< DIM >::pin_elemental_redundant_nodal_pressure_dofs().

◆ rebuild_from_sons()

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::rebuild_from_sons ( Mesh *& mesh_pt )

inlinevirtual

Rebuild from sons: empty.

Implements oomph::RefineableElement.

718 {}

◆ required_nvalue()

template<unsigned DIM>

unsigned oomph::RefineableQTaylorHoodElement< DIM >::required_nvalue ( const unsigned & n ) const

inlinevirtual

Number of values required at local node n. In order to simplify matters, we allocate storage for pressure variables at all the nodes and then pin those that are not used.

Reimplemented from oomph::QTaylorHoodElement< DIM >.

     {
       return DIM + 1;
     }

References DIM.

◆ unpin_elemental_pressure_dofs()

template<unsigned DIM>

void oomph::RefineableQTaylorHoodElement< DIM >::unpin_elemental_pressure_dofs ( )

inlineprivatevirtual

Unpin all pressure dofs.

Implements oomph::RefineableNavierStokesEquations< DIM >.

     {
       // find the index at which the pressure is stored
       int p_index = this->p_nodal_index_nst();
       unsigned n_node = this->nnode();
       // loop over nodes
       for (unsigned n = 0; n < n_node; n++)
       {
         this->node_pt(n)->unpin(p_index);
       }
     }

References n, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), oomph::QTaylorHoodElement< DIM >::p_nodal_index_nst(), and oomph::Data::unpin().

◆ vertex_node_pt()

template<unsigned DIM>

Node* oomph::RefineableQTaylorHoodElement< DIM >::vertex_node_pt ( const unsigned & j ) const

inlinevirtual

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

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return QTaylorHoodElement<DIM>::vertex_node_pt(j);
     }

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

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

refineable_navier_stokes_elements.h

Public Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

template<unsigned DIM> class oomph::RefineableQTaylorHoodElement< DIM >

Constructor & Destructor Documentation

◆ RefineableQTaylorHoodElement()

Member Function Documentation

◆ build_fp_press_adv_diff_robin_bc_element()

◆ further_setup_hanging_nodes()

◆ get_interpolated_values() [1/2]

◆ get_interpolated_values() [2/2]

◆ get_interpolating_node_at_local_coordinate()

◆ identify_load_data()

◆ 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()

template<unsigned DIM>
class oomph::RefineableQTaylorHoodElement< DIM >