#include <refineable_spherical_advection_diffusion_elements.h>

Inheritance diagram for oomph::RefineableSphericalAdvectionDiffusionEquations:

Public Member Functions
	RefineableSphericalAdvectionDiffusionEquations ()
	Empty Constructor. More...

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

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

unsigned	num_Z2_flux_terms ()
	Number of 'flux' terms for Z2 error estimation. More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)

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

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

void	further_build ()
	Further build: Copy source function pointer from father element. More...

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

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

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

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

virtual unsigned	u_index_spherical_adv_diff () const

double	du_dt_spherical_adv_diff (const unsigned &n) const

void	disable_ALE ()

void	output (std::ostream &outfile)
	Output with default number of plot points. More...

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

void	output (FILE *file_pt)
	C_style output with default number of plot points. More...

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

void	output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output exact soln: r,z,u_exact at nplot^2 plot points. More...

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Get error against and norm of exact solution. More...

SphericalAdvectionDiffusionSourceFctPt &	source_fct_pt ()
	Access function: Pointer to source function. More...

SphericalAdvectionDiffusionSourceFctPt	source_fct_pt () const
	Access function: Pointer to source function. Const version. More...

SphericalAdvectionDiffusionWindFctPt &	wind_fct_pt ()
	Access function: Pointer to wind function. More...

SphericalAdvectionDiffusionWindFctPt	wind_fct_pt () const
	Access function: Pointer to wind function. Const version. More...

const double &	pe () const
	Peclet number. More...

double *&	pe_pt ()
	Pointer to Peclet number. More...

const double &	pe_st () const
	Peclet number multiplied by Strouhal number. More...

double *&	pe_st_pt ()
	Pointer to Peclet number multipled by Strouha number. More...

virtual void	get_source_spherical_adv_diff (const unsigned &ipt, const Vector< double > &x, double &source) const

virtual void	get_wind_spherical_adv_diff (const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &wind) const

void	get_flux (const Vector< double > &s, Vector< double > &flux) const

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Add the element's contribution to its residual vector (wrapper) More...

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

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

double	interpolated_u_spherical_adv_diff (const Vector< double > &s) const
	Return FE representation of function value u(s) at local coordinate s. More...

unsigned	self_test ()
	Self-test: Return 0 for OK. More...

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

double	size () const

virtual double	compute_physical_size () const

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, 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::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	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 Member Functions inherited from oomph::RefineableElement
	RefineableElement ()

virtual	~RefineableElement ()
	Destructor, delete the allocated storage for the hanging equations. More...

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

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

Tree *	tree_pt ()
	Access function: Pointer to quadtree representation of this element. More...

void	set_tree_pt (Tree *my_tree_pt)
	Set pointer to quadtree representation of this element. More...

virtual unsigned	required_nsons () const

bool	refinement_is_enabled ()
	Flag to indicate suppression of any refinement. More...

void	disable_refinement ()
	Suppress of any refinement for this element. More...

void	enable_refinement ()
	Emnable refinement for this element. More...

template<class ELEMENT >
void	split (Vector< ELEMENT * > &son_pt) const

int	local_hang_eqn (Node *const &node_pt, const unsigned &i)

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

void	set_refinement_level (const int &refine_level)
	Set the refinement level. More...

unsigned	refinement_level () const
	Return the Refinement level. More...

void	select_for_refinement ()
	Select the element for refinement. More...

void	deselect_for_refinement ()
	Deselect the element for refinement. More...

void	select_sons_for_unrefinement ()
	Unrefinement will be performed by merging the four sons of this element. More...

void	deselect_sons_for_unrefinement ()

bool	to_be_refined ()
	Has the element been selected for refinement? More...

bool	sons_to_be_unrefined ()
	Has the element been selected for unrefinement? More...

virtual void	rebuild_from_sons (Mesh *&mesh_pt)=0

virtual void	unbuild ()

virtual void	deactivate_element ()

virtual bool	nodes_built ()
	Return true if all the nodes have been built, false if not. More...

long	number () const
	Element number (for debugging/plotting) More...

void	set_number (const long &mynumber)
	Set element number (for debugging/plotting) More...

virtual unsigned	ncont_interpolated_values () const =0

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

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

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

virtual unsigned	ninterpolating_node (const int &value_id)

virtual unsigned	ninterpolating_node_1d (const int &value_id)

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

virtual void	check_integrity (double &max_error)=0

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

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

virtual RefineableElement *	root_element_pt ()

virtual RefineableElement *	father_element_pt () const
	Return a pointer to the father element. More...

void	get_father_at_refinement_level (unsigned &refinement_level, RefineableElement *&father_at_reflevel_pt)

virtual void	initial_setup (Tree *const &adopted_father_pt=0, const unsigned &initial_p_order=0)

virtual void	pre_build (Mesh &mesh_pt, Vector< Node > &new_node_pt)
	Pre-build the element. More...

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

virtual void	further_setup_hanging_nodes ()

void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

unsigned	nshape_controlling_nodes ()

std::map< Node *, unsigned >	shape_controlling_node_lookup ()

Public Member Functions inherited from oomph::ElementWithZ2ErrorEstimator
	ElementWithZ2ErrorEstimator ()
	Default empty constructor. More...

	ElementWithZ2ErrorEstimator (const ElementWithZ2ErrorEstimator &)=delete
	Broken copy constructor. More...

void	operator= (const ElementWithZ2ErrorEstimator &)=delete
	Broken assignment operator. More...

virtual unsigned	ncompound_fluxes ()

virtual void	compute_exact_Z2_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_flux_pt, double &error, double &norm)

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)

virtual unsigned	nvertex_node () const =0
	Number of vertex nodes in the element. More...

virtual Node *	vertex_node_pt (const unsigned &j) const =0

virtual unsigned	nrecovery_order ()=0
	Order of recovery shape functions. More...

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

Protected Member Functions inherited from oomph::SphericalAdvectionDiffusionEquations
virtual double	dshape_and_dtest_eulerian_spherical_adv_diff (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

virtual double	dshape_and_dtest_eulerian_at_knot_spherical_adv_diff (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

Protected Member Functions inherited from oomph::FiniteElement
template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

virtual void	fill_in_contribution_to_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::RefineableElement
void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const

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

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

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

void	assign_hanging_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for hanging node variables. More...

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

Additional Inherited Members
Public Types inherited from oomph::SphericalAdvectionDiffusionEquations
typedef void(*	SphericalAdvectionDiffusionSourceFctPt) (const Vector< double > &x, double &f)

typedef void(*	SphericalAdvectionDiffusionWindFctPt) (const Vector< double > &x, Vector< double > &wind)

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

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

Static Public Member Functions inherited from oomph::RefineableElement
static double &	max_integrity_tolerance ()
	Max. allowed discrepancy in element integrity check. More...

Static Public Attributes inherited from oomph::FiniteElement
static double	Tolerance_for_singular_jacobian = 1.0e-16
	Tolerance below which the jacobian is considered singular. More...

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_repeated_internal_data

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

Static Protected Member Functions inherited from oomph::RefineableElement
static void	check_value_id (const int &n_continuously_interpolated_values, const int &value_id)

Protected Attributes inherited from oomph::SphericalAdvectionDiffusionEquations
double *	Pe_pt
	Pointer to global Peclet number. More...

double *	PeSt_pt
	Pointer to global Peclet number multiplied by Strouhal number. More...

SphericalAdvectionDiffusionSourceFctPt	Source_fct_pt
	Pointer to source function: More...

SphericalAdvectionDiffusionWindFctPt	Wind_fct_pt
	Pointer to wind function: More...

Protected Attributes inherited from oomph::FiniteElement
MacroElement *	Macro_elem_pt
	Pointer to the element's macro element (NULL by default) More...

Protected Attributes inherited from oomph::GeomObject
unsigned	NLagrangian
	Number of Lagrangian (intrinsic) coordinates. More...

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Protected Attributes inherited from oomph::RefineableElement
Tree *	Tree_pt
	A pointer to a general tree object. More...

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

bool	Refinement_is_enabled
	Flag to indicate suppression of any refinement. More...

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

long	Number
	Global element number – for plotting/validation purposes. More...

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default value for the number of values at a node. More...

static const double	Node_location_tolerance = 1.0e-14

static const unsigned	N2deriv [] = {0, 1, 3, 6}

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix

static std::deque< double * >	Dof_pt_deque

Static Protected Attributes inherited from oomph::RefineableElement
static double	Max_integrity_tolerance = 1.0e-8
	Max. allowed discrepancy in element integrity check. More...

Detailed Description

A version of the Advection Diffusion in spherical coordinates equations that can be used with non-uniform mesh refinement. In essence, the class overloads the fill_in_generic_residual_contribution_spherical_adv_diff() function so that contributions from hanging nodes (or alternatively in-compatible function values) are taken into account.

Constructor & Destructor Documentation

◆ RefineableSphericalAdvectionDiffusionEquations() [1/2]

oomph::RefineableSphericalAdvectionDiffusionEquations::RefineableSphericalAdvectionDiffusionEquations ( )

inline

Empty Constructor.

       : SphericalAdvectionDiffusionEquations(),
         RefineableElement(),
         ElementWithZ2ErrorEstimator()
     {
     }

◆ RefineableSphericalAdvectionDiffusionEquations() [2/2]

oomph::RefineableSphericalAdvectionDiffusionEquations::RefineableSphericalAdvectionDiffusionEquations ( const RefineableSphericalAdvectionDiffusionEquations & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ dinterpolated_u_adv_diff_ddata()

void oomph::RefineableSphericalAdvectionDiffusionEquations::dinterpolated_u_adv_diff_ddata	(	const Vector< double > &	s,
		Vector< double > &	du_ddata,
		Vector< unsigned > &	global_eqn_number
	)

inlinevirtual

Compute the derivatives of the i-th component of velocity at point s with respect to all data that can affect its value. In addition, return the global equation numbers corresponding to the data. Overload the non-refineable version to take account of hanging node information

Reimplemented from oomph::SphericalAdvectionDiffusionEquations.

     {
       // Find number of nodes
       unsigned n_node = this->nnode();
       // Local shape function
       Shape psi(n_node);
       // Find values of shape function at the given local coordinate
       this->shape(s, psi);
  
       // Find the index at which the velocity component is stored
       const unsigned u_nodal_index = this->u_index_spherical_adv_diff();
  
       // Storage for hang info pointer
       HangInfo* hang_info_pt = 0;
       // Storage for global equation
       int global_eqn = 0;
  
       // Find the number of dofs associated with interpolated u
       unsigned n_u_dof = 0;
       for (unsigned l = 0; l < n_node; l++)
       {
         unsigned n_master = 1;
  
         // Local bool (is the node hanging)
         bool is_node_hanging = this->node_pt(l)->is_hanging();
  
         // If the node is hanging, get the number of master nodes
         if (is_node_hanging)
         {
           hang_info_pt = this->node_pt(l)->hanging_pt();
           n_master = hang_info_pt->nmaster();
         }
         // Otherwise there is just one master node, the node itself
         else
         {
           n_master = 1;
         }
  
         // Loop over the master nodes
         for (unsigned m = 0; m < n_master; m++)
         {
           // Get the equation number
           if (is_node_hanging)
           {
             // Get the equation number from the master node
             global_eqn =
               hang_info_pt->master_node_pt(m)->eqn_number(u_nodal_index);
           }
           else
           {
             // Global equation number
             global_eqn = this->node_pt(l)->eqn_number(u_nodal_index);
           }
  
           // If it's positive add to the count
           if (global_eqn >= 0)
           {
             ++n_u_dof;
           }
         }
       }
  
       // Now resize the storage schemes
       du_ddata.resize(n_u_dof, 0.0);
       global_eqn_number.resize(n_u_dof, 0);
  
       // Loop over th nodes again and set the derivatives
       unsigned count = 0;
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         unsigned n_master = 1;
         double hang_weight = 1.0;
  
         // Local bool (is the node hanging)
         bool is_node_hanging = this->node_pt(l)->is_hanging();
  
         // If the node is hanging, get the number of master nodes
         if (is_node_hanging)
         {
           hang_info_pt = this->node_pt(l)->hanging_pt();
           n_master = hang_info_pt->nmaster();
         }
         // Otherwise there is just one master node, the node itself
         else
         {
           n_master = 1;
         }
  
         // Loop over the master nodes
         for (unsigned m = 0; m < n_master; m++)
         {
           // If the node is hanging get weight from master node
           if (is_node_hanging)
           {
             // Get the hang weight from the master node
             hang_weight = hang_info_pt->master_weight(m);
           }
           else
           {
             // Node contributes with full weight
             hang_weight = 1.0;
           }
  
           // Get the equation number
           if (is_node_hanging)
           {
             // Get the equation number from the master node
             global_eqn =
               hang_info_pt->master_node_pt(m)->eqn_number(u_nodal_index);
           }
           else
           {
             // Global equation number
             global_eqn = this->node_pt(l)->eqn_number(u_nodal_index);
           }
  
           if (global_eqn >= 0)
           {
             // Set the global equation number
             global_eqn_number[count] = global_eqn;
             // Set the derivative with respect to the unknown
             du_ddata[count] = psi[l] * hang_weight;
             // Increase the counter
             ++count;
           }
         }
       }
     }

References oomph::Data::eqn_number(), oomph::Node::hanging_pt(), oomph::Node::is_hanging(), m, oomph::HangInfo::master_node_pt(), oomph::HangInfo::master_weight(), oomph::HangInfo::nmaster(), oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), oomph::FiniteElement::shape(), and oomph::SphericalAdvectionDiffusionEquations::u_index_spherical_adv_diff().

◆ fill_in_generic_residual_contribution_spherical_adv_diff()

void oomph::RefineableSphericalAdvectionDiffusionEquations::fill_in_generic_residual_contribution_spherical_adv_diff	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	mass_matrix,
		unsigned	flag
	)

protectedvirtual

Add the element's contribution to the elemental residual vector and/or Jacobian matrix flag=1: compute both flag=0: compute only residual vector

Add the element's contribution to the elemental residual vector and/or elemental jacobian matrix. This function overloads the standard version so that the possible presence of hanging nodes is taken into account.

Reimplemented from oomph::SphericalAdvectionDiffusionEquations.

   {
     // Find out how many nodes there are in the element
     const unsigned n_node = nnode();
  
     // Get the nodal index at which the unknown is stored
     const unsigned u_nodal_index = this->u_index_spherical_adv_diff();
  
     // Set up memory for the shape and test functions
     Shape psi(n_node), test(n_node);
     DShape dpsidx(n_node, 2), dtestdx(n_node, 2);
  
     // Set the value of n_intpt
     const unsigned n_intpt = integral_pt()->nweight();
  
     // Set the Vector to hold local coordinates
     Vector<double> s(2);
  
     // Get Peclet number
     const double scaled_peclet = this->pe();
  
     // Get the Peclet number multiplied by the Strouhal number
     const double scaled_peclet_st = this->pe_st();
  
     // Integers used to store the local equation number and local unknown
     // indices for the residuals and jacobians
     int local_eqn = 0, local_unknown = 0;
  
     // Local storage for pointers to hang_info objects
     HangInfo *hang_info_pt = 0, *hang_info2_pt = 0;
  
     // Local variable to determine the ALE stuff
     // bool ALE_is_disabled_flag = this->ALE_is_disabled;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < 2; i++) s[i] = integral_pt()->knot(ipt, i);
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Call the derivatives of the shape and test functions
       double J = this->dshape_and_dtest_eulerian_at_knot_spherical_adv_diff(
         ipt, psi, dpsidx, test, dtestdx);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Calculate local values of the function, initialise to zero
       double dudt = 0.0;
       double interpolated_u = 0.0;
  
       // These need to be a Vector to be ANSI C++, initialise to zero
       Vector<double> interpolated_x(2, 0.0);
       Vector<double> interpolated_dudx(2, 0.0);
       // Vector<double> mesh_velocity(DIM,0.0);
  
       // Calculate function value and derivatives:
       //-----------------------------------------
  
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the value at the node
         double u_value = this->nodal_value(l, u_nodal_index);
         interpolated_u += u_value * psi(l);
         dudt += this->du_dt_spherical_adv_diff(l) * psi(l);
         // Loop over directions
         for (unsigned j = 0; j < 2; j++)
         {
           interpolated_x[j] += nodal_position(l, j) * psi(l);
           interpolated_dudx[j] += u_value * dpsidx(l, j);
         }
       }
  
       // Get the mesh velocity, if required
       /* if (!ALE_is_disabled_flag)
          {
          for(unsigned l=0;l<n_node;l++)
          {
          // Loop over directions
          for(unsigned j=0;j<2;j++)
          {
          mesh_velocity[j] += dnodal_position_dt(l,j)*psi(l);
          }
          }
          }*/
  
  
       // Get body force
       double source;
       this->get_source_spherical_adv_diff(ipt, interpolated_x, source);
  
  
       // Get wind
       //--------
       Vector<double> wind(3);
       this->get_wind_spherical_adv_diff(ipt, s, interpolated_x, wind);
  
       // r is the first position component
       double r = interpolated_x[0];
       // theta is the second position component
       double sin_th = sin(interpolated_x[1]);
       // dS is the area weighting
       double dS = r * r * sin_th;
  
  
       // Assemble residuals and Jacobian
       //================================
  
       // Loop over the nodes for the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Local variables to store the number of master nodes and
         // the weight associated with the shape function if the node is hanging
         unsigned n_master = 1;
         double hang_weight = 1.0;
         // Local bool (is the node hanging)
         bool is_node_hanging = this->node_pt(l)->is_hanging();
  
         // If the node is hanging, get the number of master nodes
         if (is_node_hanging)
         {
           hang_info_pt = this->node_pt(l)->hanging_pt();
           n_master = hang_info_pt->nmaster();
         }
         // Otherwise there is just one master node, the node itself
         else
         {
           n_master = 1;
         }
  
         // Loop over the number of master nodes
         for (unsigned m = 0; m < n_master; m++)
         {
           // Get the local equation number and hang_weight
           // If the node is hanging
           if (is_node_hanging)
           {
             // Read out the local equation from the master node
             local_eqn = this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                              u_nodal_index);
             // Read out the weight from the master node
             hang_weight = hang_info_pt->master_weight(m);
           }
           // If the node is not hanging
           else
           {
             // The local equation number comes from the node itself
             local_eqn = this->nodal_local_eqn(l, u_nodal_index);
             // The hang weight is one
             hang_weight = 1.0;
           }
  
           // If the nodal equation is not a boundary conditino
           if (local_eqn >= 0)
           {
             // Add du/dt and body force/source term here
             residuals[local_eqn] -= (scaled_peclet_st * dudt + source) * dS *
                                     test(l) * W * hang_weight;
  
             // The Advection Diffusion bit itself
             residuals[local_eqn] -=
               // radial terms
               (dS * interpolated_dudx[0] *
                  (scaled_peclet * wind[0] * test(l) + dtestdx(l, 0)) +
                // azimuthal terms
                (sin_th * interpolated_dudx[1] *
                 (r * scaled_peclet * wind[1] * test(l) + dtestdx(l, 1)))) *
               W * hang_weight;
  
             // Calculate the Jacobian
             if (flag)
             {
               // Local variables to store the number of master nodes
               // and the weights associated with each hanging node
               unsigned n_master2 = 1;
               double hang_weight2 = 1.0;
               // Loop over the nodes for the variables
               for (unsigned l2 = 0; l2 < n_node; l2++)
               {
                 // Local bool (is the node hanging)
                 bool is_node2_hanging = this->node_pt(l2)->is_hanging();
                 // If the node is hanging, get the number of master nodes
                 if (is_node2_hanging)
                 {
                   hang_info2_pt = this->node_pt(l2)->hanging_pt();
                   n_master2 = hang_info2_pt->nmaster();
                 }
                 // Otherwise there is one master node, the node itself
                 else
                 {
                   n_master2 = 1;
                 }
  
                 // Loop over the master nodes
                 for (unsigned m2 = 0; m2 < n_master2; m2++)
                 {
                   // Get the local unknown and weight
                   // If the node is hanging
                   if (is_node2_hanging)
                   {
                     // Read out the local unknown from the master node
                     local_unknown = this->local_hang_eqn(
                       hang_info2_pt->master_node_pt(m2), u_nodal_index);
                     // Read out the hanging weight from the master node
                     hang_weight2 = hang_info2_pt->master_weight(m2);
                   }
                   // If the node is not hanging
                   else
                   {
                     // The local unknown number comes from the node
                     local_unknown = this->nodal_local_eqn(l2, u_nodal_index);
                     // The hang weight is one
                     hang_weight2 = 1.0;
                   }
  
                   // If the unknown is not pinned
                   if (local_unknown >= 0)
                   {
                     // Add contribution to Elemental Matrix
                     // Mass matrix du/dt term
                     jacobian(local_eqn, local_unknown) -=
                       scaled_peclet_st * test(l) * psi(l2) *
                       this->node_pt(l2)->time_stepper_pt()->weight(1, 0) * dS *
                       W * hang_weight * hang_weight2;
  
                     // Add contribution to mass matrix
                     if (flag == 2)
                     {
                       mass_matrix(local_eqn, local_unknown) +=
                         scaled_peclet_st * test(l) * psi(l2) * dS * W *
                         hang_weight * hang_weight2;
                     }
  
                     // Add contribution to Elemental Matrix
                     // Assemble Jacobian term
                     jacobian(local_eqn, local_unknown) -=
                       // radial terms
                       (dS * dpsidx(l2, 0) *
                          (scaled_peclet * wind[0] * test(l) + dtestdx(l, 0)) +
                        // azimuthal terms
                        (sin_th * dpsidx(l2, 1) *
                         (r * scaled_peclet * wind[1] * test(l) +
                          dtestdx(l, 1)))) *
                       W * hang_weight * hang_weight2;
                   }
                 } // End of loop over master nodes
               } // End of loop over nodes
             } // End of Jacobian calculation
  
           } // End of non-zero equation
  
         } // End of loop over the master nodes for residual
       } // End of loop over nodes
  
     } // End of loop over integration points
   }

References oomph::SphericalAdvectionDiffusionEquations::dshape_and_dtest_eulerian_at_knot_spherical_adv_diff(), oomph::SphericalAdvectionDiffusionEquations::du_dt_spherical_adv_diff(), oomph::SphericalAdvectionDiffusionEquations::get_source_spherical_adv_diff(), oomph::SphericalAdvectionDiffusionEquations::get_wind_spherical_adv_diff(), oomph::Node::hanging_pt(), i, oomph::FiniteElement::integral_pt(), oomph::FiniteElement::interpolated_x(), oomph::Node::is_hanging(), J, j, oomph::Integral::knot(), oomph::RefineableElement::local_hang_eqn(), m, m2(), oomph::HangInfo::master_node_pt(), oomph::HangInfo::master_weight(), oomph::HangInfo::nmaster(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::nodal_value(), oomph::FiniteElement::node_pt(), oomph::Integral::nweight(), oomph::SphericalAdvectionDiffusionEquations::pe(), oomph::SphericalAdvectionDiffusionEquations::pe_st(), UniformPSDSelfTest::r, s, sin(), TestProblem::source(), Eigen::test, oomph::Data::time_stepper_pt(), oomph::SphericalAdvectionDiffusionEquations::u_index_spherical_adv_diff(), w, oomph::QuadTreeNames::W, oomph::Integral::weight(), and oomph::TimeStepper::weight().

◆ further_build()

void oomph::RefineableSphericalAdvectionDiffusionEquations::further_build ( )

inlinevirtual

Further build: Copy source function pointer from father element.

Reimplemented from oomph::RefineableElement.

     {
       RefineableSphericalAdvectionDiffusionEquations* cast_father_element_pt =
         dynamic_cast<RefineableSphericalAdvectionDiffusionEquations*>(
           this->father_element_pt());
  
       // Set the values of the pointers from the father
       this->Source_fct_pt = cast_father_element_pt->source_fct_pt();
       this->Wind_fct_pt = cast_father_element_pt->wind_fct_pt();
       this->Pe_pt = cast_father_element_pt->pe_pt();
       this->PeSt_pt = cast_father_element_pt->pe_st_pt();
  
       // Set the ALE status
       // this->ALE_is_disabled = cast_father_element_pt->ALE_is_disabled;
     }

References oomph::RefineableElement::father_element_pt(), oomph::SphericalAdvectionDiffusionEquations::pe_pt(), oomph::SphericalAdvectionDiffusionEquations::Pe_pt, oomph::SphericalAdvectionDiffusionEquations::pe_st_pt(), oomph::SphericalAdvectionDiffusionEquations::PeSt_pt, oomph::SphericalAdvectionDiffusionEquations::source_fct_pt(), oomph::SphericalAdvectionDiffusionEquations::Source_fct_pt, oomph::SphericalAdvectionDiffusionEquations::wind_fct_pt(), and oomph::SphericalAdvectionDiffusionEquations::Wind_fct_pt.

Referenced by oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::further_build().

◆ geometric_jacobian()

double oomph::RefineableSphericalAdvectionDiffusionEquations::geometric_jacobian ( const Vector< double > & x )

inlinevirtual

Fill in the geometric Jacobian, which in this case is r*r*sin(theta)

Reimplemented from oomph::ElementWithZ2ErrorEstimator.

     {
       return x[0] * x[0] * sin(x[1]);
     }

References sin(), and plotDoE::x.

◆ get_interpolated_values() [1/2]

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

inlinevirtual

Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here.

Implements oomph::RefineableElement.

     {
       // Set size of Vector: u
       values.resize(1);
  
       // Find number of nodes
       const unsigned n_node = nnode();
  
       // Find the index at which the unknown is stored
       const unsigned u_nodal_index = this->u_index_spherical_adv_diff();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape(s, psi);
  
       // Initialise value of u
       values[0] = 0.0;
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         values[0] += this->nodal_value(t, l, u_nodal_index) * psi[l];
       }
       // }
  
       if (t != 0)
       {
         std::string error_message =
           "Time-dependent version of get_interpolated_values() ";
         error_message += "not implemented for this element \n";
         throw OomphLibError(error_message,
                             "RefineableSphericalAdvectionDiffusionEquations::"
                             "get_interpolated_values()",
                             OOMPH_EXCEPTION_LOCATION);
       }
       else
       {
         // Make sure that we call the appropriate steady version
         //(the entire function might be overloaded lower down)
         RefineableSphericalAdvectionDiffusionEquations::get_interpolated_values(
           s, values);
       }
     }

References get_interpolated_values(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), OOMPH_EXCEPTION_LOCATION, s, oomph::FiniteElement::shape(), oomph::Global_string_for_annotation::string(), plotPSD::t, and oomph::SphericalAdvectionDiffusionEquations::u_index_spherical_adv_diff().

◆ get_interpolated_values() [2/2]

void oomph::RefineableSphericalAdvectionDiffusionEquations::get_interpolated_values	(	const Vector< double > &	s,
		Vector< double > &	values
	)

inlinevirtual

Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here.

Reimplemented from oomph::RefineableElement.

     {
       // Set size of Vector: u
       values.resize(1);
  
       // Find number of nodes
       unsigned n_node = nnode();
  
       // Find the index at which the unknown is stored
       unsigned u_nodal_index = this->u_index_spherical_adv_diff();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape(s, psi);
  
       // Initialise value of u
       values[0] = 0.0;
  
       // Loop over the local nodes and sum
       for (unsigned l = 0; l < n_node; l++)
       {
         values[0] += this->nodal_value(l, u_nodal_index) * psi[l];
       }
     }

References oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and oomph::SphericalAdvectionDiffusionEquations::u_index_spherical_adv_diff().

Referenced by get_interpolated_values(), and oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::get_interpolated_values().

◆ get_Z2_flux()

void oomph::RefineableSphericalAdvectionDiffusionEquations::get_Z2_flux	(	const Vector< double > &	s,
		Vector< double > &	flux
	)

inlinevirtual

Get 'flux' for Z2 error recovery: Standard flux.from AdvectionDiffusion equations

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       this->get_flux(s, flux);
     }

References ProblemParameters::flux(), and oomph::SphericalAdvectionDiffusionEquations::get_flux().

Referenced by oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::get_Z2_flux().

◆ num_Z2_flux_terms()

unsigned oomph::RefineableSphericalAdvectionDiffusionEquations::num_Z2_flux_terms ( )

inlinevirtual

Number of 'flux' terms for Z2 error estimation.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       return 2;
     }

Referenced by oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::get_Z2_compound_flux_indices(), and oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::get_Z2_flux().

◆ operator=()

void oomph::RefineableSphericalAdvectionDiffusionEquations::operator= ( const RefineableSphericalAdvectionDiffusionEquations & )

delete

Broken assignment operator.

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

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RefineableSphericalAdvectionDiffusionEquations() [1/2]

◆ RefineableSphericalAdvectionDiffusionEquations() [2/2]

Member Function Documentation

◆ dinterpolated_u_adv_diff_ddata()

◆ fill_in_generic_residual_contribution_spherical_adv_diff()

◆ further_build()

◆ geometric_jacobian()

◆ get_interpolated_values() [1/2]

◆ get_interpolated_values() [2/2]

◆ get_Z2_flux()

◆ num_Z2_flux_terms()

◆ operator=()