#include <flux_transport_elements.h>

Inheritance diagram for oomph::FluxTransportEquations< DIM >:

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

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

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_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Assemble the contributions to the mass matrix and residuals. More...

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

double	interpolated_u_flux_transport (const Vector< double > &s, const unsigned &i)
	Return the i-th unknown at the local coordinate s. More...

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

void	calculate_element_averages (double *&average_values)
	Compute the average values of the fluxes. More...

void	output (std::ostream &outfile)

void	output (std::ostream &outfile, const unsigned &nplot)
	Output function, print the values of all unknowns. More...

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

void	set_nodal_dimension (const unsigned &nodal_dim)

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

void	set_n_node (const unsigned &n)

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

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

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()

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

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

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

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

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

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

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

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual double	J_eulerian_at_knot (const unsigned &ipt) const

void	check_J_eulerian_at_knots (bool &passed) const

void	check_jacobian (const double &jacobian) const

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

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

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

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

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

virtual void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)

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

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

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

virtual unsigned	nnode_1d () const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)

virtual void	disable_ALE ()

virtual void	enable_ALE ()

virtual unsigned	required_nvalue (const unsigned &n) const

unsigned	nnodal_position_type () const

bool	has_hanging_nodes () const

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

virtual unsigned	nvertex_node () const

virtual Node *	vertex_node_pt (const unsigned &j) const

virtual Node *	construct_node (const unsigned &n)

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

virtual Node *	construct_boundary_node (const unsigned &n)

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

int	get_node_number (Node *const &node_pt) const

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

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

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

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

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

unsigned	dim () const

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

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

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

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

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

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

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

unsigned	ngeom_data () const

Data *	geom_data_pt (const unsigned &j)

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

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

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

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

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

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

virtual void	node_update ()

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

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

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

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

double	size () const

virtual double	compute_physical_size () const

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

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

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const

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

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

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

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

virtual unsigned	nscalar_paraview () const

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

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

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

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

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

virtual void	output (FILE *file_pt)

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

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

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

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

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

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

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

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

virtual unsigned	nplot_points (const unsigned &nplot) const

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

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

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

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

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

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

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

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

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

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

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

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

virtual unsigned	self_test ()

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

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

virtual unsigned	nnode_on_face () const

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

virtual CoordinateMappingFctPt	face_to_bulk_coordinate_fct_pt (const int &face_index) const

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const

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

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

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

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

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

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

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

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

unsigned long	eqn_number (const unsigned &ieqn_local) const

int	local_eqn_number (const unsigned long &ieqn_global) const

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

bool	external_data_fd (const unsigned &i) const

void	exclude_external_data_fd (const unsigned &i)

void	include_external_data_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	complete_setup_of_dependencies ()

virtual void	get_residuals (Vector< double > &residuals)

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

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

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

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

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

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

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

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

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

virtual void	compute_norm (Vector< double > &norm)

virtual void	compute_norm (double &norm)

virtual unsigned	ndof_types () const

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

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

	GeomObject (const unsigned &ndim)

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

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

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

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

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

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

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

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

TimeStepper *&	time_stepper_pt ()

TimeStepper *	time_stepper_pt () const

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

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

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

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

Protected Member Functions
virtual unsigned	nflux () const
	Return the number of fluxes (default zero) More...

virtual unsigned	u_index_flux_transport (const unsigned &i) const

virtual void	flux (const Vector< double > &u, DenseMatrix< double > &f)

virtual void	dflux_du (const Vector< double > &u, RankThreeTensor< double > &df_du)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)

virtual void	update_before_nodal_fd ()

virtual void	reset_after_nodal_fd ()

virtual void	update_in_nodal_fd (const unsigned &i)

virtual void	reset_in_nodal_fd (const unsigned &i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

bool	internal_data_fd (const unsigned &i) const

void	exclude_internal_data_fd (const unsigned &i)

void	include_internal_data_fd (const unsigned &i)

void	clear_global_eqn_numbers ()

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

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)

virtual void	assign_additional_local_eqn_numbers ()

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

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

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_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)

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

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

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

static bool	Accept_negative_jacobian = false

static bool	Suppress_output_while_checking_for_inverted_elements

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

static bool	Suppress_warning_about_repeated_external_data = true

static double	Default_fd_jacobian_step = 1.0e-8

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

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

unsigned	Ndim
	Number of Eulerian coordinates. More...

TimeStepper *	Geom_object_time_stepper_pt

Static 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::FluxTransportEquations< DIM >

Base class for the flux transport equations templated by the dimension DIM. The equations that are solved are

\[ \frac{\partial u_{i}}{\partial t} + \frac{\partial}{\partial x_{j}} \left(F_{ij}(u_{k})\right), \]

where \( F_{ij} \) is a matrix of flux components.

Constructor & Destructor Documentation

◆ FluxTransportEquations()

template<unsigned DIM>

oomph::FluxTransportEquations< DIM >::FluxTransportEquations ( )

inline

Constructor.

107 : FiniteElement() {}

oomph::FiniteElement::FiniteElement

FiniteElement()

Constructor.

Definition: elements.h:1782

◆ ~FluxTransportEquations()

template<unsigned DIM>

virtual oomph::FluxTransportEquations< DIM >::~FluxTransportEquations ( )

inlinevirtual

Empty destructor.

110 {}

Member Function Documentation

◆ calculate_element_averages()

template<unsigned DIM>

void oomph::FluxTransportEquations< DIM >::calculate_element_averages ( double *& average_values )

Compute the average values of the fluxes.

Calculate the averages of the flux variables.

   {
     // Find the number of fluxes
     const unsigned n_flux = this->nflux();
     // Resize the memory if necessary
     if (average_value == 0)
     {
       average_value = new double[n_flux + 1];
     }
  
     // Initialise the averages to zero
     for (unsigned i = 0; i < n_flux + 1; i++)
     {
       average_value[i] = 0.0;
     }
  
     // Find the number of nodes
     const unsigned n_node = this->nnode();
     // Storage for the shape functions
     Shape psi(n_node);
     DShape dpsidx(n_node, DIM);
  
     // Cache the nodal indices at which the unknowns are stored
     unsigned u_nodal_index[n_flux];
     for (unsigned i = 0; i < n_flux; i++)
     {
       u_nodal_index[i] = this->u_index_flux_transport(i);
     }
  
     // Find the number of integration points
     unsigned n_intpt = this->integral_pt()->nweight();
  
     // Loop over the integration points
     for (unsigned ipt = 0; ipt < n_intpt; ipt++)
     {
       // Get the shape functions and derivatives at the knot
       double J = this->dshape_eulerian_at_knot(ipt, psi, dpsidx);
  
       // Get the integral weight
       double W = this->integral_pt()->weight(ipt) * J;
  
       // Storage for the local unknowns
       Vector<double> interpolated_u(n_flux, 0.0);
  
       // Loop over the shape functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Locally cache the shape function
         const double psi_ = psi(l);
         for (unsigned i = 0; i < n_flux; i++)
         {
           // Calculate the velocity and tangent vector
           interpolated_u[i] += this->nodal_value(l, u_nodal_index[i]) * psi_;
         }
       }
  
       average_value[n_flux] += W;
       // Loop over the values
       for (unsigned i = 0; i < n_flux; i++)
       {
         average_value[i] += interpolated_u[i] * W;
       }
     }
  
     // Divide the results by the size of the element
     for (unsigned i = 0; i < n_flux; i++)
     {
       average_value[i] /= average_value[n_flux];
     }
   }

References DIM, i, J, and oomph::QuadTreeNames::W.

Referenced by oomph::DGSpectralEulerElement< 1, NNODE_1D >::calculate_element_averages(), oomph::DGSpectralEulerElement< 2, NNODE_1D >::calculate_element_averages(), oomph::DGSpectralScalarAdvectionElement< 1, NNODE_1D >::calculate_element_averages(), oomph::DGSpectralScalarAdvectionElement< 2, NNODE_1D >::calculate_element_averages(), oomph::DGScalarAdvectionElement< 1, NNODE_1D >::calculate_element_averages(), and oomph::DGScalarAdvectionElement< 2, NNODE_1D >::calculate_element_averages().

◆ dflux_du()

template<unsigned DIM>

void oomph::FluxTransportEquations< DIM >::dflux_du	(	const Vector< double > &	u,
		RankThreeTensor< double > &	df_du
	)

protectedvirtual

Return the flux derivatives as a funciton of the unknowns Default finite-different implementation

Return the derivatives of the flux components as functions of the unknowns. The default implementation is to use second-order finite-differences, but these can be overloaded in specific equations

Reimplemented in oomph::ScalarAdvectionEquations< DIM >.

   {
     // Find the number of fluxes
     const unsigned n_flux = nflux();
     // Local copy of the unknowns
     Vector<double> u_local = u;
     // Finite differences
     DenseMatrix<double> F(n_flux, DIM), F_plus(n_flux, DIM),
       F_minus(n_flux, DIM);
     const double fd_step = GeneralisedElement::Default_fd_jacobian_step;
     // Now loop over all the fluxes
     for (unsigned p = 0; p < n_flux; p++)
     {
       // Store the old value
       const double old_var = u_local[p];
       // Increment the value
       u_local[p] += fd_step;
       // Get the new values
       flux(u_local, F_plus);
  
       // Reset the value
       u_local[p] = old_var;
       // Decrement the value
       u_local[p] -= fd_step;
       // Get the new values
       flux(u_local, F_minus);
  
       // Assemble the entries of the jacobian
       for (unsigned r = 0; r < n_flux; r++)
       {
         for (unsigned j = 0; j < DIM; j++)
         {
           df_du(r, j, p) = (F_plus(r, j) - F_minus(r, j)) / (2.0 * fd_step);
         }
       }
  
       // Reset the value
       u_local[p] = old_var;
     }
   }

References oomph::GeneralisedElement::Default_fd_jacobian_step, DIM, oomph::OcTreeNames::F, ProblemParameters::flux(), j, p, and UniformPSDSelfTest::r.

◆ dshape_and_dtest_eulerian_at_knot_flux_transport()

template<unsigned DIM>

virtual double oomph::FluxTransportEquations< DIM >::dshape_and_dtest_eulerian_at_knot_flux_transport	(	const unsigned &	ipt,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

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

Implemented in oomph::QScalarAdvectionElement< DIM, NNODE_1D >, oomph::QScalarAdvectionElement< 1, NNODE_1D >, oomph::QScalarAdvectionElement< 2, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< DIM, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< 1, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< 2, NNODE_1D >, oomph::QSpectralEulerElement< DIM, NNODE_1D >, oomph::QSpectralEulerElement< 1, NNODE_1D >, and oomph::QSpectralEulerElement< 2, NNODE_1D >.

◆ dshape_and_dtest_eulerian_flux_transport()

template<unsigned DIM>

virtual double oomph::FluxTransportEquations< DIM >::dshape_and_dtest_eulerian_flux_transport	(	const Vector< double > &	s,
		Shape &	psi,
		DShape &	dpsidx,
		Shape &	test,
		DShape &	dtestdx
	)		const

protectedpure virtual

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

Implemented in oomph::QScalarAdvectionElement< DIM, NNODE_1D >, oomph::QScalarAdvectionElement< 1, NNODE_1D >, oomph::QScalarAdvectionElement< 2, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< DIM, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< 1, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< 2, NNODE_1D >, oomph::QSpectralEulerElement< DIM, NNODE_1D >, oomph::QSpectralEulerElement< 1, NNODE_1D >, and oomph::QSpectralEulerElement< 2, NNODE_1D >.

◆ du_dt_flux_transport()

template<unsigned DIM>

double oomph::FluxTransportEquations< DIM >::du_dt_flux_transport	(	const unsigned &	n,
		const unsigned &	i
	)		const

i-th component of du/dt at local node n. Uses suitably interpolated value for hanging nodes.

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

References i, oomph::TimeStepper::is_steady(), n, oomph::TimeStepper::ntstorage(), plotPSD::t, and oomph::TimeStepper::weight().

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

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

inlinevirtual

Compute the element's residual Vector and the jacobian matrix Virtual function can be overloaded by hanging-node version

Reimplemented from oomph::GeneralisedElement.

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

References oomph::GeneralisedElement::Dummy_matrix, and oomph::FluxTransportEquations< DIM >::fill_in_generic_residual_contribution_flux_transport().

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

template<unsigned DIM>

void oomph::FluxTransportEquations< 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::GeneralisedElement.

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

References oomph::FluxTransportEquations< DIM >::fill_in_generic_residual_contribution_flux_transport().

◆ fill_in_contribution_to_mass_matrix()

template<unsigned DIM>

void oomph::FluxTransportEquations< DIM >::fill_in_contribution_to_mass_matrix	(	Vector< double > &	residuals,
		DenseMatrix< double > &	mass_matrix
	)

inlinevirtual

Assemble the contributions to the mass matrix and residuals.

Reimplemented from oomph::GeneralisedElement.

     {
       fill_in_generic_residual_contribution_flux_transport(
         residuals, GeneralisedElement::Dummy_matrix, mass_matrix, 3);
     }

References oomph::GeneralisedElement::Dummy_matrix, and oomph::FluxTransportEquations< DIM >::fill_in_generic_residual_contribution_flux_transport().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

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

inlinevirtual

Compute the element's residual Vector.

Reimplemented from oomph::GeneralisedElement.

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

References oomph::GeneralisedElement::Dummy_matrix, and oomph::FluxTransportEquations< DIM >::fill_in_generic_residual_contribution_flux_transport().

◆ fill_in_generic_residual_contribution_flux_transport()

template<unsigned DIM>

void oomph::FluxTransportEquations< DIM >::fill_in_generic_residual_contribution_flux_transport	(	Vector< double > &	residuals,
		DenseMatrix< double > &	jacobian,
		DenseMatrix< double > &	mass_matrix,
		unsigned	flag
	)

virtual

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

Compute the residuals for the flux transport equations; flag=1 compute jacobian as well flag=2 compute mass matrix and jacobian as well flag=3 compute mass matrix as well

Reimplemented in oomph::DGScalarAdvectionElement< 2, NNODE_1D >, oomph::DGScalarAdvectionElement< 1, NNODE_1D >, oomph::DGSpectralScalarAdvectionElement< 2, NNODE_1D >, oomph::DGSpectralScalarAdvectionElement< 1, NNODE_1D >, oomph::DGSpectralEulerElement< 2, NNODE_1D >, and oomph::DGSpectralEulerElement< 1, NNODE_1D >.

   {
     // Find the number of fluxes
     const unsigned n_flux = this->nflux();
     // Find the number of nodes
     const unsigned n_node = this->nnode();
     // Storage for the shape function and derivatives of shape function
     Shape psi(n_node), test(n_node);
     DShape dpsidx(n_node, DIM), dtestdx(n_node, DIM);
  
     // Cache the nodal indices at which the unknowns are stored
     unsigned u_nodal_index[n_flux];
     for (unsigned i = 0; i < n_flux; i++)
     {
       u_nodal_index[i] = this->u_index_flux_transport(i);
     }
  
     // Find the number of integration points
     unsigned n_intpt = this->integral_pt()->nweight();
  
     // 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 shape functions at the knot
       double J = this->dshape_and_dtest_eulerian_at_knot_flux_transport(
         ipt, psi, dpsidx, test, dtestdx);
  
       // Get the integral weight
       double W = this->integral_pt()->weight(ipt) * J;
  
       // Storage for the local unknowns
       Vector<double> interpolated_u(n_flux, 0.0);
       Vector<double> interpolated_dudt(n_flux, 0.0);
  
       // Loop over the shape functions
       for (unsigned l = 0; l < n_node; l++)
       {
         // Locally cache the shape function
         const double psi_ = psi(l);
         for (unsigned i = 0; i < n_flux; i++)
         {
           // Calculate the velocity and tangent vector
           interpolated_u[i] += this->nodal_value(l, u_nodal_index[i]) * psi_;
           interpolated_dudt[i] += this->du_dt_flux_transport(l, i) * psi_;
         }
       }
  
       // Calculate the flux at the integration point
       DenseMatrix<double> F(n_flux, DIM);
       this->flux(interpolated_u, F);
  
       RankThreeTensor<double> dF_du(n_flux, DIM, n_flux);
       if ((flag) && (flag != 3))
       {
         this->dflux_du(interpolated_u, dF_du);
       }
  
       // We need to assemble the contributions to the volume integral
       for (unsigned l = 0; l < n_node; l++)
       {
         // Loop over the unknowns
         for (unsigned i = 0; i < n_flux; i++)
         {
           // Get the local equation number
           local_eqn = this->nodal_local_eqn(l, i);
  
           // if it's not a boundary condition
           if (local_eqn >= 0)
           {
             // Add the time derivatives
             residuals[local_eqn] -= interpolated_dudt[i] * test(l) * W;
  
  
             // Calculate the flux dot product
             double flux_dot = 0.0;
             for (unsigned k = 0; k < DIM; k++)
             {
               flux_dot += F(i, k) * dtestdx(l, k);
             }
  
             // Add the contribution to the residuals
             residuals[local_eqn] += flux_dot * W;
  
             // Now worry about the jacobian and mass matrix terms
             if (flag)
             {
               // If we are assembling the jacobian
               if (flag < 3)
               {
                 // Loop over the shape functions again
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   // Loop over the unknowns again
                   for (unsigned i2 = 0; i2 < n_flux; i2++)
                   {
                     // Get the local unknowns
                     local_unknown = this->nodal_local_eqn(l2, i2);
                     // If not pinned
                     if (local_unknown >= 0)
                     {
                       // Add the time derivative terms
                       if (i2 == i)
                       {
                         jacobian(local_eqn, local_unknown) -=
                           node_pt(l2)->time_stepper_pt()->weight(1, 0) *
                           psi(l2) * test(l) * W;
  
                         // Add the mass matrix if we are computing
                         // it and the jacobian
                         if (flag == 2)
                         {
                           mass_matrix(local_eqn, local_unknown) +=
                             psi(l2) * test(l) * W;
                         }
                       }
  
                       // Add the flux derivative terms
                       double dflux_dot = 0.0;
                       for (unsigned k = 0; k < DIM; k++)
                       {
                         dflux_dot += dF_du(i, k, i2) * dtestdx(l, k);
                       }
                       jacobian(local_eqn, local_unknown) +=
                         dflux_dot * psi(l2) * W;
                     }
                   }
                 }
               }
               // End of jacobian assembly, here we are just assembling the
               // mass matrix
               else
               {
                 for (unsigned l2 = 0; l2 < n_node; l2++)
                 {
                   local_unknown = this->nodal_local_eqn(l2, i);
                   if (local_unknown >= 0)
                   {
                     mass_matrix(local_eqn, local_unknown) +=
                       psi(l2) * test(l) * W;
                   }
                 }
               }
             }
           }
         }
       }
     }
   }

References DIM, oomph::OcTreeNames::F, ProblemParameters::flux(), i, J, k, Eigen::test, and oomph::QuadTreeNames::W.

Referenced by oomph::FluxTransportEquations< DIM >::fill_in_contribution_to_jacobian(), oomph::FluxTransportEquations< DIM >::fill_in_contribution_to_jacobian_and_mass_matrix(), oomph::FluxTransportEquations< DIM >::fill_in_contribution_to_mass_matrix(), oomph::FluxTransportEquations< DIM >::fill_in_contribution_to_residuals(), oomph::DGSpectralEulerElement< 1, NNODE_1D >::fill_in_generic_residual_contribution_flux_transport(), oomph::DGSpectralEulerElement< 2, NNODE_1D >::fill_in_generic_residual_contribution_flux_transport(), oomph::DGSpectralScalarAdvectionElement< 1, NNODE_1D >::fill_in_generic_residual_contribution_flux_transport(), oomph::DGSpectralScalarAdvectionElement< 2, NNODE_1D >::fill_in_generic_residual_contribution_flux_transport(), oomph::DGScalarAdvectionElement< 1, NNODE_1D >::fill_in_generic_residual_contribution_flux_transport(), and oomph::DGScalarAdvectionElement< 2, NNODE_1D >::fill_in_generic_residual_contribution_flux_transport().

◆ flux()

template<unsigned DIM>

virtual void oomph::FluxTransportEquations< DIM >::flux	(	const Vector< double > &	u,
		DenseMatrix< double > &	f
	)

inlineprotectedvirtual

Return the flux as a function of the unknown. This interface could (should) be generalised)

Reimplemented in oomph::ScalarAdvectionEquations< DIM >, and oomph::EulerEquations< DIM >.

     {
       std::ostringstream error_stream;
       error_stream
         << "Default empty flux function called\n"
         << "This should be overloaded with a specific flux function\n"
         << "in a derived class\n";
       throw OomphLibError(
         error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
     }

References OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ interpolated_u_flux_transport()

template<unsigned DIM>

double oomph::FluxTransportEquations< DIM >::interpolated_u_flux_transport	(	const Vector< double > &	s,
		const unsigned &	i
	)

Return the i-th unknown at the local coordinate s.

   {
     // Find the number of nodes
     const unsigned n_node = this->nnode();
     // Get the shape functions at the local coordinate
     Shape psi(n_node);
     this->shape(s, psi);
  
     // Now interpolate each unknown
     double u = 0.0;
  
     // Loop over the nodes
     for (unsigned n = 0; n < n_node; n++)
     {
       const double psi_ = psi[n];
       u += this->nodal_value(n, u_index_flux_transport(i)) * psi_;
     }
     return u;
   }

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

◆ nflux()

template<unsigned DIM>

virtual unsigned oomph::FluxTransportEquations< DIM >::nflux ( ) const

inlineprotectedvirtual

Return the number of fluxes (default zero)

Reimplemented in oomph::ScalarAdvectionEquations< DIM >, and oomph::EulerEquations< DIM >.

     {
       return 0;
     }

◆ output() [1/2]

template<unsigned DIM>

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

inlinevirtual

Output the element data — typically the values at the nodes in a format suitable for post-processing.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QScalarAdvectionElement< DIM, NNODE_1D >, oomph::QScalarAdvectionElement< 1, NNODE_1D >, oomph::QScalarAdvectionElement< 2, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< DIM, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< 1, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< 2, NNODE_1D >, oomph::QSpectralEulerElement< 1, NNODE_1D >, and oomph::QSpectralEulerElement< 2, NNODE_1D >.

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

Referenced by oomph::QSpectralScalarAdvectionElement< DIM, NNODE_1D >::output(), and oomph::QScalarAdvectionElement< DIM, NNODE_1D >::output().

◆ output() [2/2]

template<unsigned DIM>

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

virtual

Output function, print the values of all unknowns.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QScalarAdvectionElement< DIM, NNODE_1D >, oomph::QScalarAdvectionElement< 1, NNODE_1D >, oomph::QScalarAdvectionElement< 2, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< DIM, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< 1, NNODE_1D >, oomph::QSpectralScalarAdvectionElement< 2, NNODE_1D >, oomph::QSpectralEulerElement< 1, NNODE_1D >, and oomph::QSpectralEulerElement< 2, NNODE_1D >.

   {
     // Find the number of fluxes
     const unsigned n_flux = this->nflux();
  
     // Vector of local coordinates
     Vector<double> s(DIM);
  
     // Tecplot header info
     outfile << tecplot_zone_string(nplot);
  
     // Loop over plot points
     unsigned num_plot_points = nplot_points(nplot);
     for (unsigned iplot = 0; iplot < num_plot_points; iplot++)
     {
       // Get local coordinates of plot point
       get_s_plot(iplot, nplot, s);
  
       // Coordinates
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << interpolated_x(s, i) << " ";
       }
  
       // Values
       for (unsigned i = 0; i < n_flux; i++)
       {
         outfile << interpolated_u_flux_transport(s, i) << " ";
       }
  
       outfile << std::endl;
     }
     outfile << std::endl;
  
     // Write tecplot footer (e.g. FE connectivity lists)
     write_tecplot_zone_footer(outfile, nplot);
   }

References DIM, i, and s.

◆ u_index_flux_transport()

template<unsigned DIM>

virtual unsigned oomph::FluxTransportEquations< DIM >::u_index_flux_transport ( const unsigned & i ) const

inlineprotectedvirtual

Return the index at which the i-th unknown value is stored. The default value, i, is appropriate for single-physics problems. In derived multi-physics elements, this function should be overloaded to reflect the chosen storage scheme. Note that these equations require that the unknowns are always stored at the same indices at each node.

     {
       return i;
     }

References i.

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

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ FluxTransportEquations()

◆ ~FluxTransportEquations()

Member Function Documentation

◆ calculate_element_averages()

◆ dflux_du()

◆ dshape_and_dtest_eulerian_at_knot_flux_transport()

◆ dshape_and_dtest_eulerian_flux_transport()

◆ du_dt_flux_transport()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

◆ fill_in_contribution_to_mass_matrix()

◆ fill_in_contribution_to_residuals()

◆ fill_in_generic_residual_contribution_flux_transport()

◆ flux()

◆ interpolated_u_flux_transport()

◆ nflux()

◆ output() [1/2]

◆ output() [2/2]

◆ u_index_flux_transport()

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