Inheritance diagram for oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >:

Public Member Functions
	SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement (FiniteElement *const &element_pt, const int &face_index)

double	beta ()
	Return the Elasticity number. More...

double	peclet_s ()
	Return the surface peclect number. More...

double	peclet_strouhal_s ()
	Return the surface peclect strouhal number. More...

double *&	beta_pt ()
	Access function for pointer to the Elasticity number. More...

double *&	peclet_s_pt ()
	Access function for pointer to the surface Peclet number. More...

double *&	peclet_strouhal_s_pt ()
	Access function for pointer to the surface Peclet x Strouhal number. More...

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

double	integrate_c () const
	Compute the concentration intergated over the area. More...

Public Member Functions inherited from oomph::SpineAxisymmetricFluidInterfaceElement< ELEMENT >
	SpineAxisymmetricFluidInterfaceElement (FiniteElement *const &element_pt, const int &face_index)

Public Member Functions inherited from oomph::SpineUpdateFluidInterfaceElement< FluidInterfaceElement, AxisymmetricDerivatives, ELEMENT >
	SpineUpdateFluidInterfaceElement (FiniteElement *const &element_pt, const int &face_index, const unsigned &id=0)

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the contribution to the residuals and the jacobian. More...

void	add_additional_residual_contributions_interface (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag, const Shape &psif, const DShape &dpsifds, const DShape &dpsifdS, const DShape &dpsifdS_div, const Vector< double > &s, const Vector< double > &interpolated_x, const Vector< double > &interpolated_n, const double &W, const double &J)
	Helper function to calculate the additional contributions These are those filled in by the particular equations. More...

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

void	output (std::ostream &outfile, const unsigned &n_plot)
	Output the element. More...

void	output (FILE *file_pt)
	Overload the C-style output function. More...

void	output (FILE *file_pt, const unsigned &n_plot)
	C-style Output function. More...

virtual FluidInterfaceBoundingElement *	make_bounding_element (const int &face_index)

Public Member Functions inherited from oomph::Hijacked< SpineElement< FaceGeometry< ELEMENT > > >
	Hijacked ()
	Constructor, call the constructors of the base elements. More...

	Hijacked (FiniteElement *const &element_pt, const int &face_index)
	Constructor used for hijacking face elements. More...

	Hijacked (FiniteElement *const &element_pt, const int &face_index, const unsigned &id=0)

Data *	hijack_internal_value (const unsigned &n, const unsigned &i, const bool &return_data=true)

Data *	hijack_external_value (const unsigned &n, const unsigned &i, const bool &return_data=true)

Data *	hijack_nodal_value (const unsigned &n, const unsigned &i, const bool &return_data=true)

Data *	hijack_nodal_position_value (const unsigned &n, const unsigned &i, const bool &return_data=true)

Data *	hijack_nodal_spine_value (const unsigned &n, const unsigned &i, const bool &return_data=true)

void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

void	get_residuals (Vector< double > &residuals)

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

Public Member Functions inherited from oomph::SpineElement< FaceGeometry< ELEMENT > >
	SpineElement ()
	Constructor, call the constructor of the base element. More...

	SpineElement (FiniteElement *const &element_pt, const int &face_index)
	Constructor used for spine face elements. More...

	~SpineElement ()
	Destructor, clean up the storage allocated to the local equation numbers. More...

int	spine_local_eqn (const unsigned &n)

Public Member Functions inherited from oomph::ElementWithSpecificMovingNodes< ELEMENT, NODE_TYPE >
void	describe_local_dofs (std::ostream &out, const std::string &current_string) const

	ElementWithSpecificMovingNodes ()
	Constructor, call the constructor of the base element. More...

	ElementWithSpecificMovingNodes (FiniteElement *const &element_pt, const int &face_index)
	Constructor used for face elements. More...

	~ElementWithSpecificMovingNodes ()
	Empty Destructor,. More...

void	describe_local_dofs (std::ostream &out, std::string &curr_str)
	Unique final overrider for describe_dofs. More...

Node *	construct_node (const unsigned &n)

Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Overloaded node allocation for unsteady problems. More...

Node *	construct_boundary_node (const unsigned &n)
	Overload the node assignment routine to assign boundary nodes. More...

Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Overloaded boundary node allocation for unsteady problems. More...

void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Compute the element's residuals vector and jacobian matrix. More...

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

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

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

virtual	~ElementWithMovingNodes ()
	Virtual destructor (clean up and allocated memory) More...

unsigned	ngeom_dof () const
	Number of geometric dofs. More...

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

void	assemble_set_of_all_geometric_data (std::set< Data * > &unique_geom_data_pt)
	Return a set of all geometric data associated with the element. More...

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

bool	are_dresidual_dnodal_coordinates_always_evaluated_by_fd () const
	Return whether shape derivatives are evaluated by fd. More...

void	enable_always_evaluate_dresidual_dnodal_coordinates_by_fd ()

void	disable_always_evaluate_dresidual_dnodal_coordinates_by_fd ()

void	evaluate_shape_derivs_by_direct_fd ()
	Evaluate shape derivatives by direct finite differencing. More...

void	evaluate_shape_derivs_by_chain_rule (const bool &i_know_what_i_am_doing=false)

void	evaluate_shape_derivs_by_fastest_method (const bool &i_know_what_i_am_doing=false)

int &	method_for_shape_derivs ()
	Access to method (enumerated flag) for determination of shape derivs. More...

void	enable_bypass_fill_in_jacobian_from_geometric_data ()
	Bypass the call to fill_in_jacobian_from_geometric_data. More...

void	disable_bypass_fill_in_jacobian_from_geometric_data ()
	Do not bypass the call to fill_in_jacobian_from_geometric_data. More...

bool	is_fill_in_jacobian_from_geometric_data_bypassed () const

unsigned	ngeom_data () const

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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_nodal_local_dofs (std::ostream &out, const std::string &current_string) const

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	self_test ()

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

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

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	get_mass_matrix (Vector< double > &residuals, 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 Member Functions inherited from oomph::SpineFiniteElement
	SpineFiniteElement ()
	Empty constructor. More...

virtual	~SpineFiniteElement ()
	Emtpty virtual destructor. More...

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

virtual	~HijackedElementBase ()
	Destructor, destroy the storage for the equation numbers. More...

void	unhijack_all_data ()

const double &	residual_multiplier () const
	Return the value of the residual multiplier. More...

double *&	residual_multiplier_pt ()
	Return the pointer to the residual multiplier. More...

Public Member Functions inherited from oomph::FluidInterfaceElement
	FluidInterfaceElement ()
	Constructor, set the default values of the booleans and pointers (null) More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Calculate the residuals by calling the generic residual contribution. More...

const double &	ca () const
	The value of the Capillary number. More...

double *&	ca_pt ()
	Pointer to the Capillary number. More...

const double &	st () const
	The value of the Strouhal number. More...

double *&	st_pt ()
	The pointer to the Strouhal number. More...

double	u (const unsigned &j, const unsigned &i)
	Return the i-th velocity component at local node j. More...

double	interpolated_u (const Vector< double > &s, const unsigned &i)
	Calculate the i-th velocity component at the local coordinate s. More...

double	pext () const
	Return the value of the external pressure. More...

void	set_external_pressure_data (Data *external_pressure_data_pt)

void	set_external_pressure_data (Data *external_pressure_data_pt, const unsigned &index_of_external_pressure_value)

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

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::AxisymmetricDerivatives
	AxisymmetricDerivatives ()

Protected Member Functions
double	interpolated_C (const Vector< double > &s)
	Get the surfactant concentration. More...

double	dcdt_surface (const unsigned &l) const
	The time derivative of the surface concentration. More...

double	sigma (const Vector< double > &s)

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

void	add_additional_residual_contributions_interface (Vector< double > &residuals, DenseMatrix< double > &jacobian, const unsigned &flag, const Shape &psif, const DShape &dpsifds, const DShape &dpsifdS, const DShape &dpsifdS_div, const Vector< double > &s, const Vector< double > &interpolated_x, const Vector< double > &interpolated_n, const double &W, const double &J)

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

Protected Member Functions inherited from oomph::SpineUpdateFluidInterfaceElement< FluidInterfaceElement, AxisymmetricDerivatives, ELEMENT >
double	compute_surface_derivatives (const Shape &psi, const DShape &dpsids, const DenseMatrix< double > &interpolated_t, const Vector< double > &interpolated_x, DShape &surface_gradient, DShape &surface_divergence)

Protected Member Functions inherited from oomph::ElementWithMovingNodes
virtual void	get_dnodal_coordinates_dgeom_dofs (RankThreeTensor< double > &dnodal_coordinates_dgeom_dofs)

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

void	fill_in_jacobian_from_geometric_data (DenseMatrix< double > &jacobian)

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_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)

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

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

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

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

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

Protected Member Functions inherited from oomph::HijackedElementBase
void	hijack_global_eqn (long *const &global_eqn_pt)

void	unhijack_global_eqn (long *const &global_eqn_pt)

Protected Member Functions inherited from oomph::FluidInterfaceElement
int	pext_local_eqn ()

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

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::AxisymmetricDerivatives
double	compute_surface_derivatives (const Shape &psi, const DShape &dpsids, const DenseMatrix< double > &interpolated_t, const Vector< double > &interpolated_x, DShape &surface_gradient, DShape &surface_divergence)
	Fill in the specific surface derivative calculations. More...

Private Attributes
double *	Beta_pt
	Pointer to an Elasticity number. More...

double *	Peclet_S_pt
	Pointer to Surface Peclet number. More...

double *	Peclet_Strouhal_S_pt
	Pointer to the surface Peclect Strouhal number. More...

unsigned	C_index

Static Private Attributes
static double	Default_Physical_Constant_Value = 1.0
	Default value of the physical constants. More...

Additional Inherited Members
Public Types inherited from oomph::ElementWithMovingNodes
enum	{ Shape_derivs_by_chain_rule , Shape_derivs_by_direct_fd , Shape_derivs_by_fastest_method }
	Public enumeration to choose method for computing shape derivatives. More...

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

Protected Attributes inherited from oomph::ElementWithMovingNodes
Vector< Data * >	Geom_data_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

Protected Attributes inherited from oomph::HijackedElementBase
std::set< long * > *	Hijacked_global_eqn_number_pt

Vector< int > *	Hijacked_local_eqn_number_pt

double *	Residual_multiplier_pt

Protected Attributes inherited from oomph::FluidInterfaceElement
Vector< unsigned >	U_index_interface
	Nodal index at which the i-th velocity component is stored. More...

int	External_data_number_of_external_pressure

Data *	Pext_data_pt
	Pointer to the Data item that stores the external pressure. More...

unsigned	Index_of_external_pressure_value
	Which of the values in Pext_data_pt stores the external pressure. 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

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::HijackedElementBase
static double	Default_residual_multiplier = 0.0

Detailed Description

template<class ELEMENT>
class oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >

Spine-based Marangoni surface tension elements that add a linear dependence on concentration of a surface chemical to the surface tension, which decreases with increasing concentration. The non-dimensionalisation is the same as Campana et al (2004) but we may wish to revisit this.

Constructor & Destructor Documentation

◆ SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement()

template<class ELEMENT >

oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement	(	FiniteElement *const &	element_pt,
		const int &	face_index
	)

inline

Constructor that passes the bulk element and face index down to the underlying

                                                                                                                      : SpineAxisymmetricFluidInterfaceElement<ELEMENT>
                                                                (element_pt,face_index)
   {
    //Initialise the values
    Beta_pt = &Default_Physical_Constant_Value;
    Peclet_S_pt = &Default_Physical_Constant_Value;
    Peclet_Strouhal_S_pt = &Default_Physical_Constant_Value;
  
    //Add the additional surfactant terms to these surface elements
    
    //Read out the number of nodes on the face
    //For some reason I need to specify the this pointer here(!)
    unsigned n_node_face = this->nnode();
    //Set the additional data values in the face
    //There is one additional values at each node --- the lagrange multiplier
    Vector<unsigned> additional_data_values(n_node_face);
    for(unsigned i=0;i<n_node_face;i++) additional_data_values[i] = 1;
    //Resize the data arrays accordingly 
    this->resize_nodes(additional_data_values);
  
    //The C_index is the new final value
    //Minor HACK HERE
    C_index = this->node_pt(0)->nvalue()-1;
 }

References oomph::MultiDomainBoussinesqHelper::Default_Physical_Constant_Value, and i.

Member Function Documentation

◆ add_additional_residual_contributions_interface()

template<class ELEMENT >

void oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::add_additional_residual_contributions_interface	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		const unsigned &	flag,
		const Shape &	psif,
		const DShape &	dpsifds,
		const DShape &	dpsifdS,
		const DShape &	dpsifdS_div,
		const Vector< double > &	s,
		const Vector< double > &	interpolated_x,
		const Vector< double > &	interpolated_n,
		const double &	W,
		const double &	J
	)

inlineprotectedvirtual

Overload the Helper function to calculate the residuals and jacobian entries. This particular function ensures that the additional entries are calculated inside the integration loop

Reimplemented from oomph::FluidInterfaceElement.

   {
    //Flag to control whether the Campana formulation (false) 
    // or our own (true) is used
    bool Integrated_curvature = true;
    
   //Find out how many nodes there are
    unsigned n_node = this->nnode();
    
    //Storage for the local equation numbers and unknowns
    int local_eqn = 0, local_unknown = 0;
    
    //Surface advection-diffusion equation
    
    //Find the index at which the concentration is stored
    unsigned c_index = this->C_index;
    Vector<unsigned> u_index = this->U_index_interface;
  
    //Read out the surface peclect number
    const double Pe_s = this->peclet_s();
    //const double PeSt_s = this->peclet_strouhal_s();
    
    //Read out the radial position
    const double r = interpolated_x[0];
  
    //Rescale the jacobian to be the "raw" version
    const double J_raw = J/r;
    
    //Now calculate the concentration at this point
    //Assuming the same shape functions are used (which they are)
    double interpolated_C = 0.0;
    double interpolated_dCds = 0.0;
    double dCdt = 0.0;
    //The tangent vector
    const unsigned ndim = this->node_pt(0)->ndim();
    Vector<double> interpolated_tangent(ndim,0.0);
    Vector<double> interpolated_u(ndim,0.0);
    Vector<double> mesh_velocity(ndim,0.0);
    Vector<double> interpolated_duds(ndim,0.0);
    if(ndim+1 != u_index.size())
     {
       throw OomphLibError("Dimension Incompatibility",
               OOMPH_CURRENT_FUNCTION,
               OOMPH_EXCEPTION_LOCATION);
     }
    
    for(unsigned l=0;l<n_node;l++)
      {
        const double psi = psif(l);
        const double dpsi = dpsifds(l,0);
        interpolated_C += this->nodal_value(l,c_index)*psi;
        interpolated_dCds += this->nodal_value(l,c_index)*dpsi;
        dCdt += dcdt_surface(l)*psi;
        for(unsigned i=0;i<ndim;i++)
         {
          interpolated_tangent[i] += this->nodal_position(l,i)*dpsi;
          interpolated_u[i] += this->nodal_value(l,u_index[i])*psi;
          interpolated_duds[i] += this->nodal_value(l,u_index[i])*dpsi;
         }
        //Mesh Velocity
        for(unsigned j=0;j<ndim;j++)
         {
          mesh_velocity[j] += this->dnodal_position_dt(l,j)*psi;
         }
      }
    
    
    double u_tangent = 0.0, t_length = 0.0;
    for(unsigned i=0;i<ndim;i++) 
      {
        u_tangent += interpolated_u[i]*interpolated_tangent[i];
        t_length  += interpolated_tangent[i]*interpolated_tangent[i];
      }
  
    //Work out the second derivative of position
    Vector<double> d2xds(2,0.0);
    for(unsigned i=0;i<2;i++)
     {
      d2xds[i] = this->nodal_position(0,i) + 
       this->nodal_position(2,i) - 2.0*this->nodal_position(1,i);
     }
    
    //Let's do the first component of the curvature
    double k1 = 0.0;
    for(unsigned i=0;i<2;i++)
     {
      k1 += (d2xds[i]/(J_raw*J_raw) - interpolated_tangent[i]*(
              interpolated_tangent[0]*d2xds[0] 
              + interpolated_tangent[1]*d2xds[1])/(J_raw*J_raw*J_raw*J_raw))*interpolated_n[i];
     }
    
    //Second component of the curvature
    double k2 = - (interpolated_n[0] / r);
    
    //Now we add the flux term to the appropriate residuals
    for(unsigned l=0;l<n_node;l++)
     {
      //Read out the apprporiate local equation
      local_eqn = this->nodal_local_eqn(l,c_index);
      
      //If not a boundary condition
      if(local_eqn >= 0)
       {
        //Time derivative
        residuals[local_eqn] += dCdt*psif(l)*r*W*J_raw;
  
        double tmp = 0.0;
        //Compute our version in which second derivatives are not required
        if(Integrated_curvature)
         {
          for(unsigned i=0;i<2;i++)
           {
            tmp += 
             (interpolated_u[i] - mesh_velocity[i])*interpolated_tangent[i];
           }
          //First Advection term
          residuals[local_eqn] += tmp*interpolated_dCds*psif(l)*r*W/J_raw;
          //Additional term from axisymmetric formulation
          residuals[local_eqn] += interpolated_C*interpolated_u[0]*psif(l)*W*J_raw;
          //Second Advection term
          residuals[local_eqn] += interpolated_C*
           (interpolated_duds[0]*interpolated_tangent[0]
            + interpolated_duds[1]*interpolated_tangent[1])*r*W*psif(l)/J_raw;
           }
        //This is the Campana formulation
        else
         {
          //ALE term
          for(unsigned i=0;i<2;i++)
           {
            tmp += -mesh_velocity[i]*interpolated_tangent[i];
           }
          residuals[local_eqn] += tmp*interpolated_dCds*psif(l)*r*W/J_raw;
          // Curvature (normal velocity) term
          residuals[local_eqn] -= 
           interpolated_C*(k1 + k2)*psif(l)*r*W*J_raw*(
            interpolated_u[0]*interpolated_n[0]
            + interpolated_u[1]*interpolated_n[1]);
          //Integrated by parts tangential advection term
          residuals[local_eqn] -= interpolated_C*(
           interpolated_tangent[0]*interpolated_u[0] + 
           interpolated_tangent[1]*interpolated_u[1])*dpsifds(l,0)*r*W/J_raw;
         }
        
        //Diffusion term
        residuals[local_eqn] += (1.0/Pe_s)*interpolated_dCds*dpsifds(l,0)*r*W/J_raw;
        
        //We also need to worry about the jacobian terms
        if(flag)
         {
          //Loop over the nodes again
          for(unsigned l2=0;l2<n_node;l2++)
           {
            //Get the time stepper
            TimeStepper* time_stepper_pt=this->node_pt(l2)->time_stepper_pt();
            
            //Get the unknown c_index
            local_unknown =this->nodal_local_eqn(l2,c_index);
            
            if(local_unknown >=0)
             {
              jacobian(local_eqn,local_unknown) += 
               time_stepper_pt->weight(1,0)*psif(l2)*psif(l)*r*W*J_raw;
              
              if(Integrated_curvature)
               {
                jacobian(local_eqn,local_unknown) += ((interpolated_u[0] - mesh_velocity[0])*interpolated_tangent[0]
                                                      + (interpolated_u[1] - mesh_velocity[1])*interpolated_tangent[1])*dpsifds(l2,0)
                 *psif(l)*r*W/J_raw;
  
  
                jacobian(local_eqn,local_unknown) += psif(l2)*interpolated_u[0]*psif(l)*W*J_raw;
                
                jacobian(local_eqn,local_unknown) += psif(l2)*(interpolated_tangent[0]*interpolated_duds[0]
                                                               + interpolated_tangent[1]*interpolated_duds[1])*psif(l)*r*W/J_raw;
               }
              else
               {
                jacobian(local_eqn,local_unknown) -=
                 (mesh_velocity[0]*interpolated_tangent[0] + mesh_velocity[1]*interpolated_tangent[1])*dpsifds(l2,0)*psif(l)*r*W/J_raw;
                
                jacobian(local_eqn,local_unknown) -= psif(l2)*(k1 + k2)*psif(l)*r*W*J_raw*(interpolated_u[0]*interpolated_n[0]
                                                                                       + interpolated_u[1]*interpolated_n[1]);
                
                jacobian(local_eqn,local_unknown) -= psif(l2)*(interpolated_tangent[0]*interpolated_u[0] + interpolated_tangent[1]*
                                                               interpolated_u[1])*dpsifds(l,0)*r*W/J_raw;
               }
              
              jacobian(local_eqn,local_unknown) += (1.0/Pe_s)*dpsifds(l2,0)*dpsifds(l,0)*r*W/J_raw;
              
             }
  
  
            //Loop over the velocity components
            for(unsigned i2=0;i2<ndim;i2++)
             {
              
              //Get the unknown
              local_unknown = this->nodal_local_eqn(l2,u_index[i2]);
              
              
              //If not a boundary condition
              if(local_unknown >= 0)
               {
                
                // jacobian(local_eqn,local_unknown) += time_stepper_pt->weight(1,0)*psif(l2)*PeSt_s*psif(l)*r*W*J_raw;
                if(Integrated_curvature)
                 {
                  jacobian(local_eqn,local_unknown) += 
                   interpolated_dCds*psif(l2)*interpolated_tangent[i2]*psif(l)*r*W/J_raw;
  
                  if(i2==0)
                   {
                    jacobian(local_eqn,local_unknown) += interpolated_C*psif(l2)*W*J_raw;
                   }
                 }
                else
                 {
                  jacobian(local_eqn,local_unknown) -= interpolated_C*(k1 + k2)*psif(l)*r*W*J_raw*psif(l2)*interpolated_n[i2];
                  
                  jacobian(local_eqn,local_unknown) -=  interpolated_C*interpolated_tangent[i2]*psif(l2)*dpsifds(l,0)*r*W/J_raw;
                 }
                
                jacobian(local_eqn,local_unknown) += 
                 interpolated_C*interpolated_tangent[i2]*dpsifds(l2,0)*psif(l)*r*W/J_raw;
               }
             }
           }
         }
       }
     } //End of loop over the nodes
    
   }  

References i, J, j, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, oomph::Global_Physical_Variables::Pe_s, UniformPSDSelfTest::r, tmp, oomph::QuadTreeNames::W, and oomph::TimeStepper::weight().

◆ beta()

template<class ELEMENT >

double oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::beta ( )

inline

Return the Elasticity number.

558 {return *Beta_pt;}

◆ beta_pt()

template<class ELEMENT >

double* & oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::beta_pt ( )

inline

Access function for pointer to the Elasticity number.

567 {return Beta_pt;}

Referenced by InterfaceProblem< ELEMENT, TIMESTEPPER >::InterfaceProblem().

◆ dcdt_surface()

template<class ELEMENT >

double oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::dcdt_surface ( const unsigned & l ) const

inlineprotected

The time derivative of the surface concentration.

   {
    // Get the data's timestepper
     TimeStepper* time_stepper_pt= this->node_pt(l)->time_stepper_pt();
    
    //Initialise dudt
     double dcdt=0.0;
    //Loop over the timesteps, if there is a non Steady timestepper
     if (time_stepper_pt->type()!="Steady")
     {
      //Find the index at which the variable is stored
      const unsigned c_index = C_index;
  
      // Number of timsteps (past & present)
      const unsigned n_time = time_stepper_pt->ntstorage();
      
      for(unsigned t=0;t<n_time;t++)
       {
        dcdt += time_stepper_pt->weight(1,t)*this->nodal_value(t,l,c_index);
       }
     }
    return dcdt;
   }

References oomph::TimeStepper::ntstorage(), plotPSD::t, oomph::TimeStepper::type(), and oomph::TimeStepper::weight().

◆ fill_in_contribution_to_jacobian()

template<class ELEMENT >

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

inlineprotectedvirtual

Fill in the contribution to the residuals Calculate the contribution to the jacobian

Reimplemented from oomph::GeneralisedElement.

   {
    //Call the generic routine with the flag set to 1
     this->fill_in_generic_residual_contribution_interface(residuals,jacobian,1);
     {
     //Use finite differences to handle concentration variations in the
     //bulk equations
     const unsigned n_node = this->nnode();
     //Find the number of dofs in the element
     const unsigned n_dof = this->ndof();
     //Create newres vector
     Vector<double> newres(n_dof);
     
     //Integer storage for local unknown
     int local_unknown=0;
     
     //Use the default finite difference step
     const double fd_step = this->Default_fd_jacobian_step;
     
     //Loop over the nodes again
     for(unsigned n=0;n<n_node;n++)
      {
       //Get the number of values stored at the node
       unsigned c_index = this->C_index;
       
       //Get the local equation number
       local_unknown = this->nodal_local_eqn(n,c_index);
       //If it's not pinned
       if(local_unknown >= 0)
        {
         //Store a pointer to the nodal data value
         double *value_pt = this->node_pt(n)->value_pt(c_index);
         
         //Save the old value of the Nodal data
         double old_var = *value_pt;
         
         //Increment the value of the Nodal data
         *value_pt += fd_step;
         
         //Calculate the new residuals
         this->get_residuals(newres);
         
         //Do finite differences
         for(unsigned m=0;m<n_dof;m++)
          {
           double sum = (newres[m] - residuals[m])/fd_step;
           //Stick the entry into the Jacobian matrix
           jacobian(m,local_unknown) = sum;
          }
         
         //Reset the Nodal data
         *value_pt = old_var;
        }
      }
     }
  
    //Call the generic routine to handle the spine variables
     SpineElement<FaceGeometry<ELEMENT> >::fill_in_jacobian_from_geometric_data(jacobian);
   }

References GlobalFct::get_residuals(), m, and n.

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

template<class ELEMENT >

void oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::fill_in_contribution_to_jacobian_and_mass_matrix	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	mass_matrix
	)

inlineprotectedvirtual

Add the element's contribution to its residuals vector, jacobian matrix and mass matrix

Reimplemented from oomph::GeneralisedElement.

   {
     //Add the contribution to the jacobian
     this->fill_in_contribution_to_jacobian(residuals,jacobian);
     //No mass matrix terms, but should probably do kinematic bit here
   }

References oomph::fill_in_contribution_to_jacobian().

◆ integrate_c()

template<class ELEMENT >

double oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::integrate_c ( ) const

inline

Compute the concentration intergated over the area.

   {
    //Find out how many nodes there are
    unsigned n_node = this->nnode();
    
    //Set up memeory for the shape functions
    Shape psif(n_node);
    DShape dpsifds(n_node,1);
  
    //Set the value of n_intpt
    unsigned n_intpt = this->integral_pt()->nweight();
    
    //Storage for the local coordinate
    Vector<double> s(1);
  
    //Storage for the total mass
    double mass = 0.0;
    
    //Loop over the integration points
    for(unsigned ipt=0;ipt<n_intpt;ipt++)
     {
      //Get the local coordinate at the integration point
      s[0] = this->integral_pt()->knot(ipt,0);
      
      //Get the integral weight
      double W = this->integral_pt()->weight(ipt);
      
      //Call the derivatives of the shape function
      this->dshape_local_at_knot(ipt,psif,dpsifds);
      
      //Define and zero the tangent Vectors and local velocities
      Vector<double> interpolated_x(2,0.0);
      Vector<double> interpolated_t(2,0.0);
      double interpolated_c = 0.0;
      
      
      //Loop over the shape functions to compute concentration and tangent
      for(unsigned l=0;l<n_node;l++)
       {
        interpolated_c += this->nodal_value(l,C_index)*psif(l);
        //Calculate the tangent vector
        for(unsigned i=0;i<2;i++)
         {
          interpolated_x[i] += this->nodal_position(l,i)*psif(l);
          interpolated_t[i] += this->nodal_position(l,i)*dpsifds(l,0);
         }
       }
      
      //The first positional coordinate is the radial coordinate
      double r = interpolated_x[0];
  
    //Calculate the length of the tangent Vector
    double tlength = interpolated_t[0]*interpolated_t[0] + 
     interpolated_t[1]*interpolated_t[1];
    
    //Set the Jacobian of the line element
    double J = sqrt(tlength);
  
    mass += interpolated_c*r*W*J;
     }
    return mass;
   }

References i, J, UniformPSDSelfTest::r, s, sqrt(), and oomph::QuadTreeNames::W.

Referenced by InterfaceProblem< ELEMENT, TIMESTEPPER >::compute_total_mass().

◆ interpolated_C()

template<class ELEMENT >

double oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::interpolated_C ( const Vector< double > & s )

inlineprotected

Get the surfactant concentration.

   {
      //Find number of nodes
    unsigned n_node = this->nnode();
  
    //Get the nodal index at which the unknown is stored
    const unsigned c_index = C_index;
  
    //Local shape function
    Shape psi(n_node);
  
    //Find values of shape function
    this->shape(s,psi);
  
    //Initialise value of C
    double C = 0.0;
  
    //Loop over the local nodes and sum
    for(unsigned l=0;l<n_node;l++) 
      {
        C += this->nodal_value(l,c_index)*psi(l);
      }
  
    return(C);
   }

References oomph::OneDimLagrange::shape().

◆ output()

template<class ELEMENT >

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

inlinevirtual

Output the element data — pass (some measure of) the number of plot points per element

Reimplemented from oomph::FiniteElement.

   {
    outfile.precision(16);
    
    //Set output Vector
    Vector<double> s(1);
    
    //Tecplot header info 
    outfile << "ZONE I=" << n_plot << std::endl;
    
    const unsigned n_node = this->nnode();
    const unsigned dim = this->dim();
    
    Shape psi(n_node);
    DShape dpsi(n_node,dim);
    
    //Loop over plot points
    for(unsigned l=0;l<n_plot;l++)
     {
     s[0] = -1.0 + l*2.0/(n_plot-1);
         
         this->dshape_local(s,psi,dpsi);
         Vector<double> interpolated_tangent(2,0.0);
         for(unsigned l=0;l<n_node;l++)
          {
           const double dpsi_ = dpsi(l,0);
           for(unsigned i=0;i<2;i++)
            {
             interpolated_tangent[i] += this->nodal_position(l,i)*dpsi_;
            }
          }
  
         //Tangent
         double t_vel = (this->interpolated_u(s,0)*interpolated_tangent[0] + this->interpolated_u(s,1)*interpolated_tangent[1])/
          sqrt(interpolated_tangent[0]*interpolated_tangent[0] + interpolated_tangent[1]*interpolated_tangent[1]);
  
         
         //Output the x,y,u,v 
     for(unsigned i=0;i<2;i++) outfile << this->interpolated_x(s,i) << " ";
     for(unsigned i=0;i<2;i++) outfile << this->interpolated_u(s,i) << " ";      
         //Output a dummy pressure
     outfile << 0.0 << " ";
         //Output the concentration
     outfile << interpolated_C(s) << " ";
         //Output the interfacial tension
         outfile << sigma(s) << " " << t_vel << std::endl;
       }
  outfile << std::endl;
   }

References i, s, calibrate::sigma, and sqrt().

◆ peclet_s()

template<class ELEMENT >

double oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::peclet_s ( )

inline

Return the surface peclect number.

561 {return *Peclet_S_pt;}

◆ peclet_s_pt()

template<class ELEMENT >

double* & oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::peclet_s_pt ( )

inline

Access function for pointer to the surface Peclet number.

570 {return Peclet_S_pt;}

Referenced by InterfaceProblem< ELEMENT, TIMESTEPPER >::InterfaceProblem().

◆ peclet_strouhal_s()

template<class ELEMENT >

double oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::peclet_strouhal_s ( )

inline

Return the surface peclect strouhal number.

564 {return *Peclet_Strouhal_S_pt;}

◆ peclet_strouhal_s_pt()

template<class ELEMENT >

double* & oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::peclet_strouhal_s_pt ( )

inline

Access function for pointer to the surface Peclet x Strouhal number.

573 {return Peclet_Strouhal_S_pt;}

Referenced by InterfaceProblem< ELEMENT, TIMESTEPPER >::InterfaceProblem().

◆ sigma()

template<class ELEMENT >

double oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::sigma ( const Vector< double > & s )

inlineprotectedvirtual

The surface tension function is linear in the concentration with constant of proportionality equal to the elasticity number.

Reimplemented from oomph::FluidInterfaceElement.

   {
    //Find the number of shape functions
    const unsigned n_node = this->nnode();
    //Now get the shape fuctions at the local coordinate
    Shape psi(n_node);
    this->shape(s,psi);
    
    //Now interpolate the surfactant concentration
    double C=0.0;
    for(unsigned l=0;l<n_node;l++)
     {
      C += this->nodal_value(l,C_index)*psi(l);
     }
    
    //Get the Elasticity number
    double Beta = this->beta();
    //Return the variable surface tension
    return (1.0 - Beta*(C-1.0));
   } // End of sigma

References beta, Global::Beta, and oomph::OneDimLagrange::shape().

Member Data Documentation

◆ Beta_pt

template<class ELEMENT >

double* oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::Beta_pt

private

Pointer to an Elasticity number.

◆ C_index

template<class ELEMENT >

unsigned oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::C_index

private

Index at which the surfactant concentration is stored at the nodes

◆ Default_Physical_Constant_Value

template<class ELEMENT >

double oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::Default_Physical_Constant_Value = 1.0

staticprivate

Default value of the physical constants.

◆ Peclet_S_pt

template<class ELEMENT >

double* oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::Peclet_S_pt

private

Pointer to Surface Peclet number.

◆ Peclet_Strouhal_S_pt

template<class ELEMENT >

double* oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >::Peclet_Strouhal_S_pt

private

Pointer to the surface Peclect Strouhal number.

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

rayleigh_instability_insoluble_surfactant.cc

Public Member Functions

Protected Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

template<class ELEMENT> class oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >

Constructor & Destructor Documentation

◆ SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement()

Member Function Documentation

◆ add_additional_residual_contributions_interface()

◆ beta()

◆ beta_pt()

◆ dcdt_surface()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

◆ integrate_c()

◆ interpolated_C()

◆ output()

◆ peclet_s()

◆ peclet_s_pt()

◆ peclet_strouhal_s()

◆ peclet_strouhal_s_pt()

◆ sigma()

Member Data Documentation

◆ Beta_pt

◆ C_index

◆ Default_Physical_Constant_Value

◆ Peclet_S_pt

◆ Peclet_Strouhal_S_pt

template<class ELEMENT>
class oomph::SpineAxisymmetricMarangoniSurfactantFluidInterfaceElement< ELEMENT >