#include <mixed_order_petrov_galerkin_space_time_fluid_traction_elements.h>

Inheritance diagram for oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >:

Public Member Functions
	NavierStokesMixedOrderSpaceTimeTractionElement (FiniteElement *const &element_pt, const int &face_index, const bool &called_from_refineable_constructor=false)

	~NavierStokesMixedOrderSpaceTimeTractionElement ()
	Destructor should not delete anything. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	This function returns just the residuals. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	This function returns the residuals and the jacobian. More...

void	output (std::ostream &outfile)
	Overload the output function. More...

void	output (std::ostream &outfile, const unsigned &nplot)
	Output function: x,y,[z],u,v,[w],p in tecplot format. More...

Public Member Functions inherited from oomph::FaceElement
	FaceElement ()
	Constructor: Initialise all appropriate member data. More...

virtual	~FaceElement ()
	Empty virtual destructor. More...

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

const unsigned &	boundary_number_in_bulk_mesh () const
	Broken assignment operator. More...

void	set_boundary_number_in_bulk_mesh (const unsigned &b)
	Set function for the boundary number in bulk mesh. More...

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

double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

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

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

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

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

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

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

int &	normal_sign ()

int	normal_sign () const

int &	face_index ()

int	face_index () const

const Vector< double > *	tangent_direction_pt () const
	Public access function for the tangent direction pointer. More...

void	set_tangent_direction (Vector< double > *tangent_direction_pt)
	Set the tangent direction vector. More...

void	turn_on_warning_for_discontinuous_tangent ()

void	turn_off_warning_for_discontinuous_tangent ()

void	continuous_tangent_and_outer_unit_normal (const Vector< double > &s, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	continuous_tangent_and_outer_unit_normal (const unsigned &ipt, Vector< Vector< double >> &tang_vec, Vector< double > &unit_normal) const

void	outer_unit_normal (const Vector< double > &s, Vector< double > &unit_normal) const
	Compute outer unit normal at the specified local coordinate. More...

void	outer_unit_normal (const unsigned &ipt, Vector< double > &unit_normal) const
	Compute outer unit normal at ipt-th integration point. More...

FiniteElement *&	bulk_element_pt ()
	Pointer to higher-dimensional "bulk" element. More...

FiniteElement *	bulk_element_pt () const
	Pointer to higher-dimensional "bulk" element (const version) More...

CoordinateMappingFctPt &	face_to_bulk_coordinate_fct_pt ()

CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt () const

BulkCoordinateDerivativesFctPt &	bulk_coordinate_derivatives_fct_pt ()

BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt () const

Vector< double >	local_coordinate_in_bulk (const Vector< double > &s) const

void	get_local_coordinate_in_bulk (const Vector< double > &s, Vector< double > &s_bulk) const

void	get_ds_bulk_ds_face (const Vector< double > &s, DenseMatrix< double > &dsbulk_dsface, unsigned &interior_direction) const

unsigned &	bulk_position_type (const unsigned &i)

const unsigned &	bulk_position_type (const unsigned &i) const

void	bulk_node_number_resize (const unsigned &i)
	Resize the storage for the bulk node numbers. More...

unsigned &	bulk_node_number (const unsigned &n)

const unsigned &	bulk_node_number (const unsigned &n) const

void	bulk_position_type_resize (const unsigned &i)
	Resize the storage for bulk_position_type to i entries. More...

unsigned &	nbulk_value (const unsigned &n)

unsigned	nbulk_value (const unsigned &n) const

void	nbulk_value_resize (const unsigned &i)

void	resize_nodes (Vector< unsigned > &nadditional_data_values)

void	output_zeta (std::ostream &outfile, const unsigned &nplot)
	Output boundary coordinate zeta. 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

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const

double	d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const

virtual double	d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

Node *&	node_pt (const unsigned &n)
	Return a pointer to the local node n. More...

Node *const &	node_pt (const unsigned &n) const
	Return a pointer to the local node n (const version) More...

unsigned	nnode () const
	Return the number of nodes. More...

virtual unsigned	nnode_1d () const

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

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

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

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const

double	raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const

double	raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const

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

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

double	dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. More...

double	dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const

double	nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const

double	nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const

double	dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const

double	dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) 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 unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

virtual Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)

virtual Node *	construct_boundary_node (const unsigned &n)

virtual Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)

int	get_node_number (Node *const &node_pt) const

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) const

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

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

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

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

unsigned	dim () const

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

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)

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

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

virtual void	node_update ()

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

virtual void	identify_geometric_data (std::set< Data * > &geometric_data_pt)

virtual double	s_min () const
	Min value of local coordinate. More...

virtual double	s_max () const
	Max. value of local coordinate. More...

double	size () const

virtual double	compute_physical_size () const

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

void	point_output (std::ostream &outfile, const Vector< double > &s)

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

virtual void	write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const

virtual void	write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const

virtual void	write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

virtual void	output (FILE *file_pt)

virtual void	output (FILE *file_pt, const unsigned &n_plot)

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output an exact solution over the element. More...

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Calculate the norm of the error and that of the exact solution. More...

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

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

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

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

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

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

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

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

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

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

virtual unsigned	self_test ()

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

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

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

	GeomObject (const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)

	GeomObject (const GeomObject &dummy)=delete
	Broken copy constructor. More...

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

virtual	~GeomObject ()
	(Empty) destructor More...

unsigned	nlagrangian () const
	Access function to # of Lagrangian coordinates. More...

unsigned	ndim () const
	Access function to # of Eulerian coordinates. More...

void	set_nlagrangian_and_ndim (const unsigned &n_lagrangian, const unsigned &n_dim)
	Set # of Lagrangian and Eulerian coordinates. More...

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

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

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const

Public Attributes
void(*&)(const double &t, const Vector< double > &x, const Vector< double > &n, Vector< double > &result)	traction_fct_pt ()
	Access function for the imposed traction pointer. More...

Protected Member Functions
void	fill_in_generic_residual_contribution_fluid_traction (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag)

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

virtual int	u_local_eqn (const unsigned &n, const unsigned &i)

double	shape_and_test_at_knot (const unsigned &ipt, Shape &psi, Shape &test) const

void	get_traction (const double &time, const Vector< double > &x, const Vector< double > &n, Vector< double > &result)
	Function to calculate the traction applied to the fluid. More...

Protected Member Functions inherited from oomph::FaceElement
void	add_additional_values (const Vector< unsigned > &nadditional_values, const unsigned &id)

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

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

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

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

virtual double	invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

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

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

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

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const

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

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

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

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

void	transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

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

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

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

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

Protected Attributes
unsigned	Dim
	The highest dimension of the problem. More...

Protected Attributes inherited from oomph::FaceElement
unsigned	Boundary_number_in_bulk_mesh
	The boundary number in the bulk mesh to which this element is attached. More...

FiniteElement *	Bulk_element_pt
	Pointer to the associated higher-dimensional "bulk" element. More...

Vector< unsigned >	Bulk_node_number

Vector< unsigned >	Nbulk_value

Vector< double > *	Tangent_direction_pt

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

Private Attributes
void(*	Traction_fct_pt )(const double &time, const Vector< double > &x, const Vector< double > &n, Vector< double > &result)
	Pointer to an imposed traction function. More...

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

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

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

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

Detailed Description

template<class ELEMENT>
class oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >

A class for elements that allow the imposition of an applied traction to the Navier–Stokes equations The geometrical information can be read from the FaceGeometry<ELEMENT> class and and thus, we can be generic enough without the need to have a separate equations class

Constructor & Destructor Documentation

◆ NavierStokesMixedOrderSpaceTimeTractionElement()

template<class ELEMENT >

oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::NavierStokesMixedOrderSpaceTimeTractionElement	(	FiniteElement *const &	element_pt,
		const int &	face_index,
		const bool &	called_from_refineable_constructor = `false`
	)

inline

Constructor, which takes a "bulk" element and the value of the index and its limit

       : FaceGeometry<ELEMENT>(), FaceElement()
     {
       // Attach the geometrical information to the element. N.B. This function
       // also assigns nbulk_value from the required_nvalue of the bulk element
       element_pt->build_face_element(face_index, this);
  
 #ifdef PARANOID
       {
         // Check that the element is not a refineable 3D element
         if (!called_from_refineable_constructor)
         {
           // If it's 3D
           if (element_pt->dim() == 3)
           {
             // Is it refineable
             RefineableElement* ref_el_pt =
               dynamic_cast<RefineableElement*>(element_pt);
  
             // If the upcast was successful
             if (ref_el_pt != 0)
             {
               // If there are any hanging nodes
               if (this->has_hanging_nodes())
               {
                 // Create an output stream
                 std::ostringstream error_message_stream;
  
                 // Create an error message
                 error_message_stream
                   << "This flux element will not work correctly "
                   << "if nodes are hanging" << std::endl;
  
                 // Throw the error message
                 throw OomphLibError(error_message_stream.str(),
                                     OOMPH_CURRENT_FUNCTION,
                                     OOMPH_EXCEPTION_LOCATION);
               }
             } // if (ref_el_pt!=0)
           } // if (element_pt->dim()==3)
         } // if (!called_from_refineable_constructor)
       }
 #endif
  
       // Set the body force function pointer to zero
       Traction_fct_pt = 0;
  
       // Set the dimension from the dimension of the first node
       Dim = this->node_pt(0)->ndim();
     } // End of NavierStokesMixedOrderSpaceTimeTractionElement

References oomph::FiniteElement::build_face_element(), oomph::FiniteElement::dim(), oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::Dim, oomph::FaceElement::face_index(), oomph::FiniteElement::has_hanging_nodes(), oomph::Node::ndim(), oomph::FiniteElement::node_pt(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::Traction_fct_pt.

◆ ~NavierStokesMixedOrderSpaceTimeTractionElement()

template<class ELEMENT >

oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::~NavierStokesMixedOrderSpaceTimeTractionElement ( )

inline

Destructor should not delete anything.

121 {}

Member Function Documentation

◆ fill_in_contribution_to_jacobian()

template<class ELEMENT >

void oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::fill_in_contribution_to_jacobian	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inlinevirtual

This function returns the residuals and the jacobian.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::RefineableNavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >.

     {
       // Call the generic routine with the flag set to 1
       fill_in_generic_residual_contribution_fluid_traction(
         residuals, jacobian, 1);
     }

References oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::fill_in_generic_residual_contribution_fluid_traction().

◆ fill_in_contribution_to_residuals()

template<class ELEMENT >

void oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::fill_in_contribution_to_residuals ( Vector< double > & residuals )

inlinevirtual

This function returns just the residuals.

Reimplemented from oomph::GeneralisedElement.

Reimplemented in oomph::RefineableNavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >.

     {
       // Call the generic residuals function with flag set to 0
       // using a dummy matrix argument
       fill_in_generic_residual_contribution_fluid_traction(
         residuals, GeneralisedElement::Dummy_matrix, 0);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::fill_in_generic_residual_contribution_fluid_traction().

◆ fill_in_generic_residual_contribution_fluid_traction()

template<class ELEMENT >

void oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::fill_in_generic_residual_contribution_fluid_traction	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag
	)

protected

This function returns the residuals for the traction function. flag=1(or 0): do (or don't) compute the Jacobian as well.

//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////// Function that returns the residuals for the imposed traction Navier-Stokes equations

   {
     // Find out how many nodes there are
     unsigned n_node = nnode();
  
     // Set up memory for the shape functions
     Shape psif(n_node);
  
     // Set up memory for the test functions
     Shape testf(n_node);
  
     // Number of integration points
     unsigned n_intpt = integral_pt()->nweight();
  
     // Integers to store local equation numbers
     int local_eqn = 0;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Find the shape and test functions and return the Jacobian
       // of the mapping
       double J = shape_and_test_at_knot(ipt, psif, testf);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get continuous time
       double interpolated_t = 0.0;
  
       // Need to find position to feed into traction function
       Vector<double> interpolated_x(Dim - 1, 0.0);
  
       // Allocate space for the outer unit normal
       Vector<double> interpolated_spacetime_n(Dim, 0.0);
  
       // Allocate space for the outer unit normal (in the given time slice)
       Vector<double> interpolated_n(Dim - 1, 0.0);
  
       // Allocate space for the traction vector
       Vector<double> traction(Dim - 1, 0.0);
  
       // Calculate velocities and derivatives
       for (unsigned l = 0; l < n_node; l++)
       {
         // Update the interpolated time value
         interpolated_t += raw_nodal_position(l, Dim - 1) * psif(l);
  
         // Loop over velocity components
         for (unsigned i = 0; i < Dim - 1; i++)
         {
           // Update the i-th interpolated coordinate value
           interpolated_x[i] += nodal_position(l, i) * psif(l);
         }
       } // for (unsigned l=0;l<n_node;l++)
  
       // Calculate the outer unit normal
       outer_unit_normal(ipt, interpolated_spacetime_n);
  
 #ifdef PARANOID
       // Sanity check: Make sure the normal component in the time-direction is
       // zero. If it isn't then something has gone wrong...
       if (std::fabs(interpolated_spacetime_n[Dim - 1]) > 1.0e-15)
       {
         // Create an output stream
         std::ostringstream error_message_stream;
  
         // Create the error message
         error_message_stream
           << "The component of the outer unit normal in the "
           << "time-direction\nshould be zero but the actual "
           << "value is: " << interpolated_spacetime_n[Dim - 1] << std::endl;
  
         // Throw the error message
         throw OomphLibError(error_message_stream.str(),
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       // Loop over spatial coordinates
       for (unsigned i = 0; i < Dim - 1; i++)
       {
         // Copy the i-th normal component over
         interpolated_n[i] = interpolated_spacetime_n[i];
       }
  
       // Get the user-defined traction
       get_traction(interpolated_t, interpolated_x, interpolated_n, traction);
  
       // Now add to the appropriate equations:
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over the velocity components
         for (unsigned i = 0; i < Dim - 1; i++)
         {
           // Get the local equation number associated with this unknown and node
           local_eqn = u_local_eqn(l, i);
  
           // If it's not a boundary condition
           if (local_eqn >= 0)
           {
             // Add the user-defined traction terms
             residuals[local_eqn] += traction[i] * testf[l] * W;
  
             // Assuming the traction DOES NOT depend upon velocities
             // or pressures, the jacobian is always zero, so no jacobian
             // terms are required
           }
         } // for (unsigned i=0;i<Dim;i++)
       } // for (unsigned l=0;l<n_node;l++)
     } // for (unsigned ipt=0;ipt<n_intpt;ipt++)
   } // End of fill_in_generic_residual_contribution_fluid_traction

References Global_Variables::Dim, boost::multiprecision::fabs(), i, J, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, w, and oomph::QuadTreeNames::W.

Referenced by oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::fill_in_contribution_to_jacobian(), and oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::fill_in_contribution_to_residuals().

◆ get_traction()

template<class ELEMENT >

void oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::get_traction	(	const double &	time,
		const Vector< double > &	x,
		const Vector< double > &	n,
		Vector< double > &	result
	)

inlineprotected

Function to calculate the traction applied to the fluid.

     {
       // If the function pointer is zero return zero
       if (Traction_fct_pt == 0)
       {
         // Loop over the (spatial) dimensions
         for (unsigned i = 0; i < Dim - 1; i++)
         {
           // Set the i-th traction component to zero
           result[i] = 0.0;
         }
       }
       // If the traction function pointer has been set
       else
       {
         // Call the function pointer
         (*Traction_fct_pt)(time, x, n, result);
       } // if (Traction_fct_pt==0)
     } // End of get_traction

References oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::Dim, i, n, oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::Traction_fct_pt, and plotDoE::x.

◆ output() [1/2]

template<class ELEMENT >

void oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::output ( std::ostream & outfile )

inlinevirtual

Overload the output function.

Reimplemented from oomph::FiniteElement.

     {
       FiniteElement::output(outfile);
     }

References oomph::FiniteElement::output().

◆ output() [2/2]

template<class ELEMENT >

void oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

inlinevirtual

Output function: x,y,[z],u,v,[w],p in tecplot format.

Reimplemented from oomph::FiniteElement.

     {
       FiniteElement::output(outfile, nplot);
     }

References oomph::FiniteElement::output().

◆ shape_and_test_at_knot()

template<class ELEMENT >

double oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::shape_and_test_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		Shape &	test
	)		const

inlineprotected

Function to compute the shape and test functions and to return the Jacobian of mapping

     {
       // Number of nodes in each direction
       const unsigned nnode_1d = 3;
  
       // Find the dimension of the element
       const unsigned el_dim = dim();
  
       // Sanity check
       if (el_dim != 2)
       {
         // Throw an error
         throw OomphLibError(
           "Can only deal with 2D space-time traction elements!",
           OOMPH_CURRENT_FUNCTION,
           OOMPH_EXCEPTION_LOCATION);
       }
  
       // Storage for the local coordinates of the integration point
       Vector<double> s(el_dim);
  
       // Set the local coordinate
       for (unsigned i = 0; i < el_dim; i++)
       {
         // Get the i-th local coordinate associated with the ipt-th knot point
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       //--------------------------
       // Call the shape functions:
       //--------------------------
       //--------start_of_shape------------------------------------------------
       // Local storage
       double psi_values[2][nnode_1d];
  
       // Call the OneDimensional shape function (for x or y) with quadratic
       // interpolation
       OneDimLagrange::shape<3>(s[0], psi_values[0]);
  
       // Call the OneDimensional shape function. NOTE: The second local
       // coordinate will always be time for a space-time element!
       OneDimDiscontinuousGalerkinMixedOrderBasis::shape<3>(s[1], psi_values[1]);
  
       // Index for the shape functions
       unsigned index = 0;
  
       // Loop over the first local coordinate direction
       for (unsigned j = 0; j < nnode_1d; j++)
       {
         // Loop over the first local coordinate direction
         for (unsigned i = 0; i < nnode_1d; i++)
         {
           // Multiply the two 1D functions together to get the 2D function
           psi[index] = psi_values[0][i] * psi_values[1][j];
  
           // Increment the index
           index++;
         }
       } // for (unsigned j=0;j<nnode_1d;j++)
       //--------end_of_shape--------------------------------------------------
  
       //-------------------------
       // Call the test functions:
       //-------------------------
       //--------start_of_shape------------------------------------------------
       // Local storage
       double test_values[2][nnode_1d];
  
       // Call the OneDimensional shape function (for x or y) with quadratic
       // interpolation
       OneDimLagrange::shape<3>(s[0], test_values[0]);
  
       // Call the OneDimensional shape function. NOTE: The second local
       // coordinate will always be time for a space-time element!
       OneDimDiscontinuousGalerkinMixedOrderTest::shape<3>(s[1], test_values[1]);
  
       // Reset the value of index to loop over the test functions
       index = 0;
  
       // Loop over the first local coordinate direction
       for (unsigned j = 0; j < nnode_1d; j++)
       {
         // Loop over the first local coordinate direction
         for (unsigned i = 0; i < nnode_1d; i++)
         {
           // Multiply the two 1D functions together to get the 2D function
           test[index] = test_values[0][i] * test_values[1][j];
  
           // Increment the index
           index++;
         }
       } // for (unsigned j=0;j<nnode_1d;j++)
       //--------end_of_shape--------------------------------------------------
  
       // Return the value of the jacobian
       return J_eulerian_at_knot(ipt);
     } // End of shape_and_test_at_knot

References oomph::FiniteElement::dim(), el_dim, i, oomph::FiniteElement::integral_pt(), j, oomph::FaceElement::J_eulerian_at_knot(), oomph::Integral::knot(), oomph::FiniteElement::nnode_1d(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, s, oomph::OneDimLagrange::shape< 3 >(), oomph::OneDimDiscontinuousGalerkinMixedOrderBasis::shape< 3 >(), and oomph::OneDimDiscontinuousGalerkinMixedOrderTest::shape< 3 >().

◆ u_local_eqn()

template<class ELEMENT >

virtual int oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::u_local_eqn	(	const unsigned &	n,
		const unsigned &	i
	)

inlineprotectedvirtual

Access function that returns the local equation numbers for velocity components. u_local_eqn(n,i)=local equation number or < 0 if pinned. The default is to asssume that n is the local node number and the i-th velocity component is the i-th unknown stored at the node.

     {
       return nodal_local_eqn(n, i);
     }

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

◆ zeta_nodal()

template<class ELEMENT >

double oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::zeta_nodal	(	const unsigned &	n,
		const unsigned &	k,
		const unsigned &	i
	)		const

inlineprotectedvirtual

The "global" intrinsic coordinate of the element when viewed as part of a geometric object should be given by the FaceSpaceTimeElement representation, by default

Reimplemented from oomph::FaceElement.

     {
       return FaceElement::zeta_nodal(n, k, i);
     } // End of zeta_nodal

References i, k, n, and oomph::FaceElement::zeta_nodal().

Member Data Documentation

◆ Dim

template<class ELEMENT >

unsigned oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::Dim

protected

The highest dimension of the problem.

Referenced by oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::get_traction(), and oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::NavierStokesMixedOrderSpaceTimeTractionElement().

◆ traction_fct_pt

template<class ELEMENT >

void(*&)(const double& t, const Vector<double>& x, const Vector<double>& n, Vector<double>& result) oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::traction_fct_pt()

inline

Access function for the imposed traction pointer.

     {
       // Return the function pointer
       return Traction_fct_pt;
     } // End of traction_fct_pt

◆ Traction_fct_pt

template<class ELEMENT >

void(* oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::Traction_fct_pt) (const double &time, const Vector< double > &x, const Vector< double > &n, Vector< double > &result)

private

Pointer to an imposed traction function.

Referenced by oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::get_traction(), and oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >::NavierStokesMixedOrderSpaceTimeTractionElement().

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

mixed_order_petrov_galerkin_space_time_fluid_traction_elements.h

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Attributes

Additional Inherited Members

Detailed Description

template<class ELEMENT> class oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >

Constructor & Destructor Documentation

◆ NavierStokesMixedOrderSpaceTimeTractionElement()

◆ ~NavierStokesMixedOrderSpaceTimeTractionElement()

Member Function Documentation

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_fluid_traction()

◆ get_traction()

◆ output() [1/2]

◆ output() [2/2]

◆ shape_and_test_at_knot()

◆ u_local_eqn()

◆ zeta_nodal()

Member Data Documentation

◆ Dim

◆ traction_fct_pt

◆ Traction_fct_pt

template<class ELEMENT>
class oomph::NavierStokesMixedOrderSpaceTimeTractionElement< ELEMENT >