#include <spherical_buoyant_navier_stokes.h>

Inheritance diagram for oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement:

Public Member Functions
	RefineableBuoyantQSphericalCrouzeixRaviartElement ()

unsigned	required_nvalue (const unsigned &n) const

const double &	ra () const
	Access function for the Rayleigh number (const version) More...

double *&	ra_pt ()
	Access function for the pointer to the Rayleigh number. More...

void	disable_ALE ()
	Final override for disable ALE. More...

void	enable_ALE ()
	Final override for enable ALE. More...

void	output (std::ostream &outfile)
	Overload the standard output function with the broken default. More...

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

void	output (FILE *file_pt)
	C-style output function: Broken default. More...

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

void	output_fct (std::ostream &outfile, const unsigned &Nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output function for an exact solution: Broken default. More...

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

unsigned	u_index_spherical_adv_diff () const

unsigned	nvertex_node () const

Node *	vertex_node_pt (const unsigned &j) const

unsigned	ncont_interpolated_values () const

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

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

void	further_setup_hanging_nodes ()

void	rebuild_from_sons (Mesh *&mesh_pt)

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

void	further_build ()

unsigned	nrecovery_order ()
	The recovery order is that of the NavierStokes elements. More...

unsigned	num_Z2_flux_terms ()

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

unsigned	ncompound_fluxes ()

void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)

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

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

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

void	get_body_force_spherical_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &result)

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Fill in the constituent elements' contribution to the residual vector. More...

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

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

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

Public Member Functions inherited from oomph::RefineableQSphericalAdvectionDiffusionElement< 3 >
	RefineableQSphericalAdvectionDiffusionElement ()
	Empty Constructor: More...

	RefineableQSphericalAdvectionDiffusionElement (const RefineableQSphericalAdvectionDiffusionElement< NNODE_1D > &dummy)=delete
	Broken copy constructor. More...

void	operator= (const RefineableQSphericalAdvectionDiffusionElement< NNODE_1D > &)=delete
	Broken assignment operator. More...

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 1. More...

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

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: empty. More...

unsigned	nrecovery_order ()

void	further_setup_hanging_nodes ()

Public Member Functions inherited from oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >
	QSphericalAdvectionDiffusionElement ()

	QSphericalAdvectionDiffusionElement (const QSphericalAdvectionDiffusionElement< NNODE_1D > &dummy)=delete
	Broken copy constructor. More...

void	operator= (const QSphericalAdvectionDiffusionElement< NNODE_1D > &)=delete
	Broken assignment operator. More...

unsigned	required_nvalue (const unsigned &n) const

void	output (std::ostream &outfile)

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

void	output (FILE *file_pt)

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

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

Public Member Functions inherited from oomph::QElement< 2, NNODE_1D >
	QElement ()
	Constructor. More...

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

void	shape (const Vector< double > &s, Shape &psi) const
	Broken assignment operator. More...

void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
	Derivatives of shape functions for specific QElement<2,..> More...

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

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

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

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

void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
	Get local coordinates of node j in the element; vector sets its own size. More...

void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)
	Get the local fraction of node j in the element. More...

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

Node *	get_node_at_local_coordinate (const Vector< double > &s) const
	Get the node at the specified local coordinate. More...

unsigned	nnode_1d () const
	Number of nodes along each element edge. More...

unsigned	nplot_points_paraview (const unsigned &nplot) const

unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

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

unsigned	nplot_points (const unsigned &nplot) const

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

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...

CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

Public Member Functions inherited from oomph::QElementBase
	QElementBase ()
	Constructor: Initialise pointers to macro element reference coords. More...

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

virtual	~QElementBase ()
	Broken assignment operator. More...

bool	local_coord_is_valid (const Vector< double > &s)
	Check whether the local coordinate are valid or not. More...

void	move_local_coord_back_into_element (Vector< double > &s) const

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

double &	s_macro_ll (const unsigned &i)

double &	s_macro_ur (const unsigned &i)

double	s_macro_ll (const unsigned &i) const

double	s_macro_ur (const unsigned &i) const

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

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

unsigned	nnode_on_face () const

ElementGeometry::ElementGeometry	element_geometry () const
	It's a Q element! More...

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

	QElementGeometricBase (const QElementGeometricBase &)=delete
	Broken copy constructor. 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...

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

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	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_at_knot (const unsigned &ipt, Shape &psi) const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

unsigned	nodal_dimension () const
	Return the required Eulerian dimension of the nodes in this element. More...

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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 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)

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)

void	output_paraview (std::ofstream &file_out, const unsigned &nplot) 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, const SolutionFunctorBase &exact_soln) const
	Output a time-dependent exact solution over the element. More...

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 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, 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)

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

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)

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::SphericalAdvectionDiffusionEquations
	SphericalAdvectionDiffusionEquations ()

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

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

double	du_dt_spherical_adv_diff (const unsigned &n) const

void	disable_ALE ()

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

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::RefineableSphericalAdvectionDiffusionEquations
	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::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...

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)

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

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

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

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

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

void	deselect_sons_for_unrefinement ()

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

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

virtual void	unbuild ()

virtual void	deactivate_element ()

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

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

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

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

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

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

virtual unsigned	ninterpolating_node (const int &value_id)

virtual unsigned	ninterpolating_node_1d (const int &value_id)

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

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...

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

Public Member Functions inherited from oomph::RefineableQElement< 2 >
	RefineableQElement ()
	Constructor: Pass refinement level (default 0 = root) More...

	RefineableQElement (const RefineableQElement< 2 > &dummy)=delete
	Broken copy constructor. More...

virtual	~RefineableQElement ()
	Broken assignment operator. More...

unsigned	required_nsons () const
	A refineable quad element has four sons. More...

virtual Node *	node_created_by_neighbour (const Vector< double > &s_fraction, bool &is_periodic)

virtual Node *	node_created_by_son_of_neighbour (const Vector< double > &s_fraction, bool &is_periodic)

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

void	check_integrity (double &max_error)

void	output_corners (std::ostream &outfile, const std::string &colour) const
	Print corner nodes, use colour. More...

QuadTree *	quadtree_pt ()
	Pointer to quadtree representation of this element. More...

QuadTree *	quadtree_pt () const
	Pointer to quadtree representation of this element. More...

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

void	get_boundaries (const int &edge, std::set< unsigned > &boundaries) const

void	get_bcs (int bound, Vector< int > &bound_cons) const

void	interpolated_zeta_on_edge (const unsigned &boundary, const int &edge, const Vector< double > &s, Vector< double > &zeta)

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

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 3 (velocities) More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: Reconstruct pressure from the (merged) sons. More...

unsigned	nrecovery_order ()

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

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

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

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

void	further_setup_hanging_nodes ()

void	further_build ()

Public Member Functions inherited from oomph::QSphericalCrouzeixRaviartElement
	QSphericalCrouzeixRaviartElement ()
	Constructor, there are 3 internal values (for the pressure) More...

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

double	p_spherical_nst (const unsigned &i) const

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

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

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

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

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

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

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

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

void	full_output (std::ostream &outfile)

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

unsigned	ndof_types () const

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

Public Member Functions inherited from oomph::SphericalNavierStokesEquations
double	cot (const double &th) const

	SphericalNavierStokesEquations ()

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

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

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

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

const double &	viscosity_ratio () const

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

const double &	density_ratio () const

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

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

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

const double &	re_invro () const
	Global Reynolds number multiplied by inverse Rossby number. More...

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

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

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

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

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

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

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

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

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

virtual unsigned	u_index_spherical_nst (const unsigned &i) const

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

void	disable_ALE ()

void	enable_ALE ()

virtual int	p_nodal_index_spherical_nst () const

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

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

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

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

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

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

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

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

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

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

void	full_output (std::ostream &outfile)

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

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

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

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

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

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

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

void	compute_error_e (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, FiniteElement::SteadyExactSolutionFctPt exact_soln_dr_pt, FiniteElement::SteadyExactSolutionFctPt exact_soln_dtheta_pt, double &u_error, double &u_norm, double &p_error, double &p_norm)

void	compute_shear_stress (std::ostream &outfile)

void	extract_velocity (std::ostream &outfile)

Vector< double >	actual (const Vector< double > &x)

Vector< double >	actual_dr (const Vector< double > &x)

Vector< double >	actual_dth (const Vector< double > &x)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Public Member Functions inherited from oomph::RefineableSphericalNavierStokesEquations
	RefineableSphericalNavierStokesEquations ()
	Empty Constructor. 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)

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

Private Attributes
double *	Ra_pt
	Pointer to a new physical variable, the Rayleigh number. More...

Static Private Attributes
static double	Default_Physical_Constant_Value =0.0
	The static default value of the Rayleigh number. More...

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

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

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::RefineableQElement< 2 >
typedef void(RefineableQElement< 2 >::*	VoidMemberFctPt) ()

Public Types inherited from oomph::SphericalNavierStokesEquations
typedef void(*	SphericalNavierStokesBodyForceFctPt) (const double &time, const Vector< double > &x, Vector< double > &body_force)

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

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

Static Public Member Functions inherited from oomph::RefineableSphericalNavierStokesEquations
static void	pin_redundant_nodal_pressures (const Vector< GeneralisedElement * > &element_pt)

static void	unpin_all_pressure_dofs (const Vector< GeneralisedElement * > &element_pt)
	Unpin all pressure dofs in elements listed in vector. More...

Static Public 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 Public Attributes inherited from oomph::SphericalNavierStokesEquations
static Vector< double >	Gamma
	Vector to decide whether the stress-divergence form is used or not. More...

Protected Member Functions inherited from oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >
double	dshape_and_dtest_eulerian_spherical_adv_diff (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

Protected Member Functions inherited from oomph::FiniteElement
template<unsigned DIM>
double	invert_jacobian (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::RefineableSphericalAdvectionDiffusionEquations
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::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)

Protected Member Functions inherited from oomph::RefineableQElement< 2 >
void	setup_father_bounds ()

void	get_edge_bcs (const int &edge, Vector< int > &bound_cons) const
	Determine Vector of boundary conditions along edge (N/S/W/E) More...

void	setup_hang_for_value (const int &value_id)

virtual void	quad_hang_helper (const int &value_id, const int &my_edge, std::ofstream &output_hangfile)

Protected Member Functions inherited from oomph::QSphericalCrouzeixRaviartElement
double	dshape_and_dtest_eulerian_spherical_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

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

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

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

Protected Member Functions inherited from oomph::SphericalNavierStokesEquations
virtual double	get_source_spherical_nst (double time, const unsigned &ipt, const Vector< double > &x)

Protected Member Functions inherited from oomph::RefineableSphericalNavierStokesEquations
virtual Node *	pressure_node_pt (const unsigned &n_p)

virtual void	pin_elemental_redundant_nodal_pressure_dofs ()

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::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::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::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...

Protected Attributes inherited from oomph::QSphericalCrouzeixRaviartElement
unsigned	P_spherical_nst_internal_index

Protected Attributes inherited from oomph::SphericalNavierStokesEquations
double *	Viscosity_Ratio_pt

double *	Density_Ratio_pt

double *	Re_pt
	Pointer to global Reynolds number. More...

double *	ReSt_pt
	Pointer to global Reynolds number x Strouhal number (=Womersley) More...

double *	ReInvFr_pt

double *	ReInvRo_pt

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

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

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

bool	ALE_is_disabled

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...

Static Protected Attributes inherited from oomph::RefineableQElement< 2 >
static std::map< unsigned, DenseMatrix< int > >	Father_bound

Detailed Description

A RefineableElement class that solves the Boussinesq approximation of the Navier–Stokes and energy equations by coupling two pre-existing classes. The RefineableQAdvectionDiffusionElement with bi-quadratic interpolation for the scalar variable (temperature) and RefineableQCrouzeixRaviartElement which solves the Navier–Stokes equations using bi-quadratic interpolation for the velocities and a discontinuous bi-linear interpolation for the pressure. Note that we are free to choose the order in which we store the variables at the nodes. In this case we choose to store the variables in the order fluid velocities followed by temperature. We must, therefore, overload the function AdvectionDiffusionEquations<DIM>::u_index_adv_diff() to indicate that the temperature is stored at the DIM-th position not the 0-th. We do not need to overload the corresponding function in the NavierStokesEquations<DIM> class because the velocities are stored first. Finally, we choose to use the flux-recovery calculation from the fluid velocities to provide the error used in the mesh adaptation.

Constructor & Destructor Documentation

◆ RefineableBuoyantQSphericalCrouzeixRaviartElement()

oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::RefineableBuoyantQSphericalCrouzeixRaviartElement ( )

inline

Constructor: call the underlying constructors and initialise the pointer to the Rayleigh number to address the default value of 0.0

                                                      : 
   RefineableQSphericalAdvectionDiffusionElement<3>(),
   RefineableQSphericalCrouzeixRaviartElement()
   {
    Ra_pt = &Default_Physical_Constant_Value;
   }

References Default_Physical_Constant_Value, and Ra_pt.

Member Function Documentation

◆ compute_error() [1/2]

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

inlinevirtual

Validate against exact solution. Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element Overload to broken default.

Reimplemented from oomph::FiniteElement.

398 {FiniteElement::

399 compute_error(outfile,exact_soln_pt,error,norm);}

oomph::FiniteElement::compute_error

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.

Definition: elements.h:3198

calibrate.error

int error

Definition: calibrate.py:297

References oomph::FiniteElement::compute_error(), and calibrate::error.

◆ compute_error() [2/2]

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

inlinevirtual

Validate against exact solution at given time Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element Overload to broken default

Reimplemented from oomph::FiniteElement.

387 {FiniteElement::compute_error(outfile,exact_soln_pt,

388 time,error,norm);}

References oomph::FiniteElement::compute_error(), and calibrate::error.

◆ disable_ALE()

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::disable_ALE ( )

inlinevirtual

Final override for disable ALE.

Reimplemented from oomph::FiniteElement.

   {
    //Disable ALE in both sets of equations
    RefineableSphericalNavierStokesEquations::disable_ALE();
    RefineableSphericalAdvectionDiffusionEquations::disable_ALE();
   }

References oomph::SphericalAdvectionDiffusionEquations::disable_ALE(), and oomph::SphericalNavierStokesEquations::disable_ALE().

◆ enable_ALE()

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::enable_ALE ( )

inlinevirtual

Final override for enable ALE.

Reimplemented from oomph::FiniteElement.

   {
    //Enable ALE in both sets of equations
    RefineableSphericalNavierStokesEquations::enable_ALE();
    RefineableSphericalAdvectionDiffusionEquations::enable_ALE();
   }

References oomph::FiniteElement::enable_ALE(), and oomph::SphericalNavierStokesEquations::enable_ALE().

◆ fill_in_contribution_to_jacobian()

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

inlinevirtual

Compute the element's residual Vector and the jacobian matrix using full finite differences, the default implementation

Reimplemented from oomph::GeneralisedElement.

   {
 #ifdef USE_FD_JACOBIAN_FOR_REFINEABLE_BUOYANT_Q_ELEMENT
    FiniteElement::fill_in_contribution_to_jacobian(residuals,jacobian);
 #else
    //Calculate the Navier-Stokes contributions (diagonal block and residuals)
    RefineableSphericalNavierStokesEquations::
     fill_in_contribution_to_jacobian(residuals,jacobian);
  
    //Calculate the advection-diffusion contributions 
    //(diagonal block and residuals)
    RefineableSphericalAdvectionDiffusionEquations::
     fill_in_contribution_to_jacobian(residuals,jacobian);
  
    //We now fill in the off-diagonal (interaction) blocks analytically
    this->fill_in_off_diagonal_jacobian_blocks_analytic(residuals,jacobian);
 #endif
   } //End of jacobian calculation

References oomph::FiniteElement::fill_in_contribution_to_jacobian(), oomph::SphericalAdvectionDiffusionEquations::fill_in_contribution_to_jacobian(), oomph::SphericalNavierStokesEquations::fill_in_contribution_to_jacobian(), and fill_in_off_diagonal_jacobian_blocks_analytic().

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

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

inlinevirtual

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

Reimplemented from oomph::GeneralisedElement.

  {
    //Calculate the Navier-Stokes contributions (diagonal block and residuals)
    RefineableSphericalNavierStokesEquations::
     fill_in_contribution_to_jacobian_and_mass_matrix(residuals,jacobian,
                                                      mass_matrix);
  
    //Calculate the advection-diffusion contributions 
    //(diagonal block and residuals)
    RefineableSphericalAdvectionDiffusionEquations::
     fill_in_contribution_to_jacobian_and_mass_matrix(residuals,jacobian,
                                                      mass_matrix);
    
    //We now fill in the off-diagonal (interaction) blocks analytically
    this->fill_in_off_diagonal_jacobian_blocks_analytic(residuals,jacobian);
  }

References oomph::SphericalAdvectionDiffusionEquations::fill_in_contribution_to_jacobian_and_mass_matrix(), oomph::SphericalNavierStokesEquations::fill_in_contribution_to_jacobian_and_mass_matrix(), and fill_in_off_diagonal_jacobian_blocks_analytic().

◆ fill_in_contribution_to_residuals()

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

inlinevirtual

Fill in the constituent elements' contribution to the residual vector.

Reimplemented from oomph::GeneralisedElement.

   {
    //Call the residuals of the Navier-Stokes equations
    RefineableSphericalNavierStokesEquations::
     fill_in_contribution_to_residuals(residuals);
  
    //Call the residuals of the advection-diffusion equations
    RefineableSphericalAdvectionDiffusionEquations::
     fill_in_contribution_to_residuals(residuals);
   }

References oomph::SphericalAdvectionDiffusionEquations::fill_in_contribution_to_residuals(), and oomph::SphericalNavierStokesEquations::fill_in_contribution_to_residuals().

◆ fill_in_off_diagonal_jacobian_blocks_analytic()

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::fill_in_off_diagonal_jacobian_blocks_analytic	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inline

Compute the contribution of the off-diagonal blocks analytically.

   {
    //Perform another loop over the integration loops using the information
    //from the original elements' residual assembly loops to determine
    //the conributions to the jacobian
    
    // Local storage for pointers to hang_info objects
    HangInfo *hang_info_pt=0, *hang_info2_pt=0;   
    
    //Local storage for the index in the nodes at which the
    //Navier-Stokes velocities are stored (we know that this should be 0,1,2)
    unsigned u_nodal_spherical_nst[3];
    for(unsigned i=0;i<3;i++) 
     {u_nodal_spherical_nst[i] = this->u_index_spherical_nst(i);}
    
    //Local storage for the  index at which the temperature is stored
    const unsigned u_nodal_spherical_adv_diff = 
     this->u_index_spherical_adv_diff();
    
    //Find out how many nodes there are
    const unsigned n_node = this->nnode();
    
    //Set up memory for the shape and test functions and their derivatives
    Shape psif(n_node), testf(n_node);
    DShape dpsifdx(n_node,2), dtestfdx(n_node,2);
    
    //Number of integration points
    const unsigned n_intpt = this->integral_pt()->nweight();
    
    //Get Physical Variables from Element
    double Ra = this->ra();
    double Pe = this->pe();
    Vector<double> gravity = this->g();
    
    //Integers to store the local equations and unknowns
    int local_eqn=0, local_unknown=0;
    
    //Loop over the integration points
    for(unsigned ipt=0;ipt<n_intpt;ipt++)
     {
      //Get the integral weight
      double w = this->integral_pt()->weight(ipt);
      
      //Call the derivatives of the shape and test functions
      double J = 
       this->dshape_and_dtest_eulerian_at_knot_spherical_nst(ipt,psif,dpsifdx,
                                                       testf,dtestfdx);
      
      //Premultiply the weights and the Jacobian
      double W = w*J;
  
      //Work out the radius
      double r = 0.0;
      //and the angle
      double theta = 0.0;
  
      //Calculate local values of temperature derivatives
      //Allocate
      Vector<double> interpolated_du_spherical_adv_diff_dx(2,0.0);
      
      // Loop over nodes
      for(unsigned l=0;l<n_node;l++) 
       {
        //Get the nodal value
        double u_value = this->nodal_value(l,u_nodal_spherical_adv_diff);
        //Loop over the derivative directions
        for(unsigned j=0;j<2;j++)
         {
          interpolated_du_spherical_adv_diff_dx[j] += u_value*dpsifdx(l,j);
         }
        
        //Calculate the position
        r += this->nodal_position(l,0)*psif(l);
        theta += this->nodal_position(l,1)*psif(l);
       }
  
      double r2 = r*r;
      double sin_theta = sin(theta);
  
      //Overwrite gravity for the eye problem
      //gravity[0] = -cos(theta);
      //gravity[1] = sin(theta);
      //gravity[2] = 0.0;
  
  
      //Assemble the Jacobian terms
      //---------------------------
      
      //Loop over the test functions/eqns
      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 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;
           }
          
          
          //Assemble derivatives of Navier Stokes momentum w.r.t. temperature
          //-----------------------------------------------------------------
          
          // Loop over velocity components for equations
          for(unsigned i=0;i<3;i++)
           {
            
            //Get the equation number
            if(is_node_hanging)
             {
              //Get the equation number from the master node
              local_eqn = this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                               u_nodal_spherical_nst[i]);
             }
            else
             {
              // Local equation number
              local_eqn = this->nodal_local_eqn(l,u_nodal_spherical_nst[i]);
             }
            
            if(local_eqn >= 0)
             {
              //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 unknowns
              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++)
                 {
                  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_spherical_adv_diff);
                    //Read out the hanging weight from the master node
                    hang_weight2 = hang_info2_pt->master_weight(m2);
                   }
                  else
                   {
                    //The local unknown number comes from the node
                    local_unknown = 
                     this->nodal_local_eqn(l2,
                                           u_nodal_spherical_adv_diff);
                    //The hang weight is one
                    hang_weight2 = 1.0;
                   }
                  
                  if(local_unknown >= 0)
                   {
                    //Add contribution to jacobian matrix
                    jacobian(local_eqn,local_unknown) 
                     += -gravity[i]*psif(l2)*Ra*testf(l)* 
                     r2*sin_theta*W*hang_weight*hang_weight2/(pow(r,5.0));
                   }
                 }
               }
             }
           }
          
          
          //Assemble derivative of adv diff eqn w.r.t. fluid veloc
          //------------------------------------------------------
          {
           //Get the equation number
           if(is_node_hanging)
            {
             //Get the equation number from the master node
             local_eqn = this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                              u_nodal_spherical_adv_diff);
            }
           else
            {
             // Local equation number
             local_eqn = this->nodal_local_eqn(l,u_nodal_spherical_adv_diff);
            }
           
           //If it's not pinned
           if(local_eqn >= 0)
            {
             //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 unknowns
             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++)
                {
                 //If the node is hanging
                 if(is_node2_hanging)
                  {
                   //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 hang weight is one
                   hang_weight2 = 1.0;
                  }
                 
                 //Loop over the velocity degrees of freedom
                 for(unsigned i2=0;i2<2;i2++)
                  {
                   //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_spherical_nst[i2]);
                    }
                   else
                    {
                     //The local unknown number comes from the node
                     local_unknown=
                      this->nodal_local_eqn(l2, 
                                            u_nodal_spherical_nst[i2]);
                    }
                   
                   //If it's not pinned
                   if(local_unknown >= 0)
                    {
                     //Radial case
                     if(i2==0)
                      {
                       //Add the contribution to the jacobian matrix
                       jacobian(local_eqn,local_unknown)
                        -= Pe*psif(l2)*
                        interpolated_du_spherical_adv_diff_dx[i2]*testf(l)
                        *r2*sin_theta*W*hang_weight*hang_weight2;
                      }
                     if(i2==1)
                      {
                       //Add the contribution to the jacobian matrix
                       jacobian(local_eqn,local_unknown)
                        -= Pe*psif(l2)*
                        interpolated_du_spherical_adv_diff_dx[i2]*testf(l)
                        *r*sin_theta*W*hang_weight*hang_weight2;
                      }
  
                    }
                   
                  }
                }
              }
            }
          }
          
         }
       }
     }
   } //End of function

References oomph::QSphericalCrouzeixRaviartElement::dshape_and_dtest_eulerian_at_knot_spherical_nst(), oomph::SphericalNavierStokesEquations::g(), oomph::Node::hanging_pt(), i, oomph::FiniteElement::integral_pt(), oomph::Node::is_hanging(), J, j, 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(), Global_Parameters::Pe, oomph::SphericalAdvectionDiffusionEquations::pe(), Eigen::bfloat16_impl::pow(), UniformPSDSelfTest::r, Global_Parameters::Ra, ra(), sin(), BiharmonicTestFunctions2::theta, u_index_spherical_adv_diff(), oomph::SphericalNavierStokesEquations::u_index_spherical_nst(), w, oomph::QuadTreeNames::W, and oomph::Integral::weight().

Referenced by fill_in_contribution_to_jacobian(), and fill_in_contribution_to_jacobian_and_mass_matrix().

◆ further_build()

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::further_build ( )

inlinevirtual

Call the underlying single-physics element's further_build() functions and make sure that the pointer to the Rayleigh number is passed to the sons

Reimplemented from oomph::RefineableElement.

   {
    RefineableQSphericalCrouzeixRaviartElement::further_build();
    RefineableQSphericalAdvectionDiffusionElement<3>::further_build();
  
    //Cast the pointer to the father element to the specific
    //element type
    RefineableBuoyantQSphericalCrouzeixRaviartElement* cast_father_element_pt
     = dynamic_cast<RefineableBuoyantQSphericalCrouzeixRaviartElement*>(
      this->father_element_pt());
  
    //Set the pointer to the Rayleigh number to be the same as that in
    //the father
    this->Ra_pt = cast_father_element_pt->ra_pt();
   } //end of further build

References oomph::RefineableElement::father_element_pt(), oomph::RefineableSphericalAdvectionDiffusionEquations::further_build(), oomph::RefineableQSphericalCrouzeixRaviartElement::further_build(), and ra_pt().

◆ further_setup_hanging_nodes()

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::further_setup_hanging_nodes ( )

inlinevirtual

The additional hanging node information must be set up for both single-physics elements.

Implements oomph::RefineableQElement< 2 >.

   {
    RefineableQSphericalCrouzeixRaviartElement::further_setup_hanging_nodes();
    RefineableQSphericalAdvectionDiffusionElement<3>::further_setup_hanging_nodes();
   }

References oomph::RefineableQSphericalAdvectionDiffusionElement< NNODE_1D >::further_setup_hanging_nodes(), and oomph::RefineableQSphericalCrouzeixRaviartElement::further_setup_hanging_nodes().

◆ geometric_jacobian()

double oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::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.

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

plotDoE.x

list x

Definition: plotDoE.py:28

References sin(), and plotDoE::x.

◆ get_body_force_spherical_nst()

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::get_body_force_spherical_nst	(	const double &	time,
		const unsigned &	ipt,
		const Vector< double > &	s,
		const Vector< double > &	x,
		Vector< double > &	result
	)

inlinevirtual

Overload the body force in the navier-stokes equations This provides the coupling from the advection-diffusion equations to the Navier–Stokes equations, the body force is the temperature multiplied by the Rayleigh number acting in the direction opposite to gravity.

Reimplemented from oomph::SphericalNavierStokesEquations.

   {
    // Get the temperature
    const double interpolated_t = this->interpolated_u_spherical_adv_diff(s);
  
    // Get vector that indicates the direction of gravity from
    // the Navier-Stokes equations
    Vector<double> gravity(SphericalNavierStokesEquations::g());
  
    // This is for the eye problem
    //gravity[0] = -cos(x[1]);
    //gravity[1] = sin(x[1]);
    //gravity[2] = 0.0;
    
    // Temperature-dependent body force:
    for (unsigned i=0;i<3;i++)
     {
      result[i] = -gravity[i]*interpolated_t*ra()/(pow(x[0],5.0));
     }
   }

References oomph::SphericalNavierStokesEquations::g(), Gravity::gravity(), i, oomph::SphericalAdvectionDiffusionEquations::interpolated_u_spherical_adv_diff(), Eigen::bfloat16_impl::pow(), ra(), and plotDoE::x.

◆ get_interpolated_values() [1/2]

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

inlinevirtual

Get all continuously interpolated values at the local coordinate s at time level t (t=0: present; t>0: previous). We choose to put the fluid velocities first, followed by the temperature

Implements oomph::RefineableElement.

   {
    //Storage for the fluid velocities
    Vector<double> nst_values;
  
    //Get the fluid velocities from the fluid element
    RefineableQSphericalCrouzeixRaviartElement::
     get_interpolated_values(t,s,nst_values);
  
    //Storage for the temperature
    Vector<double> advection_values;
  
    //Get the temperature from the advection-diffusion element
    RefineableQSphericalAdvectionDiffusionElement<3>::
     get_interpolated_values(s,advection_values);
  
    //Add the fluid velocities to the values vector
    for(unsigned i=0;i<3;i++) {values.push_back(nst_values[i]);}   
  
    //Add the concentration to the end
    values.push_back(advection_values[0]);
  
   } // end of get_interpolated_values

References oomph::RefineableSphericalAdvectionDiffusionEquations::get_interpolated_values(), oomph::RefineableQSphericalCrouzeixRaviartElement::get_interpolated_values(), i, s, and plotPSD::t.

◆ get_interpolated_values() [2/2]

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

inlinevirtual

Get the continuously interpolated values at the local coordinate s. We choose to put the fluid velocities first, followed by the temperature.

Reimplemented from oomph::RefineableElement.

   {
    //Storage for the fluid velocities
    Vector<double> nst_values;
  
    //Get the fluid velocities from the fluid element
    RefineableQSphericalCrouzeixRaviartElement::
     get_interpolated_values(s,nst_values);
  
    //Storage for the temperature
    Vector<double> advection_values;
  
    //Get the temperature from the advection-diffusion element
    RefineableQSphericalAdvectionDiffusionElement<3>::
     get_interpolated_values(s,advection_values);
  
    //Add the fluid velocities to the values vector
    for(unsigned i=0;i<3;i++) {values.push_back(nst_values[i]);}  
  
    //Add the concentration to the end
    values.push_back(advection_values[0]);
   }

References oomph::RefineableSphericalAdvectionDiffusionEquations::get_interpolated_values(), oomph::RefineableQSphericalCrouzeixRaviartElement::get_interpolated_values(), i, and s.

◆ get_wind_spherical_adv_diff()

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

inlinevirtual

Overload the wind function in the advection-diffusion equations. This provides the coupling from the Navier–Stokes equations to the advection-diffusion equations because the wind is the fluid velocity.

Reimplemented from oomph::SphericalAdvectionDiffusionEquations.

   {
    //The wind function is simply the velocity at the points
    this->interpolated_u_spherical_nst(s,wind);
   }

References oomph::SphericalNavierStokesEquations::interpolated_u_spherical_nst().

◆ get_Z2_compound_flux_indices()

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::get_Z2_compound_flux_indices ( Vector< unsigned > & flux_index )

inlinevirtual

Fill in which flux components are associated with the fluid measure and which are associated with the temperature measure

Reimplemented from oomph::ElementWithZ2ErrorEstimator.

   {
    //Find the number of fluid fluxes
    unsigned n_fluid_flux = 
     RefineableQSphericalCrouzeixRaviartElement::num_Z2_flux_terms();
    //Find the number of temperature fluxes
    unsigned n_temp_flux =  
     RefineableQSphericalAdvectionDiffusionElement<3>::num_Z2_flux_terms();
  
    //The fluid fluxes are first 
    //The values of the flux_index vector are zero on entry, so we
    //could omit this line
    for(unsigned i=0;i<n_fluid_flux;i++) {flux_index[i] = 0;}
  
    //Set the temperature fluxes (the last set of fluxes
    for(unsigned i=0;i<n_temp_flux;i++) {flux_index[n_fluid_flux + i] = 1;}
  
   } //end of get_Z2_compound_flux_indices

References i, oomph::RefineableSphericalAdvectionDiffusionEquations::num_Z2_flux_terms(), and oomph::RefineableSphericalNavierStokesEquations::num_Z2_flux_terms().

◆ get_Z2_flux()

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

inlinevirtual

Get the Z2 flux by concatenating the fluxes from the fluid and the advection diffusion elements.

Implements oomph::ElementWithZ2ErrorEstimator.

   {
    //Find the number of fluid fluxes
    unsigned n_fluid_flux = 
     RefineableQSphericalCrouzeixRaviartElement::num_Z2_flux_terms();
  
    //Fill in the first flux entries as the velocity entries
    RefineableQSphericalCrouzeixRaviartElement::get_Z2_flux(s,flux);
  
    //Find the number of temperature fluxes
    unsigned n_temp_flux =  
     RefineableQSphericalAdvectionDiffusionElement<3>::num_Z2_flux_terms();
    Vector<double> temp_flux(n_temp_flux);
  
    //Get the temperature flux
    RefineableQSphericalAdvectionDiffusionElement<3>::get_Z2_flux(s,temp_flux);
    
    //Add the temperature flux to the end of the flux vector
    for(unsigned i=0;i<n_temp_flux;i++)
     {
      flux[n_fluid_flux+i] = temp_flux[i];
     }
  
   } //end of get_Z2_flux

References ProblemParameters::flux(), oomph::RefineableSphericalAdvectionDiffusionEquations::get_Z2_flux(), oomph::RefineableSphericalNavierStokesEquations::get_Z2_flux(), i, oomph::RefineableSphericalAdvectionDiffusionEquations::num_Z2_flux_terms(), oomph::RefineableSphericalNavierStokesEquations::num_Z2_flux_terms(), and s.

◆ ncompound_fluxes()

unsigned oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::ncompound_fluxes ( )

inlinevirtual

The number of compound fluxes is two (one for the fluid and one for the temperature)

Reimplemented from oomph::ElementWithZ2ErrorEstimator.

354 {return 2;}

◆ ncont_interpolated_values()

unsigned oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::ncont_interpolated_values ( ) const

inlinevirtual

The total number of continously interpolated values is 4 (3 fluid velocities and one temperature).

Implements oomph::RefineableElement.

205 {return 4;}

◆ nrecovery_order()

unsigned oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::nrecovery_order ( )

inlinevirtual

The recovery order is that of the NavierStokes elements.

Implements oomph::ElementWithZ2ErrorEstimator.

314 {return RefineableQSphericalCrouzeixRaviartElement::nrecovery_order();}

oomph::RefineableQSphericalCrouzeixRaviartElement::nrecovery_order

unsigned nrecovery_order()

Definition: refineable_spherical_navier_stokes_elements.h:701

References oomph::RefineableQSphericalCrouzeixRaviartElement::nrecovery_order().

◆ num_Z2_flux_terms()

unsigned oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::num_Z2_flux_terms ( )

inlinevirtual

The number of Z2 flux terms is the same as that in the fluid element plus that in the advection-diffusion element

Implements oomph::ElementWithZ2ErrorEstimator.

   {
    return (RefineableQSphericalCrouzeixRaviartElement::num_Z2_flux_terms() +
            RefineableQSphericalAdvectionDiffusionElement<3>::num_Z2_flux_terms());
   }

References oomph::RefineableSphericalNavierStokesEquations::num_Z2_flux_terms().

◆ nvertex_node()

unsigned oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::nvertex_node ( ) const

inlinevirtual

Number of vertex nodes in the element is obtained from the geometric element.

Implements oomph::ElementWithZ2ErrorEstimator.

195 {return QElement<2,3>::nvertex_node();}

QElement

◆ output() [1/4]

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::output ( FILE * file_pt )

inlinevirtual

C-style output function: Broken default.

Reimplemented from oomph::FiniteElement.

164 {FiniteElement::output(file_pt);}

oomph::FiniteElement::output

virtual void output(std::ostream &outfile)

Definition: elements.h:3050

References oomph::FiniteElement::output().

◆ output() [2/4]

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

inlinevirtual

C-style output function: Broken default.

Reimplemented from oomph::FiniteElement.

168 {FiniteElement::output(file_pt,n_plot);}

References oomph::FiniteElement::output().

◆ output() [3/4]

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::output ( std::ostream & outfile )

inlinevirtual

Overload the standard output function with the broken default.

Reimplemented from oomph::FiniteElement.

117 {FiniteElement::output(outfile);}

References oomph::FiniteElement::output().

◆ output() [4/4]

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

inlinevirtual

Output function:
x,y,u or x,y,z,u at Nplot^DIM plot points

Reimplemented from oomph::FiniteElement.

   {
    //vector of local coordinates
    Vector<double> s(2);
    
    // Tecplot header info
    outfile << this->tecplot_zone_string(nplot);
    
    // Loop over plot points
    unsigned num_plot_points=this->nplot_points(nplot);
    for (unsigned iplot=0;iplot<num_plot_points;iplot++)
     {
      // Get local coordinates of plot point
      this->get_s_plot(iplot,nplot,s);
      
      //Get r and theta
      double r = this->interpolated_x(s,0);
      double theta = this->interpolated_x(s,1);
  
      // Output the position of the plot point
      outfile << r*sin(theta) << " " << r*cos(theta) << " "
              << r << " " << theta << " ";
           
  
      // Output the fluid velocities at the plot point
      for(unsigned i=0;i<3;i++) 
       {outfile << this->interpolated_u_spherical_nst(s,i) << " ";}
      
      // Output the fluid pressure at the plot point
      outfile << this->interpolated_p_spherical_nst(s)  << " ";
   
      // Output the temperature at the plot point
      outfile << this->interpolated_u_spherical_adv_diff(s) << " " << std::endl;
     }
    outfile << std::endl;
    
    // Write tecplot footer (e.g. FE connectivity lists)
    this->write_tecplot_zone_footer(outfile,nplot);
    
   }

References cos(), oomph::QElement< 2, NNODE_1D >::get_s_plot(), i, oomph::SphericalNavierStokesEquations::interpolated_p_spherical_nst(), oomph::SphericalAdvectionDiffusionEquations::interpolated_u_spherical_adv_diff(), oomph::SphericalNavierStokesEquations::interpolated_u_spherical_nst(), oomph::FiniteElement::interpolated_x(), oomph::QElement< 2, NNODE_1D >::nplot_points(), UniformPSDSelfTest::r, s, sin(), oomph::QElement< 2, NNODE_1D >::tecplot_zone_string(), BiharmonicTestFunctions2::theta, and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output_fct() [1/2]

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

inlinevirtual

Output function for a time-dependent exact solution. Broken default

Reimplemented from oomph::FiniteElement.

   {
    FiniteElement::
     output_fct(outfile,Nplot,time,exact_soln_pt);
   }

References oomph::FiniteElement::output_fct().

◆ output_fct() [2/2]

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::output_fct	(	std::ostream &	outfile,
		const unsigned &	Nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

inlinevirtual

Output function for an exact solution: Broken default.

Reimplemented from oomph::FiniteElement.

174 {FiniteElement::output_fct(outfile,Nplot,exact_soln_pt);}

References oomph::FiniteElement::output_fct().

◆ ra()

const double& oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::ra ( ) const

inline

Access function for the Rayleigh number (const version)

92 {return *Ra_pt;}

References Ra_pt.

Referenced by fill_in_off_diagonal_jacobian_blocks_analytic(), and get_body_force_spherical_nst().

◆ ra_pt()

double* & oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::ra_pt ( )

inline

Access function for the pointer to the Rayleigh number.

95 {return Ra_pt;}

References Ra_pt.

Referenced by further_build().

◆ rebuild_from_sons()

void oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::rebuild_from_sons ( Mesh *& mesh_pt )

inlinevirtual

Call the rebuild_from_sons functions for each of the constituent multi-physics elements.

Implements oomph::RefineableElement.

   {
    RefineableQSphericalAdvectionDiffusionElement<3>::rebuild_from_sons(mesh_pt);
    RefineableQSphericalCrouzeixRaviartElement::rebuild_from_sons(mesh_pt);
   }

References oomph::RefineableQSphericalAdvectionDiffusionElement< NNODE_1D >::rebuild_from_sons(), and oomph::RefineableQSphericalCrouzeixRaviartElement::rebuild_from_sons().

◆ required_nvalue()

unsigned oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::required_nvalue ( const unsigned & n ) const

inlinevirtual

The required number of values stored at the nodes is the sum of the required values of the two single-physics elements. This step is generic for any composed element of this type.

Reimplemented from oomph::FiniteElement.

   {return 
     (RefineableQSphericalAdvectionDiffusionElement<3>::required_nvalue(n) +
      RefineableQSphericalCrouzeixRaviartElement::required_nvalue(n));}

References n, and oomph::QSphericalCrouzeixRaviartElement::required_nvalue().

◆ u_index_spherical_adv_diff()

unsigned oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::u_index_spherical_adv_diff ( ) const

inlinevirtual

Overload the index at which the temperature variable is stored. We choose to store is after the fluid velocities.

Reimplemented from oomph::SphericalAdvectionDiffusionEquations.

190 {return 3;}

Referenced by fill_in_off_diagonal_jacobian_blocks_analytic().

◆ vertex_node_pt()

Node* oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::vertex_node_pt ( const unsigned & j ) const

inlinevirtual

Pointer to the j-th vertex node in the element, Call the geometric element's function.

Implements oomph::ElementWithZ2ErrorEstimator.

200 {return QElement<2,3>::vertex_node_pt(j);}

References j.

Member Data Documentation

◆ Default_Physical_Constant_Value

double oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::Default_Physical_Constant_Value =0.0

staticprivate

The static default value of the Rayleigh number.

Set the default value of the Rayleigh number to be zero.

Referenced by RefineableBuoyantQSphericalCrouzeixRaviartElement().

◆ Ra_pt

double* oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::Ra_pt

private

Pointer to a new physical variable, the Rayleigh number.

Referenced by ra(), ra_pt(), and RefineableBuoyantQSphericalCrouzeixRaviartElement().

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

spherical_buoyant_navier_stokes.h

Public Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RefineableBuoyantQSphericalCrouzeixRaviartElement()

Member Function Documentation

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ disable_ALE()

◆ enable_ALE()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

◆ fill_in_contribution_to_residuals()

◆ fill_in_off_diagonal_jacobian_blocks_analytic()

◆ further_build()

◆ further_setup_hanging_nodes()

◆ geometric_jacobian()

◆ get_body_force_spherical_nst()

◆ get_interpolated_values() [1/2]

◆ get_interpolated_values() [2/2]

◆ get_wind_spherical_adv_diff()

◆ get_Z2_compound_flux_indices()

◆ get_Z2_flux()

◆ ncompound_fluxes()

◆ ncont_interpolated_values()

◆ nrecovery_order()

◆ num_Z2_flux_terms()

◆ nvertex_node()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ ra()

◆ ra_pt()

◆ rebuild_from_sons()

◆ required_nvalue()

◆ u_index_spherical_adv_diff()

◆ vertex_node_pt()

Member Data Documentation

◆ Default_Physical_Constant_Value

◆ Ra_pt