#include <refineable_linearised_navier_stokes_elements.h>

Inheritance diagram for oomph::RefineableLinearisedNavierStokesEquations:

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

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

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

void	further_build ()
	Further build: pass the pointers down to the sons. More...

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

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

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

const double &	lambda () const

const double &	omega () const

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

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

double *&	lambda_pt ()
	Pointer to lambda. More...

double *&	omega_pt ()
	Pointer to frequency. More...

LinearisedNavierStokesEigenfunctionNormalisationElement *	normalisation_element_pt ()
	Pointer to normalisation element. More...

void	set_eigenfunction_normalisation_element (LinearisedNavierStokesEigenfunctionNormalisationElement *const &normalisation_el_pt)
	the boolean flag check_nodal_data is set to false. More...

const double &	viscosity_ratio () const

double *&	viscosity_ratio_pt ()
	Pointer to the viscosity ratio. More...

const double &	density_ratio () const

double *&	density_ratio_pt ()
	Pointer to the density ratio. More...

virtual unsigned	npres_linearised_nst () const =0

virtual unsigned	u_index_linearised_nst (const unsigned &i) const

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

void	disable_ALE ()

void	enable_ALE ()

virtual double	p_linearised_nst (const unsigned &n_p, const unsigned &i) const =0

virtual void	pin_real_or_imag (const unsigned &real)=0

virtual void	unpin_real_or_imag (const unsigned &real)=0

virtual void	pin_pressure_normalisation_dofs ()=0
	Pin the normalisation dofs. More...

virtual int	p_index_linearised_nst (const unsigned &i) const
	Which nodal value represents the pressure? More...

void	strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate, const unsigned &real) const

void	output (std::ostream &outfile)

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

void	output (FILE *file_pt)

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

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

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

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

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

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

virtual void	output_fct (std::ostream &outfile, const unsigned &n_plot, 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

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

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

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

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

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

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

virtual unsigned	required_nsons () const

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

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

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

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

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

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

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

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

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

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

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

void	deselect_sons_for_unrefinement ()

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

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

virtual void	rebuild_from_sons (Mesh *&mesh_pt)=0

virtual void	unbuild ()

virtual void	deactivate_element ()

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

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

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

virtual unsigned	ncont_interpolated_values () const =0

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

virtual void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)=0

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

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

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

virtual unsigned	ninterpolating_node (const int &value_id)

virtual unsigned	ninterpolating_node_1d (const int &value_id)

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

virtual void	check_integrity (double &max_error)=0

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

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

virtual RefineableElement *	root_element_pt ()

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

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

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

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

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

virtual void	further_setup_hanging_nodes ()

void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

unsigned	nshape_controlling_nodes ()

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

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

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

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

virtual unsigned	ncompound_fluxes ()

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

virtual void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)

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

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

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

virtual double	geometric_jacobian (const Vector< double > &x)

Static Public Member Functions
static void	pin_redundant_nodal_pressures (const Vector< GeneralisedElement * > &element_pt)

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

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

Protected Member Functions
virtual Node *	pressure_node_pt (const unsigned &n_p)

virtual void	unpin_elemental_pressure_dofs ()=0
	Unpin all pressure dofs in the element. More...

virtual void	pin_elemental_redundant_nodal_pressure_dofs ()

Protected Member Functions inherited from oomph::LinearisedNavierStokesEquations
virtual int	p_local_eqn (const unsigned &n, const unsigned &i)=0

virtual double	dshape_and_dtest_eulerian_linearised_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0

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

virtual void	pshape_linearised_nst (const Vector< double > &s, Shape &psi) const =0
	Compute the pressure shape functions at local coordinate s. More...

virtual void	pshape_linearised_nst (const Vector< double > &s, Shape &psi, Shape &test) const =0
	Compute the pressure shape and test functions at local coordinate s. More...

virtual void	get_base_flow_u (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &result) const

virtual void	get_base_flow_dudx (const double &time, const unsigned &ipt, const Vector< double > &x, DenseMatrix< double > &result) const

int	eigenvalue_local_eqn (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

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

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

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

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

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

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

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

Protected Member Functions inherited from oomph::RefineableElement
void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const

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

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

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

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

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

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

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

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

Public Attributes inherited from oomph::LinearisedNavierStokesEquations
void(*&)(const double &time, const Vector< double > &x, Vector< double > &f)	base_flow_u_fct_pt ()
	Access function for the base flow solution pointer. More...

void(*&)(const double &time, const Vector< double > &x, DenseMatrix< double > &f)	base_flow_dudx_fct_pt ()

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

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

Protected Attributes inherited from oomph::LinearisedNavierStokesEquations
double *	Viscosity_Ratio_pt

double *	Density_Ratio_pt

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

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

double *	Lambda_pt
	Pointer to eigenvalue. More...

double *	Omega_pt
	Pointer to frequency. More...

LinearisedNavierStokesEigenfunctionNormalisationElement *	Normalisation_element_pt
	Pointer to the normalisation element. More...

unsigned	Data_number_of_eigenvalue
	Index of datum where eigenvalue is stored. More...

unsigned	Index_of_eigenvalue

void(*	Base_flow_u_fct_pt )(const double &time, const Vector< double > &x, Vector< double > &result)
	Pointer to base flow solution (velocity components) function. More...

void(*	Base_flow_dudx_fct_pt )(const double &time, const Vector< double > &x, DenseMatrix< double > &result)

bool	ALE_is_disabled

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

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

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

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

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

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

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

static const double	Node_location_tolerance = 1.0e-14

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

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

static std::deque< double * >	Dof_pt_deque

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

Detailed Description

Refineable version of the linearised axisymmetric Navier–Stokes equations

Constructor & Destructor Documentation

◆ RefineableLinearisedNavierStokesEquations()

oomph::RefineableLinearisedNavierStokesEquations::RefineableLinearisedNavierStokesEquations ( )

inline

Empty Constructor.

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

Member Function Documentation

◆ fill_in_generic_residual_contribution_linearised_nst()

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

privatevirtual

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

Compute the residuals for the refineable linearised axisymmetric Navier–Stokes equations; flag=1(or 0): do (or don't) compute the Jacobian as well.

Reimplemented from oomph::LinearisedNavierStokesEquations.

   {
     // Get the time from the first node in the element
     const double time = this->node_pt(0)->time_stepper_pt()->time();
  
     // Determine number of nodes in the element
     const unsigned n_node = nnode();
  
     // Determine how many pressure values there are associated with
     // a single pressure component
     const unsigned n_pres = npres_linearised_nst();
  
     const unsigned n_veloc = 4 * DIM;
  
     // Get the nodal indices at which the velocity is stored
     unsigned u_nodal_index[n_veloc];
     for (unsigned i = 0; i < n_veloc; ++i)
     {
       u_nodal_index[i] = u_index_linearised_nst(i);
     }
  
     // Which nodal values represent the two pressure components?
     // (Negative if pressure is not based on nodal interpolation).
     Vector<int> p_index(2);
     for (unsigned i = 0; i < 2; i++)
     {
       p_index[i] = this->p_index_linearised_nst(i);
     }
  
     // Local array of booleans that are true if the l-th pressure value is
     // hanging (avoid repeated virtual function calls)
     bool pressure_dof_is_hanging[n_pres];
  
     // If the pressure is stored at a node
     if (p_index[0] >= 0)
     {
       // Read out whether the pressure is hanging
       for (unsigned l = 0; l < n_pres; ++l)
       {
         pressure_dof_is_hanging[l] =
           pressure_node_pt(l)->is_hanging(p_index[0]);
       }
     }
     // Otherwise the pressure is not stored at a node and so cannot hang
     else
     {
       for (unsigned l = 0; l < n_pres; ++l)
       {
         pressure_dof_is_hanging[l] = false;
       }
     }
  
  
     // Set up memory for the fluid shape and test functions
     Shape psif(n_node), testf(n_node);
     DShape dpsifdx(n_node, DIM), dtestfdx(n_node, DIM);
  
     // Set up memory for the pressure shape and test functions
     Shape psip(n_pres), testp(n_pres);
  
     // Determine number of integration points
     const unsigned n_intpt = integral_pt()->nweight();
  
     // Set up memory for the vector to hold local coordinates (two dimensions)
     Vector<double> s(DIM);
  
     // Get physical variables from the element
     // (Reynolds number must be multiplied by the density ratio)
     const double scaled_re = re() * density_ratio();
     const double scaled_re_st = re_st() * density_ratio();
     const double visc_ratio = viscosity_ratio();
  
     const double eval_real = lambda();
     const double eval_imag = omega();
  
     const std::complex<double> eigenvalue(eval_real, eval_imag);
  
     // Integers used to store the local equation numbers
     int local_eqn = 0;
  
     // Local storage for pointers to hang info objects
     HangInfo* hang_info_pt = 0;
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Assign values of the local coordinates s
       for (unsigned i = 0; i < DIM; i++)
       {
         s[i] = integral_pt()->knot(ipt, i);
       }
  
       // Get the integral weight
       const double w = integral_pt()->weight(ipt);
  
       // Calculate the fluid shape and test functions, and their derivatives
       // w.r.t. the global coordinates
       const double J = dshape_and_dtest_eulerian_at_knot_linearised_nst(
         ipt, psif, dpsifdx, testf, dtestfdx);
  
       // Calculate the pressure shape and test functions
       pshape_linearised_nst(s, psip, testp);
  
       // Premultiply the weights and the Jacobian of the mapping between
       // local and global coordinates
       const double W = w * J;
  
       // Allocate storage for the position and the derivative of the
       // mesh positions w.r.t. time
       Vector<double> interpolated_x(DIM, 0.0);
       // Vector<double> mesh_velocity(2,0.0);
  
       // Allocate storage for the velocity components (six of these)
       // and their derivatives w.r.t. time
       Vector<std::complex<double>> interpolated_u(DIM);
       // Vector<double> dudt(6,0.0);
       // Allocate storage for the eigen function normalisation
       Vector<std::complex<double>> interpolated_u_normalisation(DIM);
       for (unsigned i = 0; i < DIM; ++i)
       {
         interpolated_u[i].real(0.0);
         interpolated_u[i].imag(0.0);
         interpolated_u_normalisation[i].real(0.0);
         interpolated_u_normalisation[i].imag(0.0);
       }
  
       // Allocate storage for the pressure components (two of these
       std::complex<double> interpolated_p(0.0, 0.0);
       std::complex<double> interpolated_p_normalisation(0.0, 0.0);
  
       // Allocate storage for the derivatives of the velocity components
       // w.r.t. global coordinates (r and z)
       Vector<Vector<std::complex<double>>> interpolated_dudx(DIM);
       for (unsigned i = 0; i < DIM; ++i)
       {
         interpolated_dudx[i].resize(DIM);
         for (unsigned j = 0; j < DIM; ++j)
         {
           interpolated_dudx[i][j].real(0.0);
           interpolated_dudx[i][j].imag(0.0);
         }
       }
  
       // Calculate pressure at the integration point
       // -------------------------------------------
  
       // Loop over pressure degrees of freedom (associated with a single
       // pressure component) in the element
       for (unsigned l = 0; l < n_pres; l++)
       {
         // Cache the shape function
         const double psip_ = psip(l);
  
         // Get the complex nodal pressure values
         const std::complex<double> p_value(this->p_linearised_nst(l, 0),
                                            this->p_linearised_nst(l, 1));
  
         // Add contribution
         interpolated_p += p_value * psip_;
  
         // Repeat for normalisation
         const std::complex<double> p_norm_value(this->p_linearised_nst(l, 2),
                                                 this->p_linearised_nst(l, 3));
         interpolated_p_normalisation += p_norm_value * psip_;
       }
       // End of loop over the pressure degrees of freedom in the element
  
       // Calculate velocities and their derivatives at the integration point
       // -------------------------------------------------------------------
  
       // Loop over the element's nodes
       for (unsigned l = 0; l < n_node; l++)
       {
         // Cache the shape function
         const double psif_ = psif(l);
  
         // Loop over the DIM coordinate directions
         for (unsigned i = 0; i < DIM; i++)
         {
           interpolated_x[i] += this->nodal_position(l, i) * psif_;
         }
  
         // Loop over the DIM complex velocity components
         for (unsigned i = 0; i < DIM; i++)
         {
           // Get the value
           const std::complex<double> u_value(
             this->nodal_value(l, u_nodal_index[2 * i + 0]),
             this->nodal_value(l, u_nodal_index[2 * i + 1]));
  
           // Add contribution
           interpolated_u[i] += u_value * psif_;
  
           // Add contribution to dudt
           // dudt[i] += du_dt_linearised_nst(l,i)*psif_;
  
           // Loop over two coordinate directions (for derivatives)
           for (unsigned j = 0; j < DIM; j++)
           {
             interpolated_dudx[i][j] += u_value * dpsifdx(l, j);
           }
  
           // Interpolate the normalisation function
           const std::complex<double> normalisation_value(
             this->nodal_value(l, u_nodal_index[2 * (DIM + i)]),
             this->nodal_value(l, u_nodal_index[2 * (DIM + i) + 1]));
           interpolated_u_normalisation[i] += normalisation_value * psif_;
         }
       } // End of loop over the element's nodes
  
       // Get the mesh velocity if ALE is enabled
       /*if(!ALE_is_disabled)
        {
         // Loop over the element's nodes
         for(unsigned l=0;l<n_node;l++)
          {
           // Loop over the two coordinate directions
           for(unsigned i=0;i<2;i++)
            {
             mesh_velocity[i] += this->raw_dnodal_position_dt(l,i)*psif(l);
            }
          }
          }*/
  
       // Get velocities and their derivatives from base flow problem
       // -----------------------------------------------------------
  
       // Allocate storage for the velocity components of the base state
       // solution (initialise to zero)
       Vector<double> base_flow_u(DIM, 0.0);
  
       // Get the user-defined base state solution velocity components
       get_base_flow_u(time, ipt, interpolated_x, base_flow_u);
  
       // Allocate storage for the derivatives of the base state solution's
       // velocity components w.r.t. global coordinate (r and z)
       // N.B. the derivatives of the base flow components w.r.t. the
       // azimuthal coordinate direction (theta) are always zero since the
       // base flow is axisymmetric
       DenseMatrix<double> base_flow_dudx(DIM, DIM, 0.0);
  
       // Get the derivatives of the user-defined base state solution
       // velocity components w.r.t. global coordinates
       get_base_flow_dudx(time, ipt, interpolated_x, base_flow_dudx);
  
  
       // MOMENTUM EQUATIONS
       //------------------
  
       // Number of master nodes
       unsigned n_master = 1;
  
       // Storage for the weight of the shape function
       double hang_weight = 1.0;
  
       // Loop over the test functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Local boolean to indicate whether the node is hanging
         bool is_node_hanging = node_pt(l)->is_hanging();
  
         if (is_node_hanging)
         {
           hang_info_pt = node_pt(l)->hanging_pt();
  
           // Read out number of master nodes from hanging data
           n_master = hang_info_pt->nmaster();
         }
         // Otherwise the node is its own master
         else
         {
           n_master = 1;
         }
  
         // Loop over the master nodes
         for (unsigned m = 0; m < n_master; m++)
         {
           // Loop over the velocity components
           for (unsigned i = 0; i < DIM; i++)
           {
             // Assemble the residuals
             // Time dependent term
             std::complex<double> residual_contribution =
               -scaled_re_st * eigenvalue * interpolated_u[i] * testf[l] * W;
             // Pressure term
             residual_contribution += interpolated_p * dtestfdx(l, i) * W;
             // Viscous terms
             for (unsigned k = 0; k < DIM; ++k)
             {
               residual_contribution -=
                 visc_ratio *
                 (interpolated_dudx[i][k] + Gamma[i] * interpolated_dudx[k][i]) *
                 dtestfdx(l, k) * W;
             }
  
             // Advective terms
             for (unsigned k = 0; k < DIM; ++k)
             {
               residual_contribution -=
                 scaled_re *
                 (base_flow_u[k] * interpolated_dudx[i][k] +
                  interpolated_u[k] * base_flow_dudx(i, k)) *
                 testf[l] * W;
             }
  
             // Now separate real and imaginary parts
  
             if (is_node_hanging)
             {
               local_eqn = this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                                u_nodal_index[2 * i]);
               hang_weight = hang_info_pt->master_weight(m);
             }
             // If node is not hanging number or not
             else
             {
               local_eqn = nodal_local_eqn(l, u_nodal_index[2 * i]);
               hang_weight = 1.0;
             }
  
             if (local_eqn >= 0)
             {
               residuals[local_eqn] +=
                 residual_contribution.real() * hang_weight;
             }
  
  
             if (is_node_hanging)
             {
               local_eqn = this->local_hang_eqn(hang_info_pt->master_node_pt(m),
                                                u_nodal_index[2 * i + 1]);
               hang_weight = hang_info_pt->master_weight(m);
             }
             // If node is not hanging number or not
             else
             {
               local_eqn = nodal_local_eqn(l, u_nodal_index[2 * i + 1]);
               hang_weight = 1.0;
             }
             if (local_eqn >= 0)
             {
               residuals[local_eqn] +=
                 residual_contribution.imag() * hang_weight;
             }
  
  
             // CALCULATE THE JACOBIAN
             /*if(flag)
               {
               //Loop over the velocity shape functions again
               for(unsigned l2=0;l2<n_node;l2++)
               {
               //Loop over the velocity components again
               for(unsigned i2=0;i2<DIM;i2++)
               {
               //If at a non-zero degree of freedom add in the entry
               local_unknown = nodal_local_eqn(l2,u_nodal_index[i2]);
               if(local_unknown >= 0)
               {
               //Add contribution to Elemental Matrix
               jacobian(local_eqn,local_unknown)
               -= visc_ratio*Gamma[i]*dpsifdx(l2,i)*dtestfdx(l,i2)*W;
  
               //Extra component if i2 = i
               if(i2 == i)
               {
               //Loop over velocity components
               for(unsigned k=0;k<DIM;k++)
               {
               jacobian(local_eqn,local_unknown)
               -= visc_ratio*dpsifdx(l2,k)*dtestfdx(l,k)*W;
               }
               }
  
               //Now add in the inertial terms
               jacobian(local_eqn,local_unknown)
               -= scaled_re*psif[l2]*interpolated_dudx(i,i2)*testf[l]*W;
  
               //Extra component if i2=i
               if(i2 == i)
               {
               //Add the mass matrix term (only diagonal entries)
               //Note that this is positive because the mass matrix
               //is taken to the other side of the equation when
               //formulating the generalised eigenproblem.
               if(flag==2)
               {
               mass_matrix(local_eqn,local_unknown) +=
               scaled_re_st*psif[l2]*testf[l]*W;
               }
  
               //du/dt term
               jacobian(local_eqn,local_unknown)
               -= scaled_re_st*
               node_pt(l2)->time_stepper_pt()->weight(1,0)*
               psif[l2]*testf[l]*W;
  
               //Loop over the velocity components
               for(unsigned k=0;k<DIM;k++)
               {
               double tmp=scaled_re*interpolated_u[k];
               if (!ALE_is_disabled) tmp-=scaled_re_st*mesh_velocity[k];
               jacobian(local_eqn,local_unknown) -=
               tmp*dpsifdx(l2,k)*testf[l]*W;
               }
               }
  
               }
               }
               }
  
               //Now loop over pressure shape functions
               //This is the contribution from pressure gradient
               for(unsigned l2=0;l2<n_pres;l2++)
               {
               //If we are at a non-zero degree of freedom in the entry
               local_unknown = p_local_eqn(l2);
               if(local_unknown >= 0)
               {
               jacobian(local_eqn,local_unknown)
               += psip[l2]*dtestfdx(l,i)*W;
               }
               }
               } //End of Jacobian calculation
  
               }*/ //End of if not boundary condition statement
  
           } // End of loop over dimension
         } // End of loop over master nodes
       } // End of loop over shape functions
  
  
       // CONTINUITY EQUATION
       //-------------------
  
       // Loop over the shape functions
       for (unsigned l = 0; l < n_pres; l++)
       {
         if (pressure_dof_is_hanging[l])
         {
           hang_info_pt = this->pressure_node_pt(l)->hanging_pt(p_index[0]);
           n_master = hang_info_pt->nmaster();
         }
         else
         {
           n_master = 1;
         }
  
         // Loop over the master nodes
         for (unsigned m = 0; m < n_master; ++m)
         {
           // Assemble the residuals
           std::complex<double> residual_contribution = interpolated_dudx[0][0];
           for (unsigned k = 1; k < DIM; ++k)
           {
             residual_contribution += interpolated_dudx[k][k];
           }
  
           if (pressure_dof_is_hanging[l])
           {
             local_eqn =
               this->local_hang_eqn(hang_info_pt->master_node_pt(m), p_index[0]);
             hang_weight = hang_info_pt->master_weight(m);
           }
           else
           {
             local_eqn = this->p_local_eqn(l, 0);
             hang_weight = 1.0;
           }
  
           // If not a boundary conditions
           if (local_eqn >= 0)
           {
             residuals[local_eqn] +=
               residual_contribution.real() * testp[l] * W * hang_weight;
           }
  
           if (pressure_dof_is_hanging[l])
           {
             local_eqn =
               this->local_hang_eqn(hang_info_pt->master_node_pt(m), p_index[1]);
             hang_weight = hang_info_pt->master_weight(m);
           }
           else
           {
             local_eqn = this->p_local_eqn(l, 1);
             hang_weight = 1.0;
           }
  
           // If not a boundary conditions
           if (local_eqn >= 0)
           {
             residuals[local_eqn] +=
               residual_contribution.imag() * testp[l] * W * hang_weight;
           }
  
         } // End of loop over master nodes
       } // End of loop over l
  
       // Normalisation condition. Leave this alone because there is
       // no test function involved.
       std::complex<double> residual_contribution =
         interpolated_p_normalisation * interpolated_p;
       for (unsigned k = 0; k < DIM; ++k)
       {
         residual_contribution +=
           interpolated_u_normalisation[k] * interpolated_u[k];
       }
  
       local_eqn = this->eigenvalue_local_eqn(0);
       if (local_eqn >= 0)
       {
         residuals[local_eqn] += residual_contribution.real() * W;
       }
  
       local_eqn = this->eigenvalue_local_eqn(1);
       if (local_eqn >= 0)
       {
         residuals[local_eqn] += residual_contribution.imag() * W;
       }
  
     } // End of loop over the integration points
  
   } // End of fill_in_generic_residual_contribution_linearised_nst

◆ further_build()

void oomph::RefineableLinearisedNavierStokesEquations::further_build ( )

inlinevirtual

Further build: pass the pointers down to the sons.

Reimplemented from oomph::RefineableElement.

Reimplemented in oomph::RefineableLinearisedQCrouzeixRaviartElement.

     {
       // Find the father element
       RefineableLinearisedNavierStokesEquations* cast_father_element_pt =
         dynamic_cast<RefineableLinearisedNavierStokesEquations*>(
           this->father_element_pt());
  
       // Set the viscosity ratio pointer
       this->Viscosity_Ratio_pt = cast_father_element_pt->viscosity_ratio_pt();
  
       // Set the density ratio pointer
       this->Density_Ratio_pt = cast_father_element_pt->density_ratio_pt();
  
       // Set pointer to global Reynolds number
       this->Re_pt = cast_father_element_pt->re_pt();
  
       // Set pointer to global Reynolds number x Strouhal number (=Womersley)
       this->ReSt_pt = cast_father_element_pt->re_st_pt();
  
       if (cast_father_element_pt->normalisation_element_pt() != 0)
       {
         // Pass down the normalisation element
         this->set_eigenfunction_normalisation_element(
           cast_father_element_pt->normalisation_element_pt());
       }
  
       // Set the ALE_is_disabled flag
       this->ALE_is_disabled = cast_father_element_pt->ALE_is_disabled;
     }

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

◆ get_Z2_flux()

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

inlinevirtual

Get 'flux' for Z2 error recovery: Upper triangular entries in strain rate tensor.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
 #ifdef PARANOID
       unsigned num_entries = 2 * (DIM + ((DIM * DIM) - DIM) / 2);
       if (flux.size() != num_entries)
       {
         std::ostringstream error_message;
         error_message << "The flux vector has the wrong number of entries, "
                       << flux.size() << ", whereas it should be " << num_entries
                       << std::endl;
         throw OomphLibError(
           error_message.str(),
           "RefineableLinearisedNavierStokesEquations::get_Z2_flux()",
           OOMPH_EXCEPTION_LOCATION);
       }
 #endif
  
       // Get strain rate matrix
       DenseMatrix<double> real_strainrate(DIM);
       this->strain_rate(s, real_strainrate, 0);
       DenseMatrix<double> imag_strainrate(DIM);
       this->strain_rate(s, imag_strainrate, 1);
  
  
       // Pack into flux Vector
       unsigned icount = 0;
  
       // Start with diagonal terms
       for (unsigned i = 0; i < DIM; i++)
       {
         flux[icount] = real_strainrate(i, i);
         icount++;
       }
  
       // Off diagonals row by row
       for (unsigned i = 0; i < DIM; i++)
       {
         for (unsigned j = i + 1; j < DIM; j++)
         {
           flux[icount] = real_strainrate(i, j);
           icount++;
         }
       }
  
       // Start with diagonal terms
       for (unsigned i = 0; i < DIM; i++)
       {
         flux[icount] = imag_strainrate(i, i);
         icount++;
       }
  
       // Off diagonals row by row
       for (unsigned i = 0; i < DIM; i++)
       {
         for (unsigned j = i + 1; j < DIM; j++)
         {
           flux[icount] = imag_strainrate(i, j);
           icount++;
         }
       }
     }

References DIM, ProblemParameters::flux(), i, j, OOMPH_EXCEPTION_LOCATION, and oomph::LinearisedNavierStokesEquations::strain_rate().

◆ num_Z2_flux_terms()

unsigned oomph::RefineableLinearisedNavierStokesEquations::num_Z2_flux_terms ( )

inlinevirtual

Number of 'flux' terms for Z2 error estimation.

Implements oomph::ElementWithZ2ErrorEstimator.

     {
       // 3 diagonal strain rates, 3 off diagonal real and imaginary parts
       return 2 * (DIM + ((DIM * DIM) - DIM) / 2);
     }

References DIM.

◆ pin_elemental_redundant_nodal_pressure_dofs()

virtual void oomph::RefineableLinearisedNavierStokesEquations::pin_elemental_redundant_nodal_pressure_dofs ( )

inlineprotectedvirtual

Pin unused nodal pressure dofs (empty by default, because by default pressure dofs are not associated with nodes)

Reimplemented in oomph::RefineableLinearisedQTaylorHoodElement.

65 {}

Referenced by pin_redundant_nodal_pressures().

◆ pin_redundant_nodal_pressures()

static void oomph::RefineableLinearisedNavierStokesEquations::pin_redundant_nodal_pressures ( const Vector< GeneralisedElement * > & element_pt )

inlinestatic

Loop over all elements in Vector (which typically contains all the elements in a fluid mesh) and pin the nodal pressure degrees of freedom that are not being used. Function uses the member function

RefineableLinearisedNavierStokesEquations:: pin_all_nodal_pressure_dofs()

which is empty by default and should be implemented for elements with nodal pressure degrees of freedom (e.g. for refineable Taylor-Hood.)

     {
       // Loop over all elements to brutally pin all nodal pressure degrees of
       // freedom
       const unsigned n_element = element_pt.size();
       for (unsigned e = 0; e < n_element; e++)
       {
         dynamic_cast<RefineableLinearisedNavierStokesEquations*>(element_pt[e])
           ->pin_elemental_redundant_nodal_pressure_dofs();
       }
     }

References e(), and pin_elemental_redundant_nodal_pressure_dofs().

Referenced by FlowAroundCylinderProblem< ELEMENT >::actions_after_adapt(), and FlowAroundCylinderProblem< ELEMENT >::add_eigenproblem().

◆ pressure_node_pt()

virtual Node* oomph::RefineableLinearisedNavierStokesEquations::pressure_node_pt ( const unsigned & n_p )

inlineprotectedvirtual

Pointer to n_p-th pressure node (Default: NULL, indicating that pressure is not based on nodal interpolation).

Reimplemented in oomph::RefineableLinearisedQTaylorHoodElement.

     {
       return NULL;
     }

Referenced by fill_in_generic_residual_contribution_linearised_nst().

◆ unpin_all_pressure_dofs()

static void oomph::RefineableLinearisedNavierStokesEquations::unpin_all_pressure_dofs ( const Vector< GeneralisedElement * > & element_pt )

inlinestatic

Unpin all pressure dofs in elements listed in Vector.

     {
       // Loop over all elements to brutally unpin all nodal pressure degrees of
       // freedom and internal pressure degrees of freedom
       const unsigned n_element = element_pt.size();
       for (unsigned e = 0; e < n_element; e++)
       {
         dynamic_cast<RefineableLinearisedNavierStokesEquations*>(element_pt[e])
           ->unpin_elemental_pressure_dofs();
       }
     }

References e(), and unpin_elemental_pressure_dofs().

Referenced by FlowAroundCylinderProblem< ELEMENT >::actions_after_adapt().

◆ unpin_elemental_pressure_dofs()

virtual void oomph::RefineableLinearisedNavierStokesEquations::unpin_elemental_pressure_dofs ( )

protectedpure virtual

Unpin all pressure dofs in the element.

Implemented in oomph::RefineableLinearisedQTaylorHoodElement, and oomph::RefineableLinearisedQCrouzeixRaviartElement.

Referenced by unpin_all_pressure_dofs().

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Private Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ RefineableLinearisedNavierStokesEquations()

Member Function Documentation

◆ fill_in_generic_residual_contribution_linearised_nst()

◆ further_build()

◆ get_Z2_flux()

◆ num_Z2_flux_terms()

◆ pin_elemental_redundant_nodal_pressure_dofs()

◆ pin_redundant_nodal_pressures()

◆ pressure_node_pt()

◆ unpin_all_pressure_dofs()

◆ unpin_elemental_pressure_dofs()