#include <refineable_navier_stokes_elements.h>

Inheritance diagram for oomph::PRefineableQCrouzeixRaviartElement< DIM >:

Public Member Functions
	PRefineableQCrouzeixRaviartElement ()
	Constructor. More...

	~PRefineableQCrouzeixRaviartElement ()
	Destructor. More...

	PRefineableQCrouzeixRaviartElement (const PRefineableQCrouzeixRaviartElement< DIM > &dummy)=delete
	Broken copy constructor. More...

double	p_nst (const unsigned &i) const
	Broken assignment operator. More...

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

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

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

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

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

void	rebuild_from_sons (Mesh *&mesh_pt)

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...

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

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...

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 ()

void	further_build ()

void	further_build ()

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_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

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

void	pshape_nst (const Vector< double > &s, Shape &psi, Shape &test) const
	Define the pressure shape and test functions. More...

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

void	pshape_nst (const Vector< double > &s, Shape &psi, Shape &test) const
	Define the pressure shape and test functions. More...

Public Member Functions inherited from oomph::QCrouzeixRaviartElement< DIM >
	QCrouzeixRaviartElement ()
	Constructor, there are DIM+1 internal values (for the pressure) More...

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

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

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)

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...

void	full_output (std::ostream &outfile)

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

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

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

virtual int	p_nodal_index_nst () const

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

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

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

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...

virtual Node *	pressure_node_pt (const unsigned &n_p)

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	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 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

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::PRefineableQElement< DIM, 3 >
	PRefineableQElement ()
	Empty constuctor. More...

Private Member Functions
void	unpin_elemental_pressure_dofs ()
	Unpin all internal pressure dofs. 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::QCrouzeixRaviartElement< DIM >
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

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 >
virtual void	pin_elemental_redundant_nodal_pressure_dofs ()

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::QCrouzeixRaviartElement< DIM >
unsigned	P_nst_internal_index

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::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::PRefineableQCrouzeixRaviartElement< DIM >

p-refineable version of Crouzeix Raviart elements. Generic class definitions

Constructor & Destructor Documentation

◆ PRefineableQCrouzeixRaviartElement() [1/2]

template<unsigned DIM>

oomph::PRefineableQCrouzeixRaviartElement< DIM >::PRefineableQCrouzeixRaviartElement ( )

inline

Constructor.

       : RefineableElement(),
         RefineableNavierStokesEquations<DIM>(),
         PRefineableQElement<DIM, 3>(),
         QCrouzeixRaviartElement<DIM>()
     {
       // Set the p-order
       this->p_order() = 3;
  
       // Set integration scheme
       // (To avoid memory leaks in pre-build and p-refine where new
       // integration schemes are created)
       this->set_integration_scheme(new GaussLobattoLegendre<DIM, 3>);
  
       // Resize pressure storage
       // (Constructor for QCrouzeixRaviartElement sets up DIM+1 pressure values)
       if (this->internal_data_pt(this->P_nst_internal_index)->nvalue() <=
           this->npres_nst())
       {
         this->internal_data_pt(this->P_nst_internal_index)
           ->resize(this->npres_nst());
       }
       else
       {
         Data* new_data_pt = new Data(this->npres_nst());
         delete this->internal_data_pt(this->P_nst_internal_index);
         this->internal_data_pt(this->P_nst_internal_index) = new_data_pt;
       }
     }

References oomph::GeneralisedElement::internal_data_pt(), oomph::PRefineableQCrouzeixRaviartElement< DIM >::npres_nst(), oomph::QCrouzeixRaviartElement< DIM >::P_nst_internal_index, oomph::Data::resize(), and oomph::FiniteElement::set_integration_scheme().

◆ ~PRefineableQCrouzeixRaviartElement()

template<unsigned DIM>

oomph::PRefineableQCrouzeixRaviartElement< DIM >::~PRefineableQCrouzeixRaviartElement ( )

inline

Destructor.

     {
       delete this->integral_pt();
     }

References oomph::FiniteElement::integral_pt().

◆ PRefineableQCrouzeixRaviartElement() [2/2]

template<unsigned DIM>

oomph::PRefineableQCrouzeixRaviartElement< DIM >::PRefineableQCrouzeixRaviartElement ( const PRefineableQCrouzeixRaviartElement< DIM > & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ dshape_and_dtest_eulerian_at_knot_nst() [1/3]

template<unsigned DIM>

double oomph::PRefineableQCrouzeixRaviartElement< DIM >::dshape_and_dtest_eulerian_at_knot_nst	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlinevirtual

Velocity shape and test functions and their derivs w.r.t. to global coords at ipt-th integation point (taken from geometry) Return Jacobian of mapping between local and global coordinates.

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

◆ dshape_and_dtest_eulerian_at_knot_nst() [2/3]

double oomph::PRefineableQCrouzeixRaviartElement< 2 >::dshape_and_dtest_eulerian_at_knot_nst	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlinevirtual

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

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

   {
     // Call the geometrical shape functions and derivatives
     double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
  
     // Loop over the test functions and derivatives and set them equal to the
     // shape functions
     for (unsigned i = 0; i < nnode_1d() * nnode_1d(); i++)
     {
       test[i] = psi[i];
       dtestdx(i, 0) = dpsidx(i, 0);
       dtestdx(i, 1) = dpsidx(i, 1);
     }
  
     // Return the jacobian
     return J;
   }

References i, and J.

◆ dshape_and_dtest_eulerian_at_knot_nst() [3/3]

double oomph::PRefineableQCrouzeixRaviartElement< 3 >::dshape_and_dtest_eulerian_at_knot_nst	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlinevirtual

3D Derivatives of the shape functions and test functions w.r.t. to global (Eulerian) coordinates. Return Jacobian of mapping between local and global coordinates.

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

   {
     // Call the geometrical shape functions and derivatives
     double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
  
     // Loop over the test functions and derivatives and set them equal to the
     // shape functions
     for (unsigned i = 0; i < nnode_1d() * nnode_1d() * nnode_1d(); i++)
     {
       test[i] = psi[i];
       dtestdx(i, 0) = dpsidx(i, 0);
       dtestdx(i, 1) = dpsidx(i, 1);
       dtestdx(i, 2) = dpsidx(i, 2);
     }
  
     // Return the jacobian
     return J;
   }

References i, and J.

◆ dshape_and_dtest_eulerian_nst() [1/3]

template<unsigned DIM>

double oomph::PRefineableQCrouzeixRaviartElement< DIM >::dshape_and_dtest_eulerian_nst	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlinevirtual

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

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

◆ dshape_and_dtest_eulerian_nst() [2/3]

double oomph::PRefineableQCrouzeixRaviartElement< 2 >::dshape_and_dtest_eulerian_nst	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlinevirtual

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

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

   {
     // Call the geometrical shape functions and derivatives
     double J = this->dshape_eulerian(s, psi, dpsidx);
  
     // Loop over the test functions and derivatives and set them equal to the
     // shape functions
     for (unsigned i = 0; i < nnode_1d() * nnode_1d(); i++)
     {
       test[i] = psi[i];
       dtestdx(i, 0) = dpsidx(i, 0);
       dtestdx(i, 1) = dpsidx(i, 1);
     }
  
     // Return the jacobian
     return J;
   }

References i, J, and s.

◆ dshape_and_dtest_eulerian_nst() [3/3]

double oomph::PRefineableQCrouzeixRaviartElement< 3 >::dshape_and_dtest_eulerian_nst	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

inlinevirtual

3D Derivatives of the shape functions and test functions w.r.t. to global (Eulerian) coordinates. Return Jacobian of mapping between local and global coordinates.

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

   {
     // Call the geometrical shape functions and derivatives
     double J = this->dshape_eulerian(s, psi, dpsidx);
  
     // Loop over the test functions and derivatives and set them equal to the
     // shape functions
     for (unsigned i = 0; i < nnode_1d() * nnode_1d() * nnode_1d(); i++)
     {
       test[i] = psi[i];
       dtestdx(i, 0) = dpsidx(i, 0);
       dtestdx(i, 1) = dpsidx(i, 1);
       dtestdx(i, 2) = dpsidx(i, 2);
     }
  
     // Return the jacobian
     return J;
   }

References i, J, and s.

◆ fix_pressure()

template<unsigned DIM>

void oomph::PRefineableQCrouzeixRaviartElement< DIM >::fix_pressure	(	const unsigned &	p_dof,
		const double &	p_value
	)

inlinevirtual

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

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

     {
       this->internal_data_pt(this->P_nst_internal_index)->pin(p_dof);
       this->internal_data_pt(this->P_nst_internal_index)
         ->set_value(p_dof, p_value);
     }

References oomph::GeneralisedElement::internal_data_pt(), oomph::QCrouzeixRaviartElement< DIM >::P_nst_internal_index, oomph::Data::pin(), and oomph::Data::set_value().

◆ further_build() [1/3]

void oomph::PRefineableQCrouzeixRaviartElement< 2 >::further_build ( )

virtual

2D 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::RefineableNavierStokesEquations< DIM >.

   {
     if (this->tree_pt()->father_pt() != 0)
     {
       // Call the generic further build (if there is a father)
       RefineableNavierStokesEquations<2>::further_build();
     }
     // Now do the PRefineableQElement further_build()
     PRefineableQElement<2, 3>::further_build();
  
     // Resize internal pressure storage
     if (this->internal_data_pt(this->P_nst_internal_index)->nvalue() <=
         this->npres_nst())
     {
       this->internal_data_pt(this->P_nst_internal_index)
         ->resize(this->npres_nst());
     }
     else
     {
       Data* new_data_pt = new Data(this->npres_nst());
       delete internal_data_pt(this->P_nst_internal_index);
       internal_data_pt(this->P_nst_internal_index) = new_data_pt;
     }
  
     if (this->tree_pt()->father_pt() != 0)
     {
       // Pointer to my father (in C-R element impersonation)
       PRefineableQCrouzeixRaviartElement<2>* father_element_pt =
         dynamic_cast<PRefineableQCrouzeixRaviartElement<2>*>(
           quadtree_pt()->father_pt()->object_pt());
  
       // If element has same p-order as father then do the projection problem
       // (called after h-refinement)
       if (father_element_pt->p_order() == this->p_order())
       {
         using namespace QuadTreeNames;
  
         // What type of son am I? Ask my quadtree representation...
         int son_type = quadtree_pt()->son_type();
  
         Vector<double> s_father(2);
  
         // Son midpoint is located at the following coordinates in father
         // element:
         switch (son_type)
         {
           case SW:
             // South west son
             s_father[0] = -0.5;
             s_father[1] = -0.5;
             break;
           case SE:
             // South east son
             s_father[0] = 0.5;
             s_father[1] = -0.5;
             break;
           case NE:
             // North east son
             s_father[0] = 0.5;
             s_father[1] = 0.5;
             break;
           case NW:
             // North west son
             s_father[0] = -0.5;
             s_father[1] = 0.5;
             break;
           default:
             throw OomphLibError("Invalid son type in",
                                 OOMPH_CURRENT_FUNCTION,
                                 OOMPH_EXCEPTION_LOCATION);
             break;
         }
  
         // Get pressure value in father element
         double press = father_element_pt->interpolated_p_nst(s_father);
  
         // Reset all pressures to zero
         for (unsigned p = 0; p < this->npres_nst(); p++)
         {
           internal_data_pt(this->P_nst_internal_index)->set_value(p, 0.0);
         }
  
         // Set pressure values from father (BENFLAG: projection problem hack)
         if (this->npres_nst() == 1)
         {
           internal_data_pt(this->P_nst_internal_index)->set_value(0, press);
         }
         else if (this->npres_nst() == 3)
         {
           internal_data_pt(this->P_nst_internal_index)->set_value(0, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(1, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(2, press);
         }
         else
         {
           internal_data_pt(this->P_nst_internal_index)->set_value(0, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(1, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(2, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(3, press);
         }
       } // Otherwise this is called after p-refinement
     }
   }

References oomph::RefineableNavierStokesEquations< DIM >::further_build(), oomph::NavierStokesEquations< DIM >::interpolated_p_nst(), oomph::QuadTreeNames::NE, oomph::QuadTreeNames::NW, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, p, oomph::QuadTreeNames::SE, and oomph::QuadTreeNames::SW.

◆ further_build() [2/3]

void oomph::PRefineableQCrouzeixRaviartElement< 3 >::further_build ( )

virtual

2D 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::RefineableNavierStokesEquations< DIM >.

   {
     if (this->tree_pt()->father_pt() != 0)
     {
       // Call the generic further build (if there is a father)
       RefineableNavierStokesEquations<3>::further_build();
     }
     // Now do the PRefineableQElement further_build()
     PRefineableQElement<3, 3>::further_build();
  
     // Resize internal pressure storage
     if (this->internal_data_pt(this->P_nst_internal_index)->nvalue() <=
         this->npres_nst())
     {
       this->internal_data_pt(this->P_nst_internal_index)
         ->resize(this->npres_nst());
     }
     else
     {
       Data* new_data_pt = new Data(this->npres_nst());
       delete internal_data_pt(this->P_nst_internal_index);
       internal_data_pt(this->P_nst_internal_index) = new_data_pt;
     }
  
     if (this->tree_pt()->father_pt() != 0)
     {
       // Pointer to my father (in C-R element impersonation)
       PRefineableQCrouzeixRaviartElement<3>* father_element_pt =
         dynamic_cast<PRefineableQCrouzeixRaviartElement<3>*>(
           octree_pt()->father_pt()->object_pt());
  
       // If element has same p-order as father then do the projection problem
       // (called after h-refinement)
       if (father_element_pt->p_order() == this->p_order())
       {
         using namespace OcTreeNames;
  
         // What type of son am I? Ask my quadtree representation...
         int son_type = octree_pt()->son_type();
  
         Vector<double> s_father(3);
  
  
         // Son midpoint is located at the following coordinates in father
         // element:
         for (unsigned i = 0; i < 3; i++)
         {
           s_father[i] = 0.5 * OcTree::Direction_to_vector[son_type][i];
         }
  
         // Get pressure value in father element
         double press = father_element_pt->interpolated_p_nst(s_father);
  
         // Reset all pressures to zero
         for (unsigned p = 0; p < this->npres_nst(); p++)
         {
           internal_data_pt(this->P_nst_internal_index)->set_value(p, 0.0);
         }
  
         // Set pressure values from father (BENFLAG: projection problem hack)
         if (this->npres_nst() == 1)
         {
           internal_data_pt(this->P_nst_internal_index)->set_value(0, press);
         }
         else
         {
           internal_data_pt(this->P_nst_internal_index)->set_value(0, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(1, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(2, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(3, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(4, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(5, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(6, press);
           internal_data_pt(this->P_nst_internal_index)->set_value(7, press);
         }
       } // Otherwise this is called after p-refinement
     }
   }

References oomph::OcTree::Direction_to_vector, oomph::RefineableNavierStokesEquations< DIM >::further_build(), i, oomph::NavierStokesEquations< DIM >::interpolated_p_nst(), and p.

◆ further_build() [3/3]

template<unsigned DIM>

void oomph::PRefineableQCrouzeixRaviartElement< DIM >::further_build ( )

virtual

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. This must be specialised for each dimension.

Reimplemented from oomph::RefineableNavierStokesEquations< DIM >.

◆ further_setup_hanging_nodes()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::RefineableElement.

1562 {}

◆ get_interpolated_values() [1/2]

template<unsigned DIM>

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

inlinevirtual

Get all function values [u,v..,p] 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.

     {
       // Set size of Vector: u,v,p
       values.resize(DIM);
  
       // Initialise
       for (unsigned i = 0; i < DIM; 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 nodal index at which the i-th velocity component 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];
         }
       }
     }

References DIM, i, 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::PRefineableQCrouzeixRaviartElement< 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, 0.0);
  
       // Calculate velocities: values[0],...
       for (unsigned i = 0; i < DIM; i++)
       {
         values[i] = this->interpolated_u_nst(s, i);
       }
     }

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

◆ ncont_interpolated_values()

template<unsigned DIM>

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

inlinevirtual

Number of continuously interpolated values: DIM (velocities)

Implements oomph::RefineableElement.

     {
       return DIM;
     }

References DIM.

◆ npres_nst()

template<unsigned DIM>

unsigned oomph::PRefineableQCrouzeixRaviartElement< DIM >::npres_nst ( ) const

inlinevirtual

// Return number of pressure values

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

     {
       return (this->p_order() - 2) * (this->p_order() - 2);
     }

Referenced by oomph::PRefineableQCrouzeixRaviartElement< DIM >::PRefineableQCrouzeixRaviartElement(), oomph::PRefineableQCrouzeixRaviartElement< DIM >::rebuild_from_sons(), and oomph::PRefineableQCrouzeixRaviartElement< DIM >::unpin_elemental_pressure_dofs().

◆ nrecovery_order()

template<unsigned DIM>

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

inlinevirtual

Order of recovery shape functions for Z2 error estimation:

Same order as shape functions.
Constant recovery order, since recovery order of the first element is used for the whole mesh.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return 3;
     }

◆ nvertex_node()

template<unsigned DIM>

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

inlinevirtual

Number of vertex nodes in the element.

Implements oomph::ElementWithZ2ErrorEstimator.

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

References oomph::FiniteElement::nvertex_node().

◆ p_nst() [1/2]

template<unsigned DIM>

double oomph::PRefineableQCrouzeixRaviartElement< DIM >::p_nst ( const unsigned & i ) const

inlinevirtual

Broken assignment operator.

Return the i-th pressure value (Discontinous pressure interpolation – no need to cater for hanging nodes).

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

     {
       return this->internal_data_pt(this->P_nst_internal_index)->value(i);
     }

References oomph::GeneralisedElement::internal_data_pt(), oomph::QCrouzeixRaviartElement< DIM >::P_nst_internal_index, and oomph::Data::value().

◆ p_nst() [2/2]

template<unsigned DIM>

double oomph::PRefineableQCrouzeixRaviartElement< DIM >::p_nst	(	const unsigned &	t,
		const unsigned &	i
	)		const

inlinevirtual

Return the i-th pressure value (Discontinous pressure interpolation – no need to cater for hanging nodes).

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

     {
       return this->internal_data_pt(this->P_nst_internal_index)->value(t, i);
     }

References i, oomph::GeneralisedElement::internal_data_pt(), oomph::QCrouzeixRaviartElement< DIM >::P_nst_internal_index, and oomph::Data::value().

◆ pshape_nst() [1/6]

template<unsigned DIM>

void oomph::PRefineableQCrouzeixRaviartElement< DIM >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi
	)		const

inlinevirtual

Pressure shape functions at local coordinate s.

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

◆ pshape_nst() [2/6]

void oomph::PRefineableQCrouzeixRaviartElement< 2 >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi
	)		const

inlinevirtual

2D : Pressure shape functions

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

   {
     unsigned npres = this->npres_nst();
     if (npres == 1)
     {
       psi[0] = 1.0;
     }
     else
     {
       // Get number of pressure modes
       unsigned npres_1d = (int)std::sqrt((double)npres);
  
       // Local storage
       // Call the one-dimensional modal shape functions
       OneDimensionalModalShape psi1(npres_1d, s[0]);
       OneDimensionalModalShape psi2(npres_1d, s[1]);
  
       // Now let's loop over the nodal points in the element
       // s1 is the "x" coordinate, s2 the "y"
       for (unsigned i = 0; i < npres_1d; i++)
       {
         for (unsigned j = 0; j < npres_1d; j++)
         {
           // Multiply the two 1D functions together to get the 2D function
           psi[i * npres_1d + j] = psi2[i] * psi1[j];
         }
       }
     }
   }

References i, int(), j, s, and sqrt().

◆ pshape_nst() [3/6]

void oomph::PRefineableQCrouzeixRaviartElement< 3 >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi
	)		const

inlinevirtual

3D : Pressure shape functions

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

   {
     unsigned npres = this->npres_nst();
     if (npres == 1)
     {
       psi[0] = 1.0;
     }
     else
     {
       // Get number of pressure modes
       unsigned npres_1d = (int)std::sqrt((double)npres);
  
       // Local storage
       // Call the one-dimensional modal shape functions
       OneDimensionalModalShape psi1(npres_1d, s[0]);
       OneDimensionalModalShape psi2(npres_1d, s[1]);
       OneDimensionalModalShape psi3(npres_1d, s[2]);
  
       // Now let's loop over the nodal points in the element
       // s1 is the "x" coordinate, s2 the "y"
       for (unsigned i = 0; i < npres_1d; i++)
       {
         for (unsigned j = 0; j < npres_1d; j++)
         {
           for (unsigned k = 0; k < npres_1d; k++)
           {
             // Multiply the two 1D functions together to get the 2D function
             psi[i * npres_1d * npres_1d + j * npres_1d + k] =
               psi3[i] * psi2[j] * psi1[k];
           }
         }
       }
     }
   }

References i, int(), j, k, s, and sqrt().

◆ pshape_nst() [4/6]

template<unsigned DIM>

void oomph::PRefineableQCrouzeixRaviartElement< DIM >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi,
		Shape &	test
	)		const

inlinevirtual

Pressure shape and test functions at local coordinte s.

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

◆ pshape_nst() [5/6]

void oomph::PRefineableQCrouzeixRaviartElement< 2 >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi,
		Shape &	test
	)		const

inlinevirtual

Define the pressure shape and test functions.

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

   {
     // Call the pressure shape functions
     pshape_nst(s, psi);
  
     // Loop over the test functions and set them equal to the shape functions
     if (this->npres_nst() == 1)
     {
       test[0] = psi[0];
     }
     else
     {
       for (unsigned i = 0; i < this->npres_nst(); i++) test[i] = psi[i];
     }
   }

References i, and s.

◆ pshape_nst() [6/6]

void oomph::PRefineableQCrouzeixRaviartElement< 3 >::pshape_nst	(	const Vector< double > &	s,
		Shape &	psi,
		Shape &	test
	)		const

inlinevirtual

Define the pressure shape and test functions.

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

   {
     // Call the pressure shape functions
     pshape_nst(s, psi);
  
     // Loop over the test functions and set them equal to the shape functions
     if (this->npres_nst() == 1)
     {
       test[0] = psi[0];
     }
     else
     {
       for (unsigned i = 0; i < this->npres_nst(); i++) test[i] = psi[i];
     }
   }

References i, and s.

◆ rebuild_from_sons()

template<unsigned DIM>

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

inlinevirtual

Rebuild from sons: Reconstruct pressure from the (merged) sons This must be specialised for each dimension.

Implements oomph::RefineableElement.

     {
       // Do p-refineable version
       PRefineableQElement<DIM, 3>::rebuild_from_sons(mesh_pt);
       // Do Crouzeix-Raviart version
       // Need to reconstruct pressure manually!
       for (unsigned p = 0; p < npres_nst(); p++)
       {
         // BENFLAG: Set to zero for now -- don't do projection problem yet
         this->internal_data_pt(this->P_nst_internal_index)->set_value(p, 0.0);
       }
     }

References oomph::GeneralisedElement::internal_data_pt(), oomph::PRefineableQCrouzeixRaviartElement< DIM >::npres_nst(), p, oomph::QCrouzeixRaviartElement< DIM >::P_nst_internal_index, and oomph::Data::set_value().

◆ required_nvalue()

template<unsigned DIM>

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

inlinevirtual

Number of values (pinned or dofs) required at local node n.

Number of values (pinned or dofs) required at node n.

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

     {
       return DIM;
     }

References DIM.

◆ unpin_elemental_pressure_dofs()

template<unsigned DIM>

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

inlineprivatevirtual

Unpin all internal pressure dofs.

Implements oomph::RefineableNavierStokesEquations< DIM >.

     {
       unsigned n_pres = this->npres_nst();
       n_pres = this->internal_data_pt(this->P_nst_internal_index)->nvalue();
       // loop over pressure dofs and unpin them
       for (unsigned l = 0; l < n_pres; l++)
       {
         this->internal_data_pt(this->P_nst_internal_index)->unpin(l);
       }
     }

References oomph::GeneralisedElement::internal_data_pt(), oomph::PRefineableQCrouzeixRaviartElement< DIM >::npres_nst(), oomph::Data::nvalue(), oomph::QCrouzeixRaviartElement< DIM >::P_nst_internal_index, and oomph::Data::unpin().

◆ vertex_node_pt()

template<unsigned DIM>

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

inlinevirtual

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

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return QCrouzeixRaviartElement<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::PRefineableQCrouzeixRaviartElement< DIM >

Constructor & Destructor Documentation

◆ PRefineableQCrouzeixRaviartElement() [1/2]

◆ ~PRefineableQCrouzeixRaviartElement()

◆ PRefineableQCrouzeixRaviartElement() [2/2]

Member Function Documentation

◆ dshape_and_dtest_eulerian_at_knot_nst() [1/3]

◆ dshape_and_dtest_eulerian_at_knot_nst() [2/3]

◆ dshape_and_dtest_eulerian_at_knot_nst() [3/3]

◆ dshape_and_dtest_eulerian_nst() [1/3]

◆ dshape_and_dtest_eulerian_nst() [2/3]

◆ dshape_and_dtest_eulerian_nst() [3/3]

◆ fix_pressure()

◆ further_build() [1/3]

◆ further_build() [2/3]

◆ further_build() [3/3]

◆ further_setup_hanging_nodes()

◆ get_interpolated_values() [1/2]

◆ get_interpolated_values() [2/2]

◆ ncont_interpolated_values()

◆ npres_nst()

◆ nrecovery_order()

◆ nvertex_node()

◆ p_nst() [1/2]

◆ p_nst() [2/2]

◆ pshape_nst() [1/6]

◆ pshape_nst() [2/6]

◆ pshape_nst() [3/6]

◆ pshape_nst() [4/6]

◆ pshape_nst() [5/6]

◆ pshape_nst() [6/6]

◆ rebuild_from_sons()

◆ required_nvalue()

◆ unpin_elemental_pressure_dofs()

◆ vertex_node_pt()

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