#include <spherical_advection_diffusion_elements.h>

Inheritance diagram for oomph::SphericalAdvectionDiffusionEquations:

Public Types
typedef void(*	SphericalAdvectionDiffusionSourceFctPt) (const Vector< double > &x, double &f)

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

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

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

Public Member Functions
	SphericalAdvectionDiffusionEquations ()

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

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

virtual unsigned	u_index_spherical_adv_diff () const

double	du_dt_spherical_adv_diff (const unsigned &n) const

void	disable_ALE ()

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

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

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

	GeomObject (const unsigned &ndim)

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

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

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

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

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

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

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

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

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

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

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

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

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

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

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

Protected Attributes
double *	Pe_pt
	Pointer to global Peclet number. More...

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

SphericalAdvectionDiffusionSourceFctPt	Source_fct_pt
	Pointer to source function: More...

SphericalAdvectionDiffusionWindFctPt	Wind_fct_pt
	Pointer to wind function: More...

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Static Private Attributes
static double	Default_peclet_number = 0.0
	Static default value for the Peclet number. More...

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

Detailed Description

A class for all elements that solve the Advection Diffusion equations in a spherical polar coordinate system using isoparametric elements.

\[ Pe \mathbf{w}\cdot(\mathbf{x}) \nabla u = \nabla \cdot \left( \nabla u \right) + f(\mathbf{x}) \]

This contains the generic maths. Shape functions, geometric mapping etc. must get implemented in derived class.

Member Typedef Documentation

◆ SphericalAdvectionDiffusionSourceFctPt

typedef void(* oomph::SphericalAdvectionDiffusionEquations::SphericalAdvectionDiffusionSourceFctPt) (const Vector< double > &x, double &f)

Function pointer to source function fct(x,f(x)) – x is a Vector!

◆ SphericalAdvectionDiffusionWindFctPt

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

Function pointer to wind function fct(x,w(x)) – x is a Vector!

Constructor & Destructor Documentation

◆ SphericalAdvectionDiffusionEquations() [1/2]

oomph::SphericalAdvectionDiffusionEquations::SphericalAdvectionDiffusionEquations ( )

inline

Constructor: Initialise the Source_fct_pt and Wind_fct_pt to null and set (pointer to) Peclet number to default

                                            : Source_fct_pt(0), Wind_fct_pt(0)
     {
       // Set pointer to Peclet number to the default value zero
       Pe_pt = &Default_peclet_number;
       PeSt_pt = &Default_peclet_number;
     }

References Default_peclet_number, Pe_pt, and PeSt_pt.

◆ SphericalAdvectionDiffusionEquations() [2/2]

oomph::SphericalAdvectionDiffusionEquations::SphericalAdvectionDiffusionEquations ( const SphericalAdvectionDiffusionEquations & dummy )

delete

Broken copy constructor.

Member Function Documentation

◆ compute_error()

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

virtual

Get error against and norm of exact solution.

Validate against exact solution

Solution is provided via function pointer. Plot error at a given number of plot points.

Reimplemented from oomph::FiniteElement.

   {
     // Initialise
     error = 0.0;
     norm = 0.0;
  
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Vector for coordintes
     Vector<double> x(2);
  
     // Find out how many nodes there are in the element
     unsigned n_node = nnode();
  
     Shape psi(n_node);
  
     // Set the value of n_intpt
     unsigned n_intpt = integral_pt()->nweight();
  
     // Tecplot header info
     outfile << "ZONE" << std::endl;
  
     // Exact solution Vector (here a scalar)
     Vector<double> exact_soln(1);
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < 2; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Get jacobian of mapping
       double J = J_eulerian(s);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Get x position as Vector
       interpolated_x(s, x);
  
       // Get FE function value
       double u_fe = interpolated_u_spherical_adv_diff(s);
  
       // Get exact solution at this point
       (*exact_soln_pt)(x, exact_soln);
  
       // Output x,y,...,error
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << x[i] << " ";
       }
       outfile << exact_soln[0] << " " << exact_soln[0] - u_fe << std::endl;
  
       // Add to error and norm
       norm += exact_soln[0] * exact_soln[0] * W;
       error += (exact_soln[0] - u_fe) * (exact_soln[0] - u_fe) * W;
     }
   }

References calibrate::error, ProblemParameters::exact_soln(), i, oomph::FiniteElement::integral_pt(), interpolated_u_spherical_adv_diff(), oomph::FiniteElement::interpolated_x(), J, oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::FiniteElement::nnode(), oomph::Integral::nweight(), s, w, oomph::QuadTreeNames::W, oomph::Integral::weight(), and plotDoE::x.

◆ dinterpolated_u_adv_diff_ddata()

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

inlinevirtual

Return derivative of u at point s with respect to all data that can affect its value. In addition, return the global equation numbers corresponding to the data. This is virtual so that it can be overloaded in the refineable version

Reimplemented in oomph::RefineableSphericalAdvectionDiffusionEquations.

     {
       // Find number of nodes
       const unsigned n_node = nnode();
  
       // Get the nodal index at which the unknown is stored
       const unsigned u_nodal_index = u_index_spherical_adv_diff();
  
       // Local shape function
       Shape psi(n_node);
  
       // Find values of shape function
       shape(s, psi);
  
       // Find the number of dofs associated with interpolated u
       unsigned n_u_dof = 0;
       for (unsigned l = 0; l < n_node; l++)
       {
         int global_eqn = this->node_pt(l)->eqn_number(u_nodal_index);
         // If it's positive add to the count
         if (global_eqn >= 0)
         {
           ++n_u_dof;
         }
       }
  
       // Now resize the storage schemes
       du_ddata.resize(n_u_dof, 0.0);
       global_eqn_number.resize(n_u_dof, 0);
  
       // Loop over the nodes again and set the derivatives
       unsigned count = 0;
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the global equation number
         int global_eqn = this->node_pt(l)->eqn_number(u_nodal_index);
         // If it's positive
         if (global_eqn >= 0)
         {
           // Set the global equation number
           global_eqn_number[count] = global_eqn;
           // Set the derivative with respect to the unknown
           du_ddata[count] = psi[l];
           // Increase the counter
           ++count;
         }
       }
     }

References oomph::Data::eqn_number(), oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), s, oomph::FiniteElement::shape(), and u_index_spherical_adv_diff().

◆ disable_ALE()

void oomph::SphericalAdvectionDiffusionEquations::disable_ALE ( )

inlinevirtual

Disable ALE – empty overload to suppress warning. ALE isn't implemented anyway

Reimplemented from oomph::FiniteElement.

127 {}

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

◆ dshape_and_dtest_eulerian_at_knot_spherical_adv_diff()

virtual double oomph::SphericalAdvectionDiffusionEquations::dshape_and_dtest_eulerian_at_knot_spherical_adv_diff	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping

Implemented in oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >.

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::fill_in_generic_residual_contribution_spherical_adv_diff(), and fill_in_generic_residual_contribution_spherical_adv_diff().

◆ dshape_and_dtest_eulerian_spherical_adv_diff()

virtual double oomph::SphericalAdvectionDiffusionEquations::dshape_and_dtest_eulerian_spherical_adv_diff	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

Shape/test functions and derivs w.r.t. to global coords at local coord. s; return Jacobian of mapping

Implemented in oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >.

◆ du_dt_spherical_adv_diff()

double oomph::SphericalAdvectionDiffusionEquations::du_dt_spherical_adv_diff ( const unsigned & n ) const

inline

du/dt at local node n. Uses suitably interpolated value for hanging nodes.

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

References oomph::TimeStepper::is_steady(), n, oomph::FiniteElement::nodal_value(), oomph::FiniteElement::node_pt(), oomph::TimeStepper::ntstorage(), plotPSD::t, oomph::GeomObject::time_stepper_pt(), oomph::Data::time_stepper_pt(), u_index_spherical_adv_diff(), and oomph::TimeStepper::weight().

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::fill_in_generic_residual_contribution_spherical_adv_diff(), and fill_in_generic_residual_contribution_spherical_adv_diff().

◆ fill_in_contribution_to_jacobian()

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

inlinevirtual

Add the element's contribution to its residual vector and the element Jacobian matrix (wrapper)

Reimplemented from oomph::FiniteElement.

     {
       // Call the generic routine with the flag set to 1
       fill_in_generic_residual_contribution_spherical_adv_diff(
         residuals, jacobian, GeneralisedElement::Dummy_matrix, 1);
     }

References oomph::GeneralisedElement::Dummy_matrix, and fill_in_generic_residual_contribution_spherical_adv_diff().

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

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

void oomph::SphericalAdvectionDiffusionEquations::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 residual vector and the element Jacobian matrix (wrapper) and mass matrix

Reimplemented from oomph::GeneralisedElement.

     {
       // Call the generic routine with the flag set to 2
       fill_in_generic_residual_contribution_spherical_adv_diff(
         residuals, jacobian, mass_matrix, 2);
     }

References fill_in_generic_residual_contribution_spherical_adv_diff().

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

◆ fill_in_contribution_to_residuals()

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

inlinevirtual

Add the element's contribution to its residual vector (wrapper)

Reimplemented from oomph::GeneralisedElement.

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

References oomph::GeneralisedElement::Dummy_matrix, and fill_in_generic_residual_contribution_spherical_adv_diff().

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

◆ fill_in_generic_residual_contribution_spherical_adv_diff()

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

protectedvirtual

Add the element's contribution to its residual vector only (if flag=and/or element Jacobian matrix

Compute element residual Vector and/or element Jacobian matrix

flag=1: compute both flag=0: compute only residual Vector

Pure version without hanging nodes

Reimplemented in oomph::RefineableSphericalAdvectionDiffusionEquations.

   {
     // Find out how many nodes there are
     const unsigned n_node = nnode();
  
     // Get the nodal index at which the unknown is stored
     const unsigned u_nodal_index = u_index_spherical_adv_diff();
  
     // Set up memory for the shape and test functions
     Shape psi(n_node), test(n_node);
     DShape dpsidx(n_node, 2), dtestdx(n_node, 2);
  
     // Set the value of n_intpt
     const unsigned n_intpt = integral_pt()->nweight();
  
     // Set the Vector to hold local coordinates
     Vector<double> s(2);
  
     // Get Physical Variables from Element
     const double scaled_peclet = pe();
  
     // Get peclet number multiplied by Strouhal number
     const double scaled_peclet_st = pe_st();
  
     // Integers used to store the local equation number and local unknown
     // indices for the residuals and jacobians
     int local_eqn = 0, local_unknown = 0;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of s
       for (unsigned i = 0; i < 2; i++) s[i] = integral_pt()->knot(ipt, i);
  
       // Get the integral weight
       double w = integral_pt()->weight(ipt);
  
       // Call the derivatives of the shape and test functions
       double J = dshape_and_dtest_eulerian_at_knot_spherical_adv_diff(
         ipt, psi, dpsidx, test, dtestdx);
  
       // Premultiply the weights and the Jacobian
       double W = w * J;
  
       // Calculate local values of the solution and its derivatives
       // Allocate
       double interpolated_u = 0.0;
       double dudt = 0.0;
       Vector<double> interpolated_x(2, 0.0);
       Vector<double> interpolated_dudx(2, 0.0);
  
       // Calculate function value and derivatives:
       //-----------------------------------------
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Get the value at the node
         double u_value = raw_nodal_value(l, u_nodal_index);
         interpolated_u += u_value * psi(l);
         dudt += du_dt_spherical_adv_diff(l) * psi(l);
         // Loop over the two coordinates directions
         for (unsigned j = 0; j < 2; j++)
         {
           interpolated_x[j] += raw_nodal_position(l, j) * psi(l);
           interpolated_dudx[j] += u_value * dpsidx(l, j);
         }
       }
  
       // Get source function
       //-------------------
       double source;
       get_source_spherical_adv_diff(ipt, interpolated_x, source);
  
  
       // Get wind
       //--------
       Vector<double> wind(3);
       get_wind_spherical_adv_diff(ipt, s, interpolated_x, wind);
  
       // r is the first position component
       double r = interpolated_x[0];
       // theta is the second position component
       double sin_th = sin(interpolated_x[1]);
       // dS is the area weighting
       double dS = r * r * sin_th;
  
       // TEMPERATURE EQUATION (Neglected viscous dissipation)
       // Assemble residuals and Jacobian
       //--------------------------------
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Set the local equation number
         local_eqn = nodal_local_eqn(l, u_nodal_index);
  
         /*IF it's not a boundary condition*/
         if (local_eqn >= 0)
         {
           // Add body force/source term
           residuals[local_eqn] -=
             (scaled_peclet_st * dudt + source) * dS * test(l) * W;
  
           // The Advection Diffusion bit itself
           residuals[local_eqn] -=
             // radial terms
             (dS * interpolated_dudx[0] *
                (scaled_peclet * wind[0] * test(l) + dtestdx(l, 0)) +
              // azimuthal terms
              (sin_th * interpolated_dudx[1] *
               (r * scaled_peclet * wind[1] * test(l) + dtestdx(l, 1)))) *
             W;
  
  
           // Calculate the jacobian
           //-----------------------
           if (flag)
           {
             // Loop over the velocity shape functions again
             for (unsigned l2 = 0; l2 < n_node; l2++)
             {
               // Set the number of the unknown
               local_unknown = nodal_local_eqn(l2, u_nodal_index);
  
               // If at a non-zero degree of freedom add in the entry
               if (local_unknown >= 0)
               {
                 // Mass matrix term
                 jacobian(local_eqn, local_unknown) -=
                   scaled_peclet_st * test(l) * psi(l2) *
                   node_pt(l2)->time_stepper_pt()->weight(1, 0) * dS * W;
  
                 // add the mass matrix term
                 if (flag == 2)
                 {
                   mass_matrix(local_eqn, local_unknown) +=
                     scaled_peclet_st * test(l) * psi(l2) * dS * W;
                 }
  
                 // Assemble Jacobian term
                 jacobian(local_eqn, local_unknown) -=
                   // radial terms
                   (dS * dpsidx(l2, 0) *
                      (scaled_peclet * wind[0] * test(l) + dtestdx(l, 0)) +
                    // azimuthal terms
                    (sin_th * dpsidx(l2, 1) *
                     (r * scaled_peclet * wind[1] * test(l) + dtestdx(l, 1)))) *
                   W;
               }
             }
           }
         }
       }
  
  
     } // End of loop over integration points
   }

References dshape_and_dtest_eulerian_at_knot_spherical_adv_diff(), du_dt_spherical_adv_diff(), get_source_spherical_adv_diff(), get_wind_spherical_adv_diff(), i, oomph::FiniteElement::integral_pt(), oomph::FiniteElement::interpolated_x(), J, j, oomph::Integral::knot(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::node_pt(), oomph::Integral::nweight(), pe(), pe_st(), UniformPSDSelfTest::r, oomph::FiniteElement::raw_nodal_position(), oomph::FiniteElement::raw_nodal_value(), s, sin(), TestProblem::source(), Eigen::test, oomph::Data::time_stepper_pt(), u_index_spherical_adv_diff(), w, oomph::QuadTreeNames::W, oomph::Integral::weight(), and oomph::TimeStepper::weight().

Referenced by fill_in_contribution_to_jacobian(), fill_in_contribution_to_jacobian_and_mass_matrix(), and fill_in_contribution_to_residuals().

◆ get_flux()

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

inline

Get flux:

\[ \mbox{flux}[i] = \nabla u = \mbox{d}u / \mbox{d} r + 1/r \mbox{d}u / \mbox{d} \theta \]

     {
       // Find out how many nodes there are in the element
       const unsigned n_node = nnode();
  
       // Get the nodal index at which the unknown is stored
       const unsigned u_nodal_index = u_index_spherical_adv_diff();
  
       // Set up memory for the shape and test functions
       Shape psi(n_node);
       DShape dpsidx(n_node, 2);
  
       // Call the derivatives of the shape and test functions
       dshape_eulerian(s, psi, dpsidx);
  
       // Initialise to zero
       for (unsigned j = 0; j < 2; j++)
       {
         flux[j] = 0.0;
       }
  
       // Loop over nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         const double u_value = this->nodal_value(l, u_nodal_index);
         const double r = this->nodal_position(l, 0);
         // Add in the derivative directions
         flux[0] += u_value * dpsidx(l, 0);
         flux[1] += u_value * dpsidx(l, 1) / r;
       }
     }

References oomph::FiniteElement::dshape_eulerian(), ProblemParameters::flux(), j, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::nodal_value(), UniformPSDSelfTest::r, s, and u_index_spherical_adv_diff().

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

◆ get_source_spherical_adv_diff()

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

inlinevirtual

Get source term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations

     {
       // If no source function has been set, return zero
       if (Source_fct_pt == 0)
       {
         source = 0.0;
       }
       else
       {
         // Get source strength
         (*Source_fct_pt)(x, source);
       }
     }

References TestProblem::source(), Source_fct_pt, and plotDoE::x.

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::fill_in_generic_residual_contribution_spherical_adv_diff(), and fill_in_generic_residual_contribution_spherical_adv_diff().

◆ get_wind_spherical_adv_diff()

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

inlinevirtual

Get wind at (Eulerian) position x and/or local coordinate s. This function is virtual to allow overloading in multi-physics problems where the wind function might be determined by another system of equations

Reimplemented in oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement.

     {
       // If no wind function has been set, return zero
       if (Wind_fct_pt == 0)
       {
         for (unsigned i = 0; i < 3; i++)
         {
           wind[i] = 0.0;
         }
       }
       else
       {
         // Get wind
         (*Wind_fct_pt)(x, wind);
       }
     }

References i, Wind_fct_pt, and plotDoE::x.

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::fill_in_generic_residual_contribution_spherical_adv_diff(), fill_in_generic_residual_contribution_spherical_adv_diff(), and output().

◆ interpolated_u_spherical_adv_diff()

double oomph::SphericalAdvectionDiffusionEquations::interpolated_u_spherical_adv_diff ( const Vector< double > & s ) const

inline

Return FE representation of function value u(s) at local coordinate s.

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

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

Referenced by compute_error(), oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::get_body_force_spherical_nst(), oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::output(), and output().

◆ operator=()

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

delete

Broken assignment operator.

◆ output() [1/4]

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

inlinevirtual

C_style output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >.

     {
       unsigned n_plot = 5;
       output(file_pt, n_plot);
     }

References output().

◆ output() [2/4]

void oomph::SphericalAdvectionDiffusionEquations::output	(	FILE *	file_pt,
		const unsigned &	nplot
	)

virtual

C-style output FE representation of soln: r,z,u at n_plot^2 plot points

C-style output function:

r,z,u

nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Tecplot header info
     fprintf(file_pt, "%s", tecplot_zone_string(nplot).c_str());
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       for (unsigned i = 0; i < 2; i++)
       {
         fprintf(file_pt, "%g ", interpolated_x(s, i));
       }
       // Write Cartesian coordinates
       double r = interpolated_x(s, 0);
       double theta = interpolated_x(s, 1);
       fprintf(file_pt, "%g %g ", r * sin(theta), r * cos(theta));
  
       fprintf(file_pt, "%g \n", interpolated_u_spherical_adv_diff(s));
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(file_pt, nplot);
   }

References cos(), oomph::FiniteElement::get_s_plot(), i, interpolated_u_spherical_adv_diff(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), UniformPSDSelfTest::r, s, sin(), oomph::FiniteElement::tecplot_zone_string(), BiharmonicTestFunctions2::theta, and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output() [3/4]

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

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >.

     {
       unsigned nplot = 5;
       output(outfile, nplot);
     }

Referenced by output(), and oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >::output().

◆ output() [4/4]

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

virtual

Output FE representation of soln: r,z,u at nplot^2 plot points

Output function:

r,z,u,w_r,w_z

nplot points in each coordinate direction

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Get Eulerian coordinate of plot point
       Vector<double> x(2);
       interpolated_x(s, x);
  
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << x[i] << " ";
       }
  
       // Convert to Cartesians
       outfile << x[0] * sin(x[1]) << " " << x[0] * cos(x[1]) << " ";
       // Output concentration
       outfile << this->interpolated_u_spherical_adv_diff(s) << " ";
  
       // Get the wind
       Vector<double> wind(2);
       // Dummy ipt argument needed... ?
       unsigned ipt = 0;
       get_wind_spherical_adv_diff(ipt, s, x, wind);
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << wind[i] << " ";
       }
       outfile << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

References cos(), oomph::FiniteElement::get_s_plot(), get_wind_spherical_adv_diff(), i, interpolated_u_spherical_adv_diff(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, sin(), oomph::FiniteElement::tecplot_zone_string(), oomph::FiniteElement::write_tecplot_zone_footer(), and plotDoE::x.

◆ output_fct()

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

virtual

Output exact soln: r,z,u_exact at nplot^2 plot points.

Output exact solution

Solution is provided via function pointer. Plot at a given number of plot points.

r,z,u_exact

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >.

   {
     // Vector of local coordinates
     Vector<double> s(2);
  
     // Vector for coordintes
     Vector<double> x(2);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Exact solution Vector (here a scalar)
     Vector<double> exact_soln(1);
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Get x position as Vector
       interpolated_x(s, x);
  
       // Get exact solution at this point
       (*exact_soln_pt)(x, exact_soln);
  
       // Output x,y,...,u_exact
       for (unsigned i = 0; i < 2; i++)
       {
         outfile << x[i] << " ";
       }
       outfile << exact_soln[0] << std::endl;
     }
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

References ProblemParameters::exact_soln(), oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), oomph::FiniteElement::write_tecplot_zone_footer(), and plotDoE::x.

Referenced by oomph::QSphericalAdvectionDiffusionElement< NNODE_1D >::output_fct().

◆ pe()

const double& oomph::SphericalAdvectionDiffusionEquations::pe ( ) const

inline

Peclet number.

     {
       return *Pe_pt;
     }

References Pe_pt.

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::fill_in_generic_residual_contribution_spherical_adv_diff(), fill_in_generic_residual_contribution_spherical_adv_diff(), and oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement::fill_in_off_diagonal_jacobian_blocks_analytic().

◆ pe_pt()

double*& oomph::SphericalAdvectionDiffusionEquations::pe_pt ( )

inline

Pointer to Peclet number.

     {
       return Pe_pt;
     }

References Pe_pt.

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

◆ pe_st()

const double& oomph::SphericalAdvectionDiffusionEquations::pe_st ( ) const

inline

Peclet number multiplied by Strouhal number.

     {
       return *PeSt_pt;
     }

References PeSt_pt.

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::fill_in_generic_residual_contribution_spherical_adv_diff(), and fill_in_generic_residual_contribution_spherical_adv_diff().

◆ pe_st_pt()

double*& oomph::SphericalAdvectionDiffusionEquations::pe_st_pt ( )

inline

Pointer to Peclet number multipled by Strouha number.

     {
       return PeSt_pt;
     }

References PeSt_pt.

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

◆ self_test()

unsigned oomph::SphericalAdvectionDiffusionEquations::self_test ( )

virtual

Self-test: Return 0 for OK.

Reimplemented from oomph::FiniteElement.

   {
     bool passed = true;
  
     // Check lower-level stuff
     if (FiniteElement::self_test() != 0)
     {
       passed = false;
     }
  
     // Return verdict
     if (passed)
     {
       return 0;
     }
     else
     {
       return 1;
     }
   }

References oomph::FiniteElement::self_test().

◆ source_fct_pt() [1/2]

SphericalAdvectionDiffusionSourceFctPt& oomph::SphericalAdvectionDiffusionEquations::source_fct_pt ( )

inline

Access function: Pointer to source function.

     {
       return Source_fct_pt;
     }

References Source_fct_pt.

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

◆ source_fct_pt() [2/2]

SphericalAdvectionDiffusionSourceFctPt oomph::SphericalAdvectionDiffusionEquations::source_fct_pt ( ) const

inline

Access function: Pointer to source function. Const version.

     {
       return Source_fct_pt;
     }

References Source_fct_pt.

◆ u_index_spherical_adv_diff()

virtual unsigned oomph::SphericalAdvectionDiffusionEquations::u_index_spherical_adv_diff ( ) const

inlinevirtual

Return the index at which the unknown value is stored. The default value, 0, is appropriate for single-physics problems, when there is only one variable, the value that satisfies the spherical advection-diffusion equation. In derived multi-physics elements, this function should be overloaded to reflect the chosen storage scheme. Note that these equations require that the unknown is always stored at the same index at each node.

Reimplemented in oomph::RefineableBuoyantQSphericalCrouzeixRaviartElement.

     {
       return 0;
     }

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::dinterpolated_u_adv_diff_ddata(), dinterpolated_u_adv_diff_ddata(), du_dt_spherical_adv_diff(), oomph::RefineableSphericalAdvectionDiffusionEquations::fill_in_generic_residual_contribution_spherical_adv_diff(), fill_in_generic_residual_contribution_spherical_adv_diff(), get_flux(), oomph::RefineableSphericalAdvectionDiffusionEquations::get_interpolated_values(), interpolated_u_spherical_adv_diff(), and oomph::SphericalAdvectionDiffusionFluxElement< ELEMENT >::SphericalAdvectionDiffusionFluxElement().

◆ wind_fct_pt() [1/2]

SphericalAdvectionDiffusionWindFctPt& oomph::SphericalAdvectionDiffusionEquations::wind_fct_pt ( )

inline

Access function: Pointer to wind function.

     {
       return Wind_fct_pt;
     }

References Wind_fct_pt.

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

◆ wind_fct_pt() [2/2]

SphericalAdvectionDiffusionWindFctPt oomph::SphericalAdvectionDiffusionEquations::wind_fct_pt ( ) const

inline

Access function: Pointer to wind function. Const version.

     {
       return Wind_fct_pt;
     }

References Wind_fct_pt.

Member Data Documentation

◆ Default_peclet_number

double oomph::SphericalAdvectionDiffusionEquations::Default_peclet_number = 0.0

staticprivate

Static default value for the Peclet number.

2D Steady Axisymmetric Advection Diffusion elements

Default value for Peclet number

Referenced by SphericalAdvectionDiffusionEquations().

◆ Pe_pt

double* oomph::SphericalAdvectionDiffusionEquations::Pe_pt

protected

Pointer to global Peclet number.

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::further_build(), pe(), pe_pt(), and SphericalAdvectionDiffusionEquations().

◆ PeSt_pt

double* oomph::SphericalAdvectionDiffusionEquations::PeSt_pt

protected

Pointer to global Peclet number multiplied by Strouhal number.

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::further_build(), pe_st(), pe_st_pt(), and SphericalAdvectionDiffusionEquations().

◆ Source_fct_pt

SphericalAdvectionDiffusionSourceFctPt oomph::SphericalAdvectionDiffusionEquations::Source_fct_pt

protected

Pointer to source function:

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::further_build(), get_source_spherical_adv_diff(), and source_fct_pt().

◆ Wind_fct_pt

SphericalAdvectionDiffusionWindFctPt oomph::SphericalAdvectionDiffusionEquations::Wind_fct_pt

protected

Pointer to wind function:

Referenced by oomph::RefineableSphericalAdvectionDiffusionEquations::further_build(), get_wind_spherical_adv_diff(), and wind_fct_pt().

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

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ SphericalAdvectionDiffusionSourceFctPt

◆ SphericalAdvectionDiffusionWindFctPt

Constructor & Destructor Documentation

◆ SphericalAdvectionDiffusionEquations() [1/2]

◆ SphericalAdvectionDiffusionEquations() [2/2]

Member Function Documentation

◆ compute_error()

◆ dinterpolated_u_adv_diff_ddata()

◆ disable_ALE()

◆ dshape_and_dtest_eulerian_at_knot_spherical_adv_diff()

◆ dshape_and_dtest_eulerian_spherical_adv_diff()

◆ du_dt_spherical_adv_diff()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_spherical_adv_diff()

◆ get_flux()

◆ get_source_spherical_adv_diff()

◆ get_wind_spherical_adv_diff()

◆ interpolated_u_spherical_adv_diff()

◆ operator=()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct()

◆ pe()

◆ pe_pt()

◆ pe_st()

◆ pe_st_pt()

◆ self_test()

◆ source_fct_pt() [1/2]

◆ source_fct_pt() [2/2]

◆ u_index_spherical_adv_diff()

◆ wind_fct_pt() [1/2]

◆ wind_fct_pt() [2/2]

Member Data Documentation

◆ Default_peclet_number

◆ Pe_pt

◆ PeSt_pt

◆ Source_fct_pt

◆ Wind_fct_pt