Inheritance diagram for OrrSommerfeldEquations< DIM >:

Public Member Functions
	OrrSommerfeldEquations ()
	Constructor. More...

virtual double	u (const unsigned &n, const unsigned &i) const =0

virtual double	p (const unsigned &n, const unsigned &i) const =0

virtual unsigned	npres () const =0

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

void	get_base_flow (const Vector< double > &s, double &U, double &Uz)

double *&	re_pt ()

double *&	a_real_pt ()

double *&	a_imag_pt ()

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

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

void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Assemble the contributions to the jacobian and mass matrices. More...

double	interpolated_p (const Vector< double > &s, const unsigned &i) const
	Return FE representation of the pressure. More...

double	interpolated_u (const Vector< double > &s, const unsigned &i) const
	Return FE representation of function value u(s) at local coordinate s. 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 &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	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

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 (FILE *file_pt)

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	self_test ()

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const =0

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)

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_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)

virtual void	fill_in_contribution_to_residuals (Vector< double > &residuals)

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
DenseMatrix< int >	U_local_eqn
	Array to hold local eqn numbers: Local_eqn[n] (=-1 for BC) More...

DenseMatrix< int >	P_local_eqn

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

Private Attributes
double *	Re_pt

double *	A_Real_pt

double *	A_Imag_pt

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 > &)

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

template<unsigned DIM>
class OrrSommerfeldEquations< DIM >

A class for all elements that solve the simple orr-sommerfeld equations for a given base flow. The formulation is in primitive variables and so contains quite a large pressure NULL space. The equations are derived from the Navier–Stokes equations by posing a perturbation to an axially uniform base-flow of the form:

\[ u = U(z) + \hat{u}, \quad v = \hat{v}, \quad w = \hat{w} \]

where the perturbation is of the form

\[ \hat{u} = \mbox{e}^{\lambda t + \mbox{i}\alpha x} \]

The equations are split into real and imaginary parts and is currently only implemented for the two-dimensional equations. This contains the generic maths. Shape functions, geometric mapping etc. must get implemented in derived class.

Constructor & Destructor Documentation

◆ OrrSommerfeldEquations()

template<unsigned DIM>

OrrSommerfeldEquations< DIM >::OrrSommerfeldEquations ( )

inline

Constructor.

72 {}

Member Function Documentation

◆ a_imag_pt()

template<unsigned DIM>

double* & OrrSommerfeldEquations< DIM >::a_imag_pt ( )

inline

98 {return A_Imag_pt;}

OrrSommerfeldEquations::A_Imag_pt

double * A_Imag_pt

Definition: orr_sommerfeld.cc:556

◆ a_real_pt()

template<unsigned DIM>

double* & OrrSommerfeldEquations< DIM >::a_real_pt ( )

inline

96 {return A_Real_pt;}

OrrSommerfeldEquations::A_Real_pt

double * A_Real_pt

Definition: orr_sommerfeld.cc:555

◆ dshape_eulerian()

template<unsigned DIM>

virtual double OrrSommerfeldEquations< DIM >::dshape_eulerian	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx
	)		const

protectedpure virtual

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

◆ dshape_eulerian_at_knot()

template<unsigned DIM>

virtual double OrrSommerfeldEquations< DIM >::dshape_eulerian_at_knot	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx
	)		const

protectedpure virtual

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

Reimplemented from oomph::FiniteElement.

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

template<unsigned DIM>

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

inlinevirtual

Assemble the contributions to the jacobian and mass matrices.

Reimplemented from oomph::GeneralisedElement.

   {
    //Find out how many nodes there are
    unsigned n_node = nnode();
    //Number of pressure degrees of freedom
    unsigned n_pres = npres();
  
    //Set up memory for the shape functions
    Shape psi(n_node);
    DShape dpsidx(n_node,DIM);
    Shape psip(n_pres);
  
    //Set the value of n_intpt
    unsigned n_intpt = integral_pt()->nweight();
    
    //Set the Vector to hold local coordinates
    Vector<double> s(DIM);
    
    //Integers to store the local equation and unknown numbers
    int local_eqn=0, local_unknown=0;
  
    //Storage for the base flow
    double Ubar=0.0, Ubardz=0.0;
  
    //Get the Reynolds number
    double Re = *Re_pt;
    double A_real = *A_Real_pt;
    double A_imag = *A_Imag_pt;
  
    //Loop over the integration points
    for(unsigned ipt=0;ipt<n_intpt;ipt++)
     {
      //Assign values of s
      for(unsigned i=0;i<DIM;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_eulerian_at_knot(ipt,
                                         psi,dpsidx);
  
      //Get the pressure shape functions
      pshape(s,psip);
  
      //Get the base velocity field
      get_base_flow(s,Ubar,Ubardz);
      
      //Calculate the real and imaginary parts of our variable B
      double B_real = (A_real*A_real - A_imag*A_imag)/Re - A_imag*Ubar;
      double B_imag = 2.0*A_real*A_imag/Re + A_real*Ubar;
  
      //Premultiply the weights and the Jacobian
      double W = w*J;
  
      //Assemble the contributions to the matrices
      
      // Loop over the test functions
      for(unsigned l=0;l<n_node;l++)
       {
        //REAL PART OF THE U EQUATION
        //Get the local equation
        local_eqn = U_local_eqn(l,0);
        /*IF it's not a boundary condition*/
        if(local_eqn >= 0)
         {
          //Loop over the shape functions
          for(unsigned l2=0;l2<n_node;l2++)
           { 
            //Get the contribution from the real part of u
            local_unknown = U_local_eqn(l2,0);
            //If at a non-zero degree of freedom add in the entry
            if(local_unknown >= 0)
             {
              //Mass matrix
              mass_matrix(local_eqn,local_unknown) += psi(l)*psi(l2)*W;
              //Jacobian terms
              jacobian(local_eqn,local_unknown) -= 
               B_real*psi(l2)*psi(l)*W;
              jacobian(local_eqn,local_unknown) -= 
               (1.0/Re)*dpsidx(l2,0)*dpsidx(l,0)*W;
             }
  
            //Get the contribution from the imaginary part of u
            local_unknown = U_local_eqn(l2,1);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += B_imag*psi(l2)*psi(l)*W;
             }
  
            //Get the contribution from the real part of w
            local_unknown = U_local_eqn(l2,2);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) -= Ubardz*psi(l2)*psi(l)*W;
             }
  
           }
          
          //Loop over the pressure shape functions
          for(unsigned l2=0;l2<n_pres;l2++)
           {
            //Get the real pressure contribution to the equation
            local_unknown = P_local_eqn(l2,0);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += 
               A_imag*psip(l2)*psi(l)*W;
             }
            //Get the imaginary pressure contribution to the equation
            local_unknown = P_local_eqn(l2,1);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += 
               A_real*psip(l2)*psi(l)*W;
             }
           }
         }
  
        //IMAGINARY PART OF THE U EQUATION
        //Get the local equation
        local_eqn = U_local_eqn(l,1);
        /*IF it's not a boundary condition*/
        if(local_eqn >= 0)
         {
          //Loop over the shape functions
          for(unsigned l2=0;l2<n_node;l2++)
           { 
            //Get the contribution from the real part of u
            local_unknown = U_local_eqn(l2,0);
            //If at a non-zero degree of freedom add in the entry
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) -= B_imag*psi(l2)*psi(l)*W;
             }
  
            //Get the contribution from the imaginary part of u
            local_unknown = U_local_eqn(l2,1);
            if(local_unknown >= 0)
             {
              //Mass matrix
              mass_matrix(local_eqn,local_unknown) += psi(l)*psi(l2)*W;
              //Jacobian terms
              jacobian(local_eqn,local_unknown) -= B_real*psi(l2)*psi(l)*W;
              jacobian(local_eqn,local_unknown) -=
               (1.0/Re)*dpsidx(l2,0)*dpsidx(l,0)*W;
             }
  
            //Get the contibution from the imaginary part of w
            local_unknown = U_local_eqn(l2,3);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) -= Ubardz*psi(l2)*psi(l)*W;
             }
           }
  
          //Loop over the pressure shape functions
          for(unsigned l2=0;l2<n_pres;l2++)
           {
            //Get the real pressure contribution to the equation
            local_unknown = P_local_eqn(l2,0);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) -= 
               A_real*psip(l2)*psi(l)*W;
             }
            //Get the imaginary pressure contribution to the equation
            local_unknown = P_local_eqn(l2,1);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) +=
               A_imag*psip(l2)*psi(l)*W;
             }
           }
         }
  
        
        //REAL PART OF THE W EQUATION
        //Get the local equation
        local_eqn = U_local_eqn(l,2);
        /*IF it's not a boundary condition*/
        if(local_eqn >= 0)
         {
          //Loop over the shape functions
          for(unsigned l2=0;l2<n_node;l2++)
           { 
            //Get the contribution from the real part of w
            local_unknown = U_local_eqn(l2,2);
            //If at a non-zero degree of freedom add in the entry
            if(local_unknown >= 0)
             {
              //Mass matrix
              mass_matrix(local_eqn,local_unknown) += psi(l)*psi(l2)*W;
              //Jacobian terms
              jacobian(local_eqn,local_unknown) -= B_real*psi(l2)*psi(l)*W;
              jacobian(local_eqn,local_unknown) -= 
               (1.0/Re)*dpsidx(l2,0)*dpsidx(l,0)*W;
             }
  
            //Get the contribution from the imaginary part of w
            local_unknown = U_local_eqn(l2,3);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += B_imag*psi(l2)*psi(l)*W;
             }
  
           } //End of loop over the shape functions
          
  
          //Loop over the pressure shape functions
          for(unsigned l2=0;l2<n_pres;l2++)
           {
            //Get the real pressure contribution to the equation
            local_unknown = P_local_eqn(l2,0);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += 
               psip(l2)*dpsidx(l,0)*W;
             }
           }
         }
  
        //IMAGINARY PART OF THE W EQUATION
        //Get the local equation
        local_eqn = U_local_eqn(l,3);
        /*IF it's not a boundary condition*/
        if(local_eqn >= 0)
         {
          //Loop over the shape functions
          for(unsigned l2=0;l2<n_node;l2++)
           { 
            //Get the contribution from the real part of w
            local_unknown = U_local_eqn(l2,2);
            //If at a non-zero degree of freedom add in the entry
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) -= B_imag*psi(l2)*psi(l)*W;
             }
  
            //Get the contribution from the imaginary part of w
            local_unknown = U_local_eqn(l2,3);
            if(local_unknown >= 0)
             {
              //Mass matrix
              mass_matrix(local_eqn,local_unknown) += psi(l)*psi(l2)*W;
              //Jacobian terms
              jacobian(local_eqn,local_unknown) -= B_real*psi(l2)*psi(l)*W;
              jacobian(local_eqn,local_unknown) -= 
               (1.0/Re)*dpsidx(l2,0)*dpsidx(l,0)*W;
             }
           }
  
          //Loop over the pressure shape functions
          for(unsigned l2=0;l2<n_pres;l2++)
           {
            //Get the imaginary pressure contribution to the equation
            local_unknown = P_local_eqn(l2,1);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) +=
               psip(l2)*dpsidx(l,0)*W;
             }
           }
         }
       }
  
      //Loop over the pressure shape functions
      for(unsigned l=0;l<n_pres;l++)
       {
        //Real part of the continuity equation
        local_eqn = P_local_eqn(l,0);
        if(local_eqn >= 0)
         {
          //Loop over the shape functions
          for(unsigned l2=0;l2<n_node;l2++)
           {
            //REAL U conributions
            local_unknown = U_local_eqn(l2,0);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) -=  
               A_imag*psi(l2)*psip(l)*W;
             }
  
            //IMAGINARY U contributions
            local_unknown = U_local_eqn(l2,1);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) -=
               A_real*psi(l2)*psip(l)*W;
             }
  
            //REAL W contribution
            local_unknown = U_local_eqn(l2,2);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += dpsidx(l2,0)*psip(l)*W;
             }
           }
         }
  
  
        //Imaginary part of the continuity equation
        local_eqn = P_local_eqn(l,1);
        if(local_eqn >= 0)
         {
          //Loop over the shape functions
          for(unsigned l2=0;l2<n_node;l2++)
           {
            //REAL U conributions
            local_unknown = U_local_eqn(l2,0);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += 
               A_real*psi(l2)*psip(l)*W;
             }
  
            //IMAGINARY U contributions
            local_unknown = U_local_eqn(l2,1);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) -=
               A_imag*psi(l2)*psip(l)*W;
             }
  
            //IMAGINARY W contribution
            local_unknown = U_local_eqn(l2,3);
            if(local_unknown >= 0)
             {
              jacobian(local_eqn,local_unknown) += dpsidx(l2,0)*psip(l)*W;
             }
           }
         }
       } //End of loop over pressure shape functions
     }
   }

References Param::A_imag, DIM, i, J, Param::Re, s, w, and oomph::QuadTreeNames::W.

◆ get_base_flow()

template<unsigned DIM>

void OrrSommerfeldEquations< DIM >::get_base_flow	(	const Vector< double > &	s,
		double &	U,
		double &	Uz
	)

inline

   {
    //Get the coordinate
    double z = interpolated_x(s,0);
    //Return the value of the base flow
    U = (1.0-z*z);
    Uz = -2.0*z;
   }

References s, and RachelsAdvectionDiffusion::U.

◆ interpolated_p()

template<unsigned DIM>

double OrrSommerfeldEquations< DIM >::interpolated_p	(	const Vector< double > &	s,
		const unsigned &	i
	)		const

inline

Return FE representation of the pressure.

   {
    unsigned n_pres = npres();
  
    //Pressure shape functions
    Shape psip(n_pres);
  
    //Find values of shape function
    this->pshape(s,psip);
  
    //Initialise value of p
    double interpolated_p = 0.0;
  
    //Loop over the local nodes and sum
    for(unsigned l=0;l<n_pres;l++) 
     {
      interpolated_p+=p(l,i)*psip[l];
     }
  
    return(interpolated_p);
   }

References i, p, and s.

◆ interpolated_u()

template<unsigned DIM>

double OrrSommerfeldEquations< DIM >::interpolated_u	(	const Vector< double > &	s,
		const unsigned &	i
	)		const

inline

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

   {
    unsigned n_node = nnode();
  
    //Local shape functions
    Shape psi(n_node);
  
    //Find values of basis function
    this->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+=u(l,i)*psi[l];
     }
  
    return(interpolated_u);
   }

References i, and oomph::OneDimLagrange::shape().

◆ npres()

template<unsigned DIM>

virtual unsigned OrrSommerfeldEquations< DIM >::npres ( ) const

pure virtual

Implemented in QOrrSommerfeldElement< 1, NNODE_1D >.

◆ output() [1/2]

template<unsigned DIM>

void OrrSommerfeldEquations< DIM >::output ( ostream & outfile )

inlinevirtual

Output with default number of plot points.

Reimplemented from oomph::FiniteElement.

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

References output().

Referenced by QOrrSommerfeldElement< 1, NNODE_1D >::output().

◆ output() [2/2]

template<unsigned DIM>

void OrrSommerfeldEquations< DIM >::output	(	ostream &	outfile,
		const unsigned &	nplot
	)

inlinevirtual

Output FE representation of soln: x,y,u or x,y,z,u at Nplot^DIM plot points

Reimplemented from oomph::FiniteElement.

   {
    //Vector of local coordinates
    Vector<double> s(DIM);
  
    // 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);
  
      for(unsigned i=0;i<DIM;i++) 
       {
        outfile << interpolated_x(s,i) << " ";
       }
      
      for(unsigned i=0;i<4;i++)
       {
        outfile << interpolated_u(s,i) << " ";
        }
  
      outfile << interpolated_p(s,0) << " " 
              << interpolated_p(s,1) << " ";
      outfile << std::endl;
     }
  
    // Write tecplot footer (e.g. FE connectivity lists)
    write_tecplot_zone_footer(outfile,nplot);
   }

References DIM, i, and s.

◆ p()

template<unsigned DIM>

virtual double OrrSommerfeldEquations< DIM >::p	(	const unsigned &	n,
		const unsigned &	i
	)		const

pure virtual

Implemented in QOrrSommerfeldElement< 1, NNODE_1D >.

◆ pshape()

template<unsigned DIM>

virtual void OrrSommerfeldEquations< DIM >::pshape	(	const Vector< double > &	s,
		Shape &	psi
	)		const

pure virtual

◆ re_pt()

template<unsigned DIM>

double* & OrrSommerfeldEquations< DIM >::re_pt ( )

inline

94 {return Re_pt;}

◆ u()

template<unsigned DIM>

virtual double OrrSommerfeldEquations< DIM >::u	(	const unsigned &	n,
		const unsigned &	i
	)		const

pure virtual

Access function: Nodal function value at local node n Uses suitably interpolated value for hanging nodes.

Implemented in QOrrSommerfeldElement< 1, NNODE_1D >.

Member Data Documentation

◆ A_Imag_pt

template<unsigned DIM>

double* OrrSommerfeldEquations< DIM >::A_Imag_pt

private

◆ A_Real_pt

template<unsigned DIM>

double* OrrSommerfeldEquations< DIM >::A_Real_pt

private

◆ P_local_eqn

template<unsigned DIM>

DenseMatrix<int> OrrSommerfeldEquations< DIM >::P_local_eqn

protected

◆ Re_pt

template<unsigned DIM>

double* OrrSommerfeldEquations< DIM >::Re_pt

private

◆ U_local_eqn

template<unsigned DIM>

DenseMatrix<int> OrrSommerfeldEquations< DIM >::U_local_eqn

protected

Array to hold local eqn numbers: Local_eqn[n] (=-1 for BC)

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

orr_sommerfeld.cc

Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Additional Inherited Members

Detailed Description

template<unsigned DIM> class OrrSommerfeldEquations< DIM >

Constructor & Destructor Documentation

◆ OrrSommerfeldEquations()

Member Function Documentation

◆ a_imag_pt()

◆ a_real_pt()

◆ dshape_eulerian()

◆ dshape_eulerian_at_knot()

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

◆ get_base_flow()

◆ interpolated_p()

◆ interpolated_u()

◆ npres()

◆ output() [1/2]

◆ output() [2/2]

◆ p()

◆ pshape()

◆ re_pt()

◆ u()

Member Data Documentation

◆ A_Imag_pt

◆ A_Real_pt

◆ P_local_eqn

◆ Re_pt

◆ U_local_eqn

template<unsigned DIM>
class OrrSommerfeldEquations< DIM >