#include <boussinesq_elements.h>

Inheritance diagram for oomph::BuoyantQCrouzeixRaviartElement< DIM >:

Public Member Functions
	BuoyantQCrouzeixRaviartElement ()

void	unfix_pressure (const unsigned &p_dof)
	Unpin p_dof-th pressure dof. More...

unsigned	required_nvalue (const unsigned &n) const

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

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

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

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

unsigned	nscalar_paraview () const

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

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

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

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

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

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

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

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

unsigned	u_index_adv_diff () const

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

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

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

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

void	fill_in_contribution_to_residuals (Vector< double > &residuals)

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

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

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

Public Member Functions inherited from oomph::QAdvectionDiffusionElement< DIM, 3 >
	QAdvectionDiffusionElement ()

	QAdvectionDiffusionElement (const QAdvectionDiffusionElement< DIM, NNODE_1D > &dummy)=delete
	Broken copy constructor. More...

void	operator= (const QAdvectionDiffusionElement< DIM, NNODE_1D > &)=delete
	Broken assignment operator. More...

unsigned	required_nvalue (const unsigned &n) const

void	output (std::ostream &outfile)

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

void	output (FILE *file_pt)

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

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

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

Public Member Functions inherited from oomph::AdvectionDiffusionEquations< DIM >
	AdvectionDiffusionEquations ()

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

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

double	du_dt_adv_diff (const unsigned &n) const

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

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

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

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

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

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

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

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

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

void	get_flux (const Vector< double > &s, Vector< double > &flux) const
	Get flux: \(\mbox{flux}[i] = \mbox{d}u / \mbox{d}x_i \). More...

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

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

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

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

virtual unsigned	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)

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::QCrouzeixRaviartElement< DIM >
	QCrouzeixRaviartElement ()
	Constructor, there are DIM+1 internal values (for the pressure) More...

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

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

double	p_nst (const unsigned &i) const

double	p_nst (const unsigned &t, const unsigned &i) const

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

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

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

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

void	build_fp_press_adv_diff_robin_bc_element (const unsigned &face_index)

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

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

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

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

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

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

void	full_output (std::ostream &outfile)

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

unsigned	ndof_types () const

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

void	pshape_nst (const Vector< double > &s, Shape &psi) const

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

void	pshape_nst (const Vector< double > &s, Shape &psi) const

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const

Public Member Functions inherited from oomph::NavierStokesEquations< DIM >
	NavierStokesEquations ()

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

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

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

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

const double &	viscosity_ratio () const

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

const double &	density_ratio () const

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

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

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

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

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

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

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

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

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

NavierStokesPressureAdvDiffSourceFctPt &	source_fct_for_pressure_adv_diff ()

NavierStokesPressureAdvDiffSourceFctPt	source_fct_for_pressure_adv_diff () const

int &	pinned_fp_pressure_eqn ()

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

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

virtual unsigned	u_index_nst (const unsigned &i) const

unsigned	n_u_nst () const

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

void	disable_ALE ()

void	enable_ALE ()

virtual int	p_nodal_index_nst () const

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

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

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

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

void	get_vorticity (const Vector< double > &s, double &vorticity) const
	Compute the scalar vorticity at local coordinate s (2D) More...

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

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

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

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

void	get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction_p, Vector< double > &traction_visc_n, Vector< double > &traction_visc_t)

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

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

unsigned	nscalar_paraview () const

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

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

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

void	full_output (std::ostream &outfile)

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

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

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

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

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

void	compute_norm (double &norm)
	Compute norm of solution: square of the L2 norm of the velocities. More...

void	compute_norm (Vector< double > &norm)
	Compute the vector norm of the FEM solution. More...

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

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

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

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

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

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

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

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

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

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

void	fill_in_pressure_advection_diffusion_residuals (Vector< double > &residuals)

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

void	pin_all_non_pressure_dofs (std::map< Data *, std::vector< int >> &eqn_number_backup)
	Pin all non-pressure dofs and backup eqn numbers. More...

void	output_pressure_advection_diffusion_robin_elements (std::ostream &outfile)

void	delete_pressure_advection_diffusion_robin_elements ()

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

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

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

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

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

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

double	interpolated_p_nst (const unsigned &t, const Vector< double > &s) const
	Return FE interpolated pressure at local coordinate s at time level t. More...

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

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

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const

void	get_vorticity (const Vector< double > &s, double &vorticity) const

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
	Compute 3D vorticity vector at local coordinate s. More...

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

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

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

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

virtual	~TemplateFreeNavierStokesEquationsBase ()
	Virtual destructor (empty) More...

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

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

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

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

Private Member Functions
double	Default_Physical_Constant_Value
	Set the default physical value to be zero. More...

double	Default_Physical_Constant_Value

Private Attributes
double *	Ra_pt
	Pointer to a private data member, the Rayleigh number. More...

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

Additional Inherited Members
Public Types inherited from oomph::AdvectionDiffusionEquations< DIM >
typedef void(*	AdvectionDiffusionSourceFctPt) (const Vector< double > &x, double &f)

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

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

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

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

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

typedef double(*	NavierStokesPressureAdvDiffSourceFctPt) (const Vector< double > &x)

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

Protected Member Functions inherited from oomph::QAdvectionDiffusionElement< DIM, 3 >
double	dshape_and_dtest_eulerian_adv_diff (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

Protected Member Functions inherited from oomph::AdvectionDiffusionEquations< DIM >
virtual void	fill_in_generic_residual_contribution_adv_diff (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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

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

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

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

virtual void	update_before_internal_fd ()

virtual void	reset_after_internal_fd ()

virtual void	update_in_internal_fd (const unsigned &i)

virtual void	reset_in_internal_fd (const unsigned &i)

virtual void	update_before_external_fd ()

virtual void	reset_after_external_fd ()

virtual void	update_in_external_fd (const unsigned &i)

virtual void	reset_in_external_fd (const unsigned &i)

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

virtual void	fill_in_contribution_to_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::QCrouzeixRaviartElement< DIM >
double	dshape_and_dtest_eulerian_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const

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

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

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

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

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

virtual double	get_source_nst (const double &time, const unsigned &ipt, const Vector< double > &x)

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

virtual void	fill_in_generic_residual_contribution_nst (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag)

virtual void	fill_in_generic_pressure_advection_diffusion_contribution_nst (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)

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

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

Protected Attributes inherited from oomph::AdvectionDiffusionEquations< DIM >
double *	Pe_pt
	Pointer to global Peclet number. More...

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

AdvectionDiffusionSourceFctPt	Source_fct_pt
	Pointer to source function: More...

AdvectionDiffusionWindFctPt	Wind_fct_pt
	Pointer to wind function: More...

bool	ALE_is_disabled

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Protected Attributes inherited from oomph::QCrouzeixRaviartElement< DIM >
unsigned	P_nst_internal_index

Protected Attributes inherited from oomph::NavierStokesEquations< DIM >
double *	Viscosity_Ratio_pt

double *	Density_Ratio_pt

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

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

double *	ReInvFr_pt

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

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

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

NavierStokesPressureAdvDiffSourceFctPt	Press_adv_diff_source_fct_pt

bool	ALE_is_disabled

Vector< FpPressureAdvDiffRobinBCElementBase * >	Pressure_advection_diffusion_robin_element_pt

int	Pinned_fp_pressure_eqn

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 oomph::BuoyantQCrouzeixRaviartElement< DIM >

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

Constructor & Destructor Documentation

◆ BuoyantQCrouzeixRaviartElement()

template<unsigned DIM>

oomph::BuoyantQCrouzeixRaviartElement< DIM >::BuoyantQCrouzeixRaviartElement ( )

inline

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

       : QAdvectionDiffusionElement<DIM, 3>(), QCrouzeixRaviartElement<DIM>()
     {
       Ra_pt = &Default_Physical_Constant_Value;
     }

References oomph::BuoyantQCrouzeixRaviartElement< DIM >::Default_Physical_Constant_Value, and oomph::BuoyantQCrouzeixRaviartElement< DIM >::Ra_pt.

Member Function Documentation

◆ compute_error() [1/2]

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::compute_error	(	std::ostream &	outfile,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt,
		double &	error,
		double &	norm
	)

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       FiniteElement::compute_error(outfile, exact_soln_pt, error, norm);
     }

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

◆ compute_error() [2/2]

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       FiniteElement::compute_error(outfile, exact_soln_pt, time, error, norm);
     }

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

◆ Default_Physical_Constant_Value() [1/2]

double oomph::BuoyantQCrouzeixRaviartElement< 2 >::Default_Physical_Constant_Value

private

Set the default physical value to be zero.

◆ Default_Physical_Constant_Value() [2/2]

double oomph::BuoyantQCrouzeixRaviartElement< 3 >::Default_Physical_Constant_Value

private

◆ disable_ALE()

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::disable_ALE ( )

inlinevirtual

Final override for disable ALE.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       // Disable ALE in both sets of equations
       NavierStokesEquations<DIM>::disable_ALE();
       AdvectionDiffusionEquations<DIM>::disable_ALE();
     }

References oomph::AdvectionDiffusionEquations< DIM >::disable_ALE(), and oomph::NavierStokesEquations< DIM >::disable_ALE().

◆ enable_ALE()

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::enable_ALE ( )

inlinevirtual

Final override for enable ALE.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       // Enable ALE in both sets of equations
       NavierStokesEquations<DIM>::enable_ALE();
       AdvectionDiffusionEquations<DIM>::enable_ALE();
     }

References oomph::AdvectionDiffusionEquations< DIM >::enable_ALE(), and oomph::NavierStokesEquations< DIM >::enable_ALE().

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

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

inlinevirtual

Compute the element's residual Vector and the Jacobian matrix. Use analytic expressions for the off-diagonal blocks

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       // Calculate the Navier-Stokes contributions (diagonal block and
       // residuals)
       NavierStokesEquations<DIM>::fill_in_contribution_to_jacobian(residuals,
                                                                    jacobian);
  
       // Calculate the advection-diffusion contributions
       //(diagonal block and residuals)
       AdvectionDiffusionEquations<DIM>::fill_in_contribution_to_jacobian(
         residuals, jacobian);
  
       // Fill in the off diagonal blocks analytically
       fill_in_off_diagonal_jacobian_blocks_analytic(residuals, jacobian);
     }

References oomph::AdvectionDiffusionEquations< DIM >::fill_in_contribution_to_jacobian(), oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_jacobian(), and oomph::BuoyantQCrouzeixRaviartElement< DIM >::fill_in_off_diagonal_jacobian_blocks_analytic().

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       // Get the analytic diagonal terms for the jacobian and mass matrix
       NavierStokesEquations<
         DIM>::fill_in_contribution_to_jacobian_and_mass_matrix(residuals,
                                                                jacobian,
                                                                mass_matrix);
  
       AdvectionDiffusionEquations<
         DIM>::fill_in_contribution_to_jacobian_and_mass_matrix(residuals,
                                                                jacobian,
                                                                mass_matrix);
  
       // Now fill in the off-diagonal blocks in the jacobian matrix
       fill_in_off_diagonal_jacobian_blocks_analytic(residuals, jacobian);
     }

References DIM, and oomph::BuoyantQCrouzeixRaviartElement< DIM >::fill_in_off_diagonal_jacobian_blocks_analytic().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

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

inlinevirtual

Calculate the element's contribution to the residual vector. Recall that fill_in_* functions MUST NOT initialise the entries in the vector to zero. This allows us to call the fill_in_* functions of the constituent single-physics elements sequentially, without wiping out any previously computed entries.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       // Fill in the residuals of the Navier-Stokes equations
       NavierStokesEquations<DIM>::fill_in_contribution_to_residuals(residuals);
  
       // Fill in the residuals of the advection-diffusion eqautions
       AdvectionDiffusionEquations<DIM>::fill_in_contribution_to_residuals(
         residuals);
     }

References oomph::AdvectionDiffusionEquations< DIM >::fill_in_contribution_to_residuals(), and oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_residuals().

◆ fill_in_off_diagonal_jacobian_blocks_analytic()

template<unsigned DIM>

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

inline

Helper function to get the off-diagonal blocks of the Jacobian matrix analytically

     {
       // We now fill in the off-diagonal (interaction) blocks analytically
       // This requires knowledge of exactly how the residuals are assembled
       // within the parent elements and involves yet another loop over
       // the integration points!
  
       // Local storage for the index in the nodes at which the
       // Navier-Stokes velocities are stored (we know that this should be 0,1,2)
       unsigned u_nodal_nst[DIM];
       for (unsigned i = 0; i < DIM; i++)
       {
         u_nodal_nst[i] = this->u_index_nst(i);
       }
  
       // Local storage for the  index at which the temperature is stored
       const unsigned u_nodal_adv_diff = this->u_index_adv_diff();
  
       // Find out how many nodes there are
       const unsigned n_node = this->nnode();
  
       // Set up memory for the shape and test functions and their derivatives
       Shape psif(n_node), testf(n_node);
       DShape dpsifdx(n_node, DIM), dtestfdx(n_node, DIM);
  
       // Number of integration points
       const unsigned n_intpt = this->integral_pt()->nweight();
  
       // Get Physical Variables from Element
       double Ra = this->ra();
       double Pe = this->pe();
       Vector<double> gravity = this->g();
  
       // Integers to store the local equations and unknowns
       int local_eqn = 0, local_unknown = 0;
  
       // Loop over the integration points
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Get the integral weight
         double w = this->integral_pt()->weight(ipt);
  
         // Call the derivatives of the shape and test functions
         double J = this->dshape_and_dtest_eulerian_at_knot_nst(
           ipt, psif, dpsifdx, testf, dtestfdx);
  
         // Premultiply the weights and the Jacobian
         double W = w * J;
  
         // Calculate local values of temperature derivatives
         // Allocate
         Vector<double> interpolated_du_adv_diff_dx(DIM, 0.0);
  
         // Loop over nodes
         for (unsigned l = 0; l < n_node; l++)
         {
           // Get the nodal value
           double u_value = this->raw_nodal_value(l, u_nodal_adv_diff);
           // Loop over the derivative directions
           for (unsigned j = 0; j < DIM; j++)
           {
             interpolated_du_adv_diff_dx[j] += u_value * dpsifdx(l, j);
           }
         }
  
         // Assemble the jacobian terms
  
         // Loop over the test functions
         for (unsigned l = 0; l < n_node; l++)
         {
           // Assemble the contributions of the temperature to
           // the Navier--Stokes equations (which arise through the buoyancy
           // body-force term)
  
           // Loop over the velocity components in the Navier--Stokes equtions
           for (unsigned i = 0; i < DIM; i++)
           {
             // If it's not a boundary condition
             local_eqn = this->nodal_local_eqn(l, u_nodal_nst[i]);
             if (local_eqn >= 0)
             {
               // Loop over the velocity shape functions again
               for (unsigned l2 = 0; l2 < n_node; l2++)
               {
                 // We have only the temperature degree of freedom to consider
                 // If it's non-zero add in the contribution
                 local_unknown = this->nodal_local_eqn(l2, u_nodal_adv_diff);
                 if (local_unknown >= 0)
                 {
                   // Add contribution to jacobian matrix
                   jacobian(local_eqn, local_unknown) +=
                     -gravity[i] * psif(l2) * Ra * testf(l) * W;
                 }
               }
             }
           }
  
           // Assemble the contributions of the fluid velocities to the
           // advection-diffusion equation for the temperature
           {
             local_eqn = this->nodal_local_eqn(l, u_nodal_adv_diff);
             // If it's not pinned
             if (local_eqn >= 0)
             {
               // Loop over the shape functions again
               for (unsigned l2 = 0; l2 < n_node; l2++)
               {
                 // Loop over the velocity degrees of freedom
                 for (unsigned i2 = 0; i2 < DIM; i2++)
                 {
                   // Get the local unknown
                   local_unknown = this->nodal_local_eqn(l2, u_nodal_nst[i2]);
                   // If it's not pinned
                   if (local_unknown >= 0)
                   {
                     // Add the contribution to the jacobian matrix
                     jacobian(local_eqn, local_unknown) -=
                       Pe * psif(l2) * interpolated_du_adv_diff_dx[i2] *
                       testf(l) * W;
                   }
                 }
               }
             }
           }
         }
       }
     }

References DIM, oomph::QCrouzeixRaviartElement< DIM >::dshape_and_dtest_eulerian_at_knot_nst(), oomph::NavierStokesEquations< DIM >::g(), i, oomph::FiniteElement::integral_pt(), J, j, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::Integral::nweight(), Global_Parameters::Pe, oomph::AdvectionDiffusionEquations< DIM >::pe(), Global_Parameters::Ra, oomph::BuoyantQCrouzeixRaviartElement< DIM >::ra(), oomph::FiniteElement::raw_nodal_value(), oomph::BuoyantQCrouzeixRaviartElement< DIM >::u_index_adv_diff(), oomph::NavierStokesEquations< DIM >::u_index_nst(), w, oomph::QuadTreeNames::W, and oomph::Integral::weight().

Referenced by oomph::BuoyantQCrouzeixRaviartElement< DIM >::fill_in_contribution_to_jacobian(), and oomph::BuoyantQCrouzeixRaviartElement< DIM >::fill_in_contribution_to_jacobian_and_mass_matrix().

◆ get_body_force_nst()

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::get_body_force_nst	(	const double &	time,
		const unsigned &	ipt,
		const Vector< double > &	s,
		const Vector< double > &	x,
		Vector< double > &	result
	)

inlinevirtual

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

Reimplemented from oomph::NavierStokesEquations< DIM >.

     {
       // Get the temperature
       const double interpolated_t = this->interpolated_u_adv_diff(s);
  
       // Get vector that indicates the direction of gravity from
       // the Navier-Stokes equations
       Vector<double> gravity(NavierStokesEquations<DIM>::g());
  
       // Temperature-dependent body force:
       for (unsigned i = 0; i < DIM; i++)
       {
         result[i] = -gravity[i] * interpolated_t * ra();
       }
     } // end of get_body_force

References DIM, Gravity::gravity(), i, oomph::AdvectionDiffusionEquations< DIM >::interpolated_u_adv_diff(), and oomph::BuoyantQCrouzeixRaviartElement< DIM >::ra().

◆ get_wind_adv_diff()

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::get_wind_adv_diff	(	const unsigned &	ipt,
		const Vector< double > &	s,
		const Vector< double > &	x,
		Vector< double > &	wind
	)		const

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

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

References oomph::NavierStokesEquations< DIM >::interpolated_u_nst().

◆ nscalar_paraview()

template<unsigned DIM>

unsigned oomph::BuoyantQCrouzeixRaviartElement< DIM >::nscalar_paraview ( ) const

inlinevirtual

Number of scalars/fields output by this element. Broken virtual. Needs to be implemented for each new specific element type. Temporary dummy

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       throw OomphLibError(
         "This function hasn't been implemented for this element",
         OOMPH_CURRENT_FUNCTION,
         OOMPH_EXCEPTION_LOCATION);
  
       // Dummy unsigned
       return 0;
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ output() [1/4]

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::output ( FILE * file_pt )

inlinevirtual

C-style output function: Broken default.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       FiniteElement::output(file_pt);
     }

References oomph::FiniteElement::output().

◆ output() [2/4]

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::output	(	FILE *	file_pt,
		const unsigned &	n_plot
	)

inlinevirtual

C-style output function: Broken default.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

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

References oomph::FiniteElement::output().

◆ output() [3/4]

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::output ( std::ostream & outfile )

inlinevirtual

Overload the standard output function with the broken default.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       FiniteElement::output(outfile);
     }

References oomph::FiniteElement::output().

◆ output() [4/4]

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::output	(	std::ostream &	outfile,
		const unsigned &	nplot
	)

inlinevirtual

Output function: Output x, y, u, v, p, theta at Nplot^DIM plot points

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       // vector of local coordinates
       Vector<double> s(DIM);
  
       // Tecplot header info
       outfile << this->tecplot_zone_string(nplot);
  
       // Loop over plot points
       unsigned num_plot_points = this->nplot_points(nplot);
       for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
       {
         // Get local coordinates of plot point
         this->get_s_plot(iplot, nplot, s);
  
         // Output the position of the plot point
         for (unsigned i = 0; i < DIM; i++)
         {
           outfile << this->interpolated_x(s, i) << " ";
         }
  
         // Output the fluid velocities at the plot point
         for (unsigned i = 0; i < DIM; i++)
         {
           outfile << this->interpolated_u_nst(s, i) << " ";
         }
  
         // Output the fluid pressure at the plot point
         outfile << this->interpolated_p_nst(s) << " ";
  
         // Output the temperature (the advected variable) at the plot point
         outfile << this->interpolated_u_adv_diff(s) << std::endl;
       }
       outfile << std::endl;
  
       // Write tecplot footer (e.g. FE connectivity lists)
       this->write_tecplot_zone_footer(outfile, nplot);
     } // End of output function

References DIM, oomph::FiniteElement::get_s_plot(), i, oomph::NavierStokesEquations< DIM >::interpolated_p_nst(), oomph::AdvectionDiffusionEquations< DIM >::interpolated_u_adv_diff(), oomph::NavierStokesEquations< DIM >::interpolated_u_nst(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().

◆ output_fct() [1/2]

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::output_fct	(	std::ostream &	outfile,
		const unsigned &	Nplot,
		const double &	time,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_soln_pt
	)

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

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

References oomph::FiniteElement::output_fct().

◆ output_fct() [2/2]

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::output_fct	(	std::ostream &	outfile,
		const unsigned &	Nplot,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt
	)

inlinevirtual

Output function for an exact solution: Broken default.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

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

References oomph::FiniteElement::output_fct().

◆ ra()

template<unsigned DIM>

const double& oomph::BuoyantQCrouzeixRaviartElement< DIM >::ra ( ) const

inline

Access function for the Rayleigh number (const version)

     {
       return *Ra_pt;
     }

References oomph::BuoyantQCrouzeixRaviartElement< DIM >::Ra_pt.

Referenced by oomph::BuoyantQCrouzeixRaviartElement< DIM >::fill_in_off_diagonal_jacobian_blocks_analytic(), and oomph::BuoyantQCrouzeixRaviartElement< DIM >::get_body_force_nst().

◆ ra_pt()

template<unsigned DIM>

double*& oomph::BuoyantQCrouzeixRaviartElement< DIM >::ra_pt ( )

inline

Access function for the pointer to the Rayleigh number.

     {
       return Ra_pt;
     }

References oomph::BuoyantQCrouzeixRaviartElement< DIM >::Ra_pt.

◆ required_nvalue()

template<unsigned DIM>

unsigned oomph::BuoyantQCrouzeixRaviartElement< DIM >::required_nvalue ( const unsigned & n ) const

inlinevirtual

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

Reimplemented from oomph::QCrouzeixRaviartElement< DIM >.

     {
       return (QAdvectionDiffusionElement<DIM, 3>::required_nvalue(n) +
               QCrouzeixRaviartElement<DIM>::required_nvalue(n));
     }

References n.

◆ scalar_name_paraview()

template<unsigned DIM>

std::string oomph::BuoyantQCrouzeixRaviartElement< DIM >::scalar_name_paraview ( const unsigned & i ) const

inlinevirtual

Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       return "V" + StringConversion::to_string(i);
     }

References i, and oomph::StringConversion::to_string().

◆ scalar_value_paraview()

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::scalar_value_paraview	(	std::ofstream &	file_out,
		const unsigned &	i,
		const unsigned &	nplot
	)		const

inlinevirtual

Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. Temporary dummy

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       throw OomphLibError(
         "This function hasn't been implemented for this element",
         OOMPH_CURRENT_FUNCTION,
         OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ u_index_adv_diff()

template<unsigned DIM>

unsigned oomph::BuoyantQCrouzeixRaviartElement< DIM >::u_index_adv_diff ( ) const

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

     {
       return DIM;
     }

References DIM.

Referenced by oomph::BuoyantQCrouzeixRaviartElement< DIM >::fill_in_off_diagonal_jacobian_blocks_analytic().

◆ unfix_pressure()

template<unsigned DIM>

void oomph::BuoyantQCrouzeixRaviartElement< DIM >::unfix_pressure ( const unsigned & p_dof )

inline

Unpin p_dof-th pressure dof.

     {
       this->internal_data_pt(this->P_nst_internal_index)->unpin(p_dof);
     }

References oomph::GeneralisedElement::internal_data_pt(), oomph::QCrouzeixRaviartElement< DIM >::P_nst_internal_index, and oomph::Data::unpin().

Member Data Documentation

◆ Default_Physical_Constant_Value

template<unsigned DIM>

double oomph::BuoyantQCrouzeixRaviartElement< DIM >::Default_Physical_Constant_Value

staticprivate

The static default value of the Rayleigh number.

Referenced by oomph::BuoyantQCrouzeixRaviartElement< DIM >::BuoyantQCrouzeixRaviartElement().

◆ Ra_pt

template<unsigned DIM>

double* oomph::BuoyantQCrouzeixRaviartElement< DIM >::Ra_pt

private

Pointer to a private data member, the Rayleigh number.

Referenced by oomph::BuoyantQCrouzeixRaviartElement< DIM >::BuoyantQCrouzeixRaviartElement(), oomph::BuoyantQCrouzeixRaviartElement< DIM >::ra(), and oomph::BuoyantQCrouzeixRaviartElement< DIM >::ra_pt().

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

boussinesq_elements.h

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

template<unsigned DIM> class oomph::BuoyantQCrouzeixRaviartElement< DIM >

Constructor & Destructor Documentation

◆ BuoyantQCrouzeixRaviartElement()

Member Function Documentation

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ Default_Physical_Constant_Value() [1/2]

◆ Default_Physical_Constant_Value() [2/2]

◆ disable_ALE()

◆ enable_ALE()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

◆ fill_in_contribution_to_residuals()

◆ fill_in_off_diagonal_jacobian_blocks_analytic()

◆ get_body_force_nst()

◆ get_wind_adv_diff()

◆ nscalar_paraview()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ ra()

◆ ra_pt()

◆ required_nvalue()

◆ scalar_name_paraview()

◆ scalar_value_paraview()

◆ u_index_adv_diff()

◆ unfix_pressure()

Member Data Documentation

◆ Default_Physical_Constant_Value

◆ Ra_pt

template<unsigned DIM>
class oomph::BuoyantQCrouzeixRaviartElement< DIM >