#include <multi_domain_axisym_boussinesq_elements.h>

Inheritance diagram for RefineableQAxisymCrouzeixRaviartBoussinesqElement:

Public Member Functions
	RefineableQAxisymCrouzeixRaviartBoussinesqElement ()

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	further_build ()

void	get_body_force_axi_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &body_force)

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

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

void	get_dbody_force_axi_nst_dexternal_element_data (const unsigned &ipt, DenseMatrix< double > &result, Vector< unsigned > &global_eqn_number)

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

	RefineableQAxisymCrouzeixRaviartBoussinesqElement ()

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	further_build ()

void	get_body_force_axi_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &body_force)

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

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

void	get_dbody_force_axi_nst_dexternal_element_data (const unsigned &ipt, DenseMatrix< double > &result, Vector< unsigned > &global_eqn_number)

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

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

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

double	p_axi_nst (const unsigned &i) const

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

void	fix_pressure (const unsigned &p_dof, const double &pvalue)
	Function to fix the internal pressure dof idof_internal. More...

void	get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction) const
	Compute traction at local coordinate s for outer unit normal N. More...

int	p_local_eqn (const unsigned &n) const

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

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

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

void	output (FILE *file_pt, const unsigned &n_plot)
	Redirect output to NavierStokesEquations output. More...

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::AxisymmetricNavierStokesEquations
	AxisymmetricNavierStokesEquations ()
	Constructor: NULL the body force and source function. More...

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 &	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...

const double &	density_ratio () const

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

const double &	viscosity_ratio () const

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

virtual unsigned	u_index_axi_nst (const unsigned &i) const

unsigned	u_index_nst (const unsigned &i) const

unsigned	n_u_nst () const

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

void	disable_ALE ()

void	enable_ALE ()

virtual int	p_nodal_index_axi_nst () const
	Which nodal value represents the pressure? More...

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...

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

void	strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate) const
	Strain-rate tensor: \( e_{ij} \) where \( i,j = r,z,\theta \) (in that order) More...

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

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

unsigned	nscalar_paraview () const

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

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

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

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

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

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

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

void	fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Compute the element's residual Vector. More...

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

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

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

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

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

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

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

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

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

double	interpolated_d_dudx_dX_axi_nst (const Vector< double > &s, const unsigned &p, const unsigned &q, const unsigned &i, const unsigned &k) const

double	compute_physical_size () const
	Compute the volume of the element. 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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

double	size () const

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, 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)

virtual unsigned	self_test ()

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

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

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

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::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::RefineableAxisymmetricNavierStokesEquations
	RefineableAxisymmetricNavierStokesEquations ()
	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 r. More...

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

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 unsigned	ncompound_fluxes ()

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

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)

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::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::ElementWithExternalElement
	ElementWithExternalElement ()

virtual	~ElementWithExternalElement ()
	The destructor, clean up any allocated memory. More...

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

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

bool	storage_has_been_allocated () const
	Helper function to check if storage has actually been allocated. More...

FiniteElement *&	external_element_pt (const unsigned &interaction_index, const unsigned &ipt)

FiniteElement *const &	external_element_pt (const unsigned &interaction_index, const unsigned &ipt) const
	Access function to source element, const version. More...

Vector< double > &	external_element_local_coord (const unsigned &interaction_index, const unsigned &ipt)

Vector< double > const &	external_element_local_coord (const unsigned &interaction_index, const unsigned &ipt) const
	Access function to get source element's coords, const version. More...

void	output_external_elements (std::ostream &outfile, const unsigned &interaction_index)

void	initialise_external_element_storage ()

void	flush_all_external_element_storage ()
	Flush the storage for external elements. More...

void	set_ninteraction (const unsigned &n_interaction)

unsigned	ninteraction () const
	Return the number of interactions in the element. More...

virtual void	identify_all_field_data_for_external_interaction (Vector< std::set< FiniteElement * >> const &external_elements_pt, std::set< std::pair< Data *, unsigned >> &paired_interaction_data)

virtual void	identify_all_geometric_data_for_external_interaction (Vector< std::set< FiniteElement * >> const &external_elements_pt, std::set< Data * > &external_geometric_data_pt)

unsigned	nexternal_interaction_field_data () const

Vector< Data * >	external_interaction_field_data_pt () const

unsigned	nexternal_interaction_geometric_data () const

bool	add_external_geometric_data ()
	Are we including external geometric data in the element's Jacobian. More...

bool	add_external_interaction_data ()
	Are we including external data in the element's Jacobian. More...

Vector< Data * >	external_interaction_geometric_data_pt () const

void	ignore_external_geometric_data ()

void	ignore_external_interaction_data ()

void	include_external_geometric_data ()

void	include_external_interaction_data ()

bool	external_geometric_data_is_included () const

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

Private Attributes
double *	Ra_pt
	Pointer to a private data member, 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::RefineableQElement< 2 >
typedef void(RefineableQElement< 2 >::*	VoidMemberFctPt) ()

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

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

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

Public Attributes inherited from oomph::AxisymmetricNavierStokesEquations
void(*&)(const double &time, const Vector< double > &x, Vector< double > &f)	axi_nst_body_force_fct_pt ()
	Access function for the body-force pointer. More...

double(*&)(const double &time, const Vector< double > &x)	source_fct_pt ()
	Access function for the source-function pointer. More...

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

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

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

double	dshape_and_dtest_eulerian_at_knot_axi_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const

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

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

Protected Member Functions inherited from oomph::AxisymmetricNavierStokesEquations
virtual void	get_body_force_gradient_axi_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, DenseMatrix< double > &d_body_force_dx)

double	get_source_fct (const double &time, const unsigned &ipt, const Vector< double > &x)
	Calculate the source fct at given time and Eulerian position. More...

virtual void	get_source_fct_gradient (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &gradient)

virtual void	get_viscosity_ratio_axisym_nst (const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, double &visc_ratio)

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

virtual void	pin_elemental_redundant_nodal_pressure_dofs ()

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::ElementWithExternalElement
void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

void	assign_external_interaction_data_local_eqn_numbers (const bool &store_local_dof_pt)

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

void	fill_in_jacobian_from_external_interaction_by_fd (DenseMatrix< double > &jacobian)

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

void	fill_in_jacobian_from_external_interaction_field_by_fd (DenseMatrix< double > &jacobian)

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

void	fill_in_jacobian_from_external_interaction_geometric_by_fd (DenseMatrix< double > &jacobian)

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

virtual void	update_before_external_interaction_field_fd ()

virtual void	reset_after_external_interaction_field_fd ()

virtual void	update_in_external_interaction_field_fd (const unsigned &i)

virtual void	reset_in_external_interaction_field_fd (const unsigned &i)

virtual void	update_before_external_interaction_geometric_fd ()

virtual void	reset_after_external_interaction_geometric_fd ()

virtual void	update_in_external_interaction_geometric_fd (const unsigned &i)

virtual void	reset_in_external_interaction_geometric_fd (const unsigned &i)

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::AxisymmetricQCrouzeixRaviartElement
unsigned	P_axi_nst_internal_index

Protected Attributes inherited from oomph::AxisymmetricNavierStokesEquations
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...

void(*	Body_force_fct_pt )(const double &time, const Vector< double > &x, Vector< double > &result)
	Pointer to body force function. More...

double(*	Source_fct_pt )(const double &time, const Vector< double > &x)
	Pointer to volumetric source function. More...

bool	ALE_is_disabled

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

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

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

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

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

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

Protected Attributes inherited from oomph::ElementWithExternalElement
bool	Add_external_interaction_data
	Boolean flag to indicate whether to include the external data. More...

bool	Add_external_geometric_data
	Boolean flag to indicate whether to include the external geometric data. More...

Data **	External_interaction_field_data_pt

Data **	External_interaction_geometric_data_pt

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

Static Protected Attributes inherited from oomph::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

////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////// Build a RefineableQAxisymCrouzeixRaviart element that inherits from ElementWithExternalElement so that it can "communicate" with an advection diffusion element that provides the temperature in the body force term.

Constructor & Destructor Documentation

◆ RefineableQAxisymCrouzeixRaviartBoussinesqElement() [1/2]

RefineableQAxisymCrouzeixRaviartBoussinesqElement::RefineableQAxisymCrouzeixRaviartBoussinesqElement ( )

inline

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

                                                      : 
   RefineableAxisymmetricQCrouzeixRaviartElement(),
   ElementWithExternalElement()
   {
    Ra_pt = &Default_Physical_Constant_Value;
  
    //There is one interaction: The effect of the advection-diffusion
    //element onto the buoyancy term
    this->set_ninteraction(1);
   } 

References oomph::MultiDomainBoussinesqHelper::Default_Physical_Constant_Value.

◆ RefineableQAxisymCrouzeixRaviartBoussinesqElement() [2/2]

RefineableQAxisymCrouzeixRaviartBoussinesqElement::RefineableQAxisymCrouzeixRaviartBoussinesqElement ( )

inline

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

                                                      : 
   RefineableAxisymmetricQCrouzeixRaviartElement(),
   ElementWithExternalElement()
   {
    Ra_pt = &Default_Physical_Constant_Value;
  
    //There is one interaction: The effect of the advection-diffusion
    //element onto the buoyancy term
    this->set_ninteraction(1);
   } 

References oomph::MultiDomainBoussinesqHelper::Default_Physical_Constant_Value.

Member Function Documentation

◆ fill_in_contribution_to_jacobian() [1/2]

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

inlinevirtual

Compute the element's residual vector and the Jacobian matrix.

Reimplemented from oomph::GeneralisedElement.

  {
  
    //Get the analytical contribution from the basic Navier-Stokes element
    RefineableAxisymmetricQCrouzeixRaviartElement::
     fill_in_contribution_to_jacobian(residuals,jacobian);
    
 #ifdef USE_FD_FOR_DERIVATIVES_WRT_EXTERNAL_DATA
  
    //Get the off-diagonal terms by finite differencing
    this->fill_in_jacobian_from_external_interaction_by_fd(residuals,jacobian);
  
 #else
  
    //Get the off-diagonal terms analytically
    this->fill_in_off_diagonal_block_analytic(residuals,jacobian);
  
 #endif
  
   }

References oomph::AxisymmetricNavierStokesEquations::fill_in_contribution_to_jacobian().

◆ fill_in_contribution_to_jacobian() [2/2]

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

inlinevirtual

Compute the element's residual vector and the Jacobian matrix.

Reimplemented from oomph::GeneralisedElement.

  {
  
    //Get the analytical contribution from the basic Navier-Stokes element
    RefineableAxisymmetricQCrouzeixRaviartElement::
     fill_in_contribution_to_jacobian(residuals,jacobian);
    
 #ifdef USE_FD_FOR_DERIVATIVES_WRT_EXTERNAL_DATA
  
    //Get the off-diagonal terms by finite differencing
    this->fill_in_jacobian_from_external_interaction_by_fd(residuals,jacobian);
  
 #else
  
    //Get the off-diagonal terms analytically
    this->fill_in_off_diagonal_block_analytic(residuals,jacobian);
  
 #endif
  
   }

References oomph::AxisymmetricNavierStokesEquations::fill_in_contribution_to_jacobian().

◆ fill_in_contribution_to_jacobian_and_mass_matrix() [1/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::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.

   {
    //Call the standard (Broken) function
    //which will prevent these elements from being used
    //in eigenproblems until replaced.
    FiniteElement::fill_in_contribution_to_jacobian_and_mass_matrix(
      residuals,jacobian,mass_matrix);
   }

References oomph::GeneralisedElement::fill_in_contribution_to_jacobian_and_mass_matrix().

◆ fill_in_contribution_to_jacobian_and_mass_matrix() [2/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::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.

   {
    //Call the standard (Broken) function
    //which will prevent these elements from being used
    //in eigenproblems until replaced.
    FiniteElement::fill_in_contribution_to_jacobian_and_mass_matrix(
      residuals,jacobian,mass_matrix);
   }

References oomph::GeneralisedElement::fill_in_contribution_to_jacobian_and_mass_matrix().

◆ fill_in_off_diagonal_block_analytic() [1/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::fill_in_off_diagonal_block_analytic	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inline

Compute the contribution of the external degrees of freedom (temperatures) on the Navier-Stokes equations

   {
    //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_axi_nst[3];
    for(unsigned i=0;i<3;i++) 
     {u_nodal_axi_nst[i] = this->u_index_axi_nst(i);}
  
    //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();
    
    //Integers to store the local equations and unknowns
    int local_eqn=0, local_unknown=0;
    
    // Local storage for pointers to hang_info objects
    HangInfo *hang_info_pt=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_axi_nst(ipt,psif,dpsifdx,
                                                       testf,dtestfdx);
      
      //Premultiply the weights and the Jacobian
      double W = w*J;
  
      //Get the radius
      double r=0.0;
      for(unsigned l=0;l<n_node;l++)
       {
        r += this->nodal_position(l,0)*psif(l);
       }
      
      //Assemble the jacobian terms
      
      //Get the derivatives of the body force wrt the unknowns
      //of the external element
      DenseMatrix<double> dbody_dexternal_element_data;
  
      //Vector of global equation number corresponding to the external
      //element's data
      Vector<unsigned> global_eqn_number_of_external_element_data;
  
      //Get the appropriate derivatives
      this->get_dbody_force_axi_nst_dexternal_element_data(
       ipt,dbody_dexternal_element_data,
       global_eqn_number_of_external_element_data);
  
      //Find out how many external data there are
      const unsigned n_external_element_data = 
       global_eqn_number_of_external_element_data.size();
  
      //Loop over the test functions
      for(unsigned l=0;l<n_node;l++)
       {
        //Assemble the contributions of the temperature to 
        //the Navier--Stokes equations (which arise through the buoyancy
        //body-force term)
        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;
           }
          
          
          //Loop over the velocity components in the Navier--Stokes equtions
          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_axi_nst[i]);
             }
            else
             {
              // Local equation number
              local_eqn = this->nodal_local_eqn(l,u_nodal_axi_nst[i]);
             }
            
            if(local_eqn >= 0)
             {
              //Loop over the external data
              for(unsigned l2=0;l2<n_external_element_data;l2++)
               { 
                //Find the local equation number corresponding to the global
                //unknown
                local_unknown = 
                 this->local_eqn_number(
                  global_eqn_number_of_external_element_data[l2]);
                if(local_unknown >= 0)
                 {
                  //Add contribution to jacobian matrix
                  jacobian(local_eqn,local_unknown) 
                   += 
                   dbody_dexternal_element_data(i,l2)*testf(l)*hang_weight*r*W;
                 }
               }
             }
           }
         }
       }
     }
   }

References i, J, m, oomph::HangInfo::master_node_pt(), oomph::HangInfo::master_weight(), oomph::HangInfo::nmaster(), UniformPSDSelfTest::r, w, and oomph::QuadTreeNames::W.

◆ fill_in_off_diagonal_block_analytic() [2/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::fill_in_off_diagonal_block_analytic	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian
	)

inline

Compute the contribution of the external degrees of freedom (temperatures) on the Navier-Stokes equations

   {
    //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_axi_nst[3];
    for(unsigned i=0;i<3;i++) 
     {u_nodal_axi_nst[i] = this->u_index_axi_nst(i);}
  
    //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();
    
    //Integers to store the local equations and unknowns
    int local_eqn=0, local_unknown=0;
    
    // Local storage for pointers to hang_info objects
    HangInfo *hang_info_pt=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_axi_nst(ipt,psif,dpsifdx,
                                                       testf,dtestfdx);
      
      //Premultiply the weights and the Jacobian
      double W = w*J;
  
      //Get the radius
      double r=0.0;
      for(unsigned l=0;l<n_node;l++)
       {
        r += this->nodal_position(l,0)*psif(l);
       }
      
      //Assemble the jacobian terms
      
      //Get the derivatives of the body force wrt the unknowns
      //of the external element
      DenseMatrix<double> dbody_dexternal_element_data;
  
      //Vector of global equation number corresponding to the external
      //element's data
      Vector<unsigned> global_eqn_number_of_external_element_data;
  
      //Get the appropriate derivatives
      this->get_dbody_force_axi_nst_dexternal_element_data(
       ipt,dbody_dexternal_element_data,
       global_eqn_number_of_external_element_data);
  
      //Find out how many external data there are
      const unsigned n_external_element_data = 
       global_eqn_number_of_external_element_data.size();
  
      //Loop over the test functions
      for(unsigned l=0;l<n_node;l++)
       {
        //Assemble the contributions of the temperature to 
        //the Navier--Stokes equations (which arise through the buoyancy
        //body-force term)
        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;
           }
          
          
          //Loop over the velocity components in the Navier--Stokes equtions
          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_axi_nst[i]);
             }
            else
             {
              // Local equation number
              local_eqn = this->nodal_local_eqn(l,u_nodal_axi_nst[i]);
             }
            
            if(local_eqn >= 0)
             {
              //Loop over the external data
              for(unsigned l2=0;l2<n_external_element_data;l2++)
               { 
                //Find the local equation number corresponding to the global
                //unknown
                local_unknown = 
                 this->local_eqn_number(
                  global_eqn_number_of_external_element_data[l2]);
                if(local_unknown >= 0)
                 {
                  //Add contribution to jacobian matrix
                  jacobian(local_eqn,local_unknown) 
                   += 
                   dbody_dexternal_element_data(i,l2)*testf(l)*hang_weight*r*W;
                 }
               }
             }
           }
         }
       }
     }
   }

References i, J, m, oomph::HangInfo::master_node_pt(), oomph::HangInfo::master_weight(), oomph::HangInfo::nmaster(), UniformPSDSelfTest::r, w, and oomph::QuadTreeNames::W.

◆ further_build() [1/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::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. Also make sure that if the external geometric Data was ignored in the father it's also ignored in the sons

Reimplemented from oomph::RefineableElement.

   {
    RefineableAxisymmetricQCrouzeixRaviartElement::further_build();
  
    //Cast the pointer to the father element to the specific
    //element type
    RefineableQAxisymCrouzeixRaviartBoussinesqElement* 
     cast_father_element_pt
     = dynamic_cast<RefineableQAxisymCrouzeixRaviartBoussinesqElement*>(
      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();
  
    // Retain ignorance about external geometric data...
    if (!cast_father_element_pt->external_geometric_data_is_included())
     {
      this->ignore_external_geometric_data();
     }
  
   }

References oomph::ElementWithExternalElement::external_geometric_data_is_included(), oomph::RefineableAxisymmetricQCrouzeixRaviartElement::further_build(), and ra_pt().

◆ further_build() [2/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::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. Also make sure that if the external geometric Data was ignored in the father it's also ignored in the sons

Reimplemented from oomph::RefineableElement.

   {
    RefineableAxisymmetricQCrouzeixRaviartElement::further_build();
  
    //Cast the pointer to the father element to the specific
    //element type
    RefineableQAxisymCrouzeixRaviartBoussinesqElement* 
     cast_father_element_pt
     = dynamic_cast<RefineableQAxisymCrouzeixRaviartBoussinesqElement*>(
      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();
  
    // Retain ignorance about external geometric data...
    if (!cast_father_element_pt->external_geometric_data_is_included())
     {
      this->ignore_external_geometric_data();
     }
  
   }

References oomph::ElementWithExternalElement::external_geometric_data_is_included(), oomph::RefineableAxisymmetricQCrouzeixRaviartElement::further_build(), and ra_pt().

◆ get_body_force_axi_nst() [1/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::get_body_force_axi_nst	(	const double &	time,
		const unsigned &	ipt,
		const Vector< double > &	s,
		const Vector< double > &	x,
		Vector< double > &	body_force
	)

inlinevirtual

Overload get_body_force_nst() to return the temperature-dependent buoyancy force, using the temperature computed by the "external" advection diffusion element associated with integration point ipt.

Reimplemented from oomph::AxisymmetricNavierStokesEquations.

  {
  
   // Set interaction index -- there's only one interaction...
   const unsigned interaction=0;
   
   // Get a pointer to the external element that computes the
   // the temperature -- we know it's an advection diffusion element.
   const AxisymAdvectionDiffusionEquations* adv_diff_el_pt=
    dynamic_cast<AxisymAdvectionDiffusionEquations*>(
     external_element_pt(interaction,ipt));
   
   // Get the temperature interpolated from the external element
   const double interpolated_t =adv_diff_el_pt->
    interpolated_u_axi_adv_diff(external_element_local_coord(interaction,ipt));
   
   // Get vector that indicates the direction of gravity from
   // the Navier-Stokes equations
   Vector<double> gravity(AxisymmetricNavierStokesEquations::g());
   
   // Set the temperature-dependent body force:
   for (unsigned i=0;i<3;i++)
    {
     body_force[i] = -gravity[i]*interpolated_t*ra();
    }
  
  } // end overloaded body force

References Global_Parameters::body_force(), oomph::AxisymmetricNavierStokesEquations::g(), Gravity::gravity(), and i.

◆ get_body_force_axi_nst() [2/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::get_body_force_axi_nst	(	const double &	time,
		const unsigned &	ipt,
		const Vector< double > &	s,
		const Vector< double > &	x,
		Vector< double > &	body_force
	)

inlinevirtual

Overload get_body_force_nst() to return the temperature-dependent buoyancy force, using the temperature computed by the "external" advection diffusion element associated with integration point ipt.

Reimplemented from oomph::AxisymmetricNavierStokesEquations.

  {
  
   // Set interaction index -- there's only one interaction...
   const unsigned interaction=0;
   
   // Get a pointer to the external element that computes the
   // the temperature -- we know it's an advection diffusion element.
   const AxisymAdvectionDiffusionEquations* adv_diff_el_pt=
    dynamic_cast<AxisymAdvectionDiffusionEquations*>(
     external_element_pt(interaction,ipt));
   
   // Get the temperature interpolated from the external element
   const double interpolated_t =adv_diff_el_pt->
    interpolated_u_axi_adv_diff(external_element_local_coord(interaction,ipt));
   
   // Get vector that indicates the direction of gravity from
   // the Navier-Stokes equations
   Vector<double> gravity(AxisymmetricNavierStokesEquations::g());
   
   // Set the temperature-dependent body force:
   for (unsigned i=0;i<3;i++)
    {
     body_force[i] = -gravity[i]*interpolated_t*ra();
    }
  
  } // end overloaded body force

References Global_Parameters::body_force(), oomph::AxisymmetricNavierStokesEquations::g(), Gravity::gravity(), and i.

◆ get_dbody_force_axi_nst_dexternal_element_data() [1/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::get_dbody_force_axi_nst_dexternal_element_data	(	const unsigned &	ipt,
		DenseMatrix< double > &	result,
		Vector< unsigned > &	global_eqn_number
	)

Fill in the derivatives of the body force with respect to the external unknowns

////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////// Fill in the derivatives of the body force with respect to the external unknowns in the Navier–Stokes equations

 {
  // The interaction index is 0 in this case
  unsigned interaction=0;
  
  // Dynamic cast "other" element to correct type
  RefineableQAxisymAdvectionDiffusionBoussinesqElement* source_el_pt=
   dynamic_cast<RefineableQAxisymAdvectionDiffusionBoussinesqElement*>
   (external_element_pt(interaction,ipt));
  
  // Get vector that indicates the direction of gravity from
  // the Navier-Stokes equations
  Vector<double> gravity(AxisymmetricNavierStokesEquations::g());
  
  // Get the external element's derivatives
  Vector<double> du_adv_diff_ddata;
  source_el_pt->dinterpolated_u_axi_adv_diff_ddata(
   external_element_local_coord(interaction,ipt),du_adv_diff_ddata,
   global_eqn_number);
   
  //Find the number of external data
  unsigned n_external_element_data = du_adv_diff_ddata.size();
  //Set the size of the matrix to be returned
  result.resize(3,n_external_element_data);
  
  // Temperature-dependent body force:
  for (unsigned i=0;i<3;i++)
   {
    //Loop over the external data
    for(unsigned n=0;n<n_external_element_data;n++)
     {
      result(i,n) = -gravity[i]*du_adv_diff_ddata[n]*ra();
     }
   }
  
 } // end_of_get_dbody_force

References oomph::AxisymAdvectionDiffusionEquations::dinterpolated_u_axi_adv_diff_ddata(), oomph::AxisymmetricNavierStokesEquations::g(), Gravity::gravity(), i, n, and oomph::DenseMatrix< T >::resize().

◆ get_dbody_force_axi_nst_dexternal_element_data() [2/2]

void RefineableQAxisymCrouzeixRaviartBoussinesqElement::get_dbody_force_axi_nst_dexternal_element_data	(	const unsigned &	ipt,
		DenseMatrix< double > &	result,
		Vector< unsigned > &	global_eqn_number
	)

Fill in the derivatives of the body force with respect to the external unknowns

◆ ra() [1/2]

const double& RefineableQAxisymCrouzeixRaviartBoussinesqElement::ra ( ) const

inline

Access function for the Rayleigh number (const version)

74 {return *Ra_pt;}

◆ ra() [2/2]

const double& RefineableQAxisymCrouzeixRaviartBoussinesqElement::ra ( ) const

inline

Access function for the Rayleigh number (const version)

74 {return *Ra_pt;}

◆ ra_pt() [1/2]

double* & RefineableQAxisymCrouzeixRaviartBoussinesqElement::ra_pt ( )

inline

Access function for the pointer to the Rayleigh number.

77 {return Ra_pt;}

Referenced by further_build().

◆ ra_pt() [2/2]

double* & RefineableQAxisymCrouzeixRaviartBoussinesqElement::ra_pt ( )

inline

Access function for the pointer to the Rayleigh number.

77 {return Ra_pt;}

Member Data Documentation

◆ Default_Physical_Constant_Value

double RefineableQAxisymCrouzeixRaviartBoussinesqElement::Default_Physical_Constant_Value =0.0

staticprivate

The static default value of the Rayleigh number.

Set the default physical value for the Rayleigh number to be zero.

////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////

◆ Ra_pt

double * RefineableQAxisymCrouzeixRaviartBoussinesqElement::Ra_pt

private

Pointer to a private data member, the Rayleigh number.

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

axisym_heat_sphere/multi_domain_axisym_boussinesq_elements.h

Public Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RefineableQAxisymCrouzeixRaviartBoussinesqElement() [1/2]

◆ RefineableQAxisymCrouzeixRaviartBoussinesqElement() [2/2]

Member Function Documentation

◆ fill_in_contribution_to_jacobian() [1/2]

◆ fill_in_contribution_to_jacobian() [2/2]

◆ fill_in_contribution_to_jacobian_and_mass_matrix() [1/2]

◆ fill_in_contribution_to_jacobian_and_mass_matrix() [2/2]

◆ fill_in_off_diagonal_block_analytic() [1/2]

◆ fill_in_off_diagonal_block_analytic() [2/2]

◆ further_build() [1/2]

◆ further_build() [2/2]

◆ get_body_force_axi_nst() [1/2]

◆ get_body_force_axi_nst() [2/2]

◆ get_dbody_force_axi_nst_dexternal_element_data() [1/2]

◆ get_dbody_force_axi_nst_dexternal_element_data() [2/2]

◆ ra() [1/2]

◆ ra() [2/2]

◆ ra_pt() [1/2]

◆ ra_pt() [2/2]

Member Data Documentation

◆ Default_Physical_Constant_Value

◆ Ra_pt