Base class for Euler equations. More...

#include <euler_elements.h>

Inheritance diagram for oomph::EulerEquations< DIM >:

Public Member Functions
	EulerEquations ()
	Return the flux derivatives as a function of the unknowns. More...

virtual	~EulerEquations ()
	Destructor. More...

double	pressure (const Vector< double > &u) const
	Calculate the pressure from the unknowns. More...

double	gamma () const
	Return the value of gamma. More...

double *&	gamma_pt ()
	Access function for the pointer to gamma. More...

double *const &	gamma_pt () const
	Access function for the pointer to gamma (const version) More...

unsigned	required_nvalue (const unsigned &n) const

void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_solution_pt, const double &t, Vector< double > &error, Vector< double > &norm)

void	output (std::ostream &outfile)

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

void	allocate_memory_for_averages ()

double &	average_gradient (const unsigned &i, const unsigned &j)
	Return access to the average gradient. More...

double &	average_prim_value (const unsigned &i)
	Return the average values. More...

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

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_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
unsigned	nflux () const
	DIM momentum-components, a density and an energy are transported. More...

void	flux (const Vector< double > &u, DenseMatrix< double > &f)
	Return the flux as a function of the unknown. More...

Protected Member Functions inherited from oomph::FluxTransportEquations< DIM >
virtual unsigned	u_index_flux_transport (const unsigned &i) const

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)

Private Member Functions
double	Default_Gamma_Value

double	Default_Gamma_Value

double	Default_Gamma_Value

Private Attributes
double *	Gamma_pt

double *	Average_prim_value
	Storage for the average primitive values. More...

double *	Average_gradient
	Storage for the approximated gradients. More...

Static Private Attributes
static double	Default_Gamma_Value

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::EulerEquations< DIM >

Base class for Euler equations.

Constructor & Destructor Documentation

◆ EulerEquations()

template<unsigned DIM>

oomph::EulerEquations< DIM >::EulerEquations ( )

inline

Return the flux derivatives as a function of the unknowns.

Constructor

       : FluxTransportEquations<DIM>(),
         Average_prim_value(0),
         Average_gradient(0)
     {
       // Set the default value of gamma
       Gamma_pt = &Default_Gamma_Value;
     }

References oomph::EulerEquations< DIM >::Default_Gamma_Value, and oomph::EulerEquations< DIM >::Gamma_pt.

◆ ~EulerEquations()

template<unsigned DIM>

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

inlinevirtual

Destructor.

     {
       if (this->Average_prim_value != 0)
       {
         delete[] Average_prim_value;
         Average_prim_value = 0;
       }
       if (this->Average_gradient != 0)
       {
         delete[] Average_gradient;
         Average_gradient = 0;
       }
     }

References oomph::EulerEquations< DIM >::Average_gradient, and oomph::EulerEquations< DIM >::Average_prim_value.

Member Function Documentation

◆ allocate_memory_for_averages()

template<unsigned DIM>

void oomph::EulerEquations< DIM >::allocate_memory_for_averages ( )

inline

     {
       // Find the number of fluxes
       const unsigned n_flux = this->nflux();
       // Resize the memory if necessary
       if (this->Average_prim_value == 0)
       {
         this->Average_prim_value = new double[n_flux];
       }
       // Will move this one day
       if (this->Average_gradient == 0)
       {
         this->Average_gradient = new double[n_flux * DIM];
       }
     }

References DIM, and oomph::EulerEquations< DIM >::nflux().

◆ average_gradient()

template<unsigned DIM>

double& oomph::EulerEquations< DIM >::average_gradient	(	const unsigned &	i,
		const unsigned &	j
	)

inline

Return access to the average gradient.

     {
       if (Average_gradient == 0)
       {
         throw OomphLibError("Averages not calculated yet",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
       }
       return Average_gradient[DIM * i + j];
     }

References oomph::EulerEquations< DIM >::Average_gradient, DIM, i, j, OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ average_prim_value()

template<unsigned DIM>

double& oomph::EulerEquations< DIM >::average_prim_value ( const unsigned & i )

inline

Return the average values.

     {
       if (Average_prim_value == 0)
       {
         throw OomphLibError("Averages not calculated yet",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
       }
       return Average_prim_value[i];
     }

References oomph::EulerEquations< DIM >::Average_prim_value, i, OOMPH_CURRENT_FUNCTION, and OOMPH_EXCEPTION_LOCATION.

◆ compute_error()

template<unsigned DIM>

void oomph::EulerEquations< DIM >::compute_error	(	std::ostream &	outfile,
		FiniteElement::UnsteadyExactSolutionFctPt	exact_solution_pt,
		const double &	t,
		Vector< double > &	error,
		Vector< double > &	norm
	)

inlinevirtual

Compute the error and norm of solution integrated over the element Does not plot the error in the outfile

Reimplemented from oomph::FiniteElement.

     {
       // 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);
       DShape dpsidx(n_node, DIM);
  
       // Find the number of integration points
       unsigned n_intpt = this->integral_pt()->nweight();
  
       error.resize(n_flux);
       norm.resize(n_flux);
       for (unsigned i = 0; i < n_flux; i++)
       {
         error[i] = 0.0;
         norm[i] = 0.0;
       }
  
       Vector<double> s(DIM);
  
       // Loop over the integration points
       for (unsigned ipt = 0; ipt < n_intpt; ipt++)
       {
         // Get the shape functions 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 functions
         Vector<double> interpolated_x(DIM, 0.0);
         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 < DIM; i++)
           {
             interpolated_x[i] += this->nodal_position(l, i) * psi_;
           }
  
           for (unsigned i = 0; i < n_flux; i++)
           {
             // Calculate the velocity and tangent vector
             interpolated_u[i] += this->nodal_value(l, i) * psi_;
           }
         }
  
         // Now get the exact solution at this value of x and t
         Vector<double> exact_u(n_flux, 0.0);
         (*exact_solution_pt)(t, interpolated_x, exact_u);
  
         // Loop over the unknowns
         for (unsigned i = 0; i < n_flux; i++)
         {
           error[i] += pow((interpolated_u[i] - exact_u[i]), 2.0) * W;
           norm[i] += interpolated_u[i] * interpolated_u[i] * W;
         }
       }
     }

References DIM, oomph::FiniteElement::dshape_eulerian_at_knot(), calibrate::error, TanhSolnForLinearWave::exact_u(), i, oomph::FiniteElement::integral_pt(), oomph::FiniteElement::interpolated_x(), J, oomph::EulerEquations< DIM >::nflux(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::nodal_value(), oomph::Integral::nweight(), Eigen::bfloat16_impl::pow(), s, plotPSD::t, oomph::QuadTreeNames::W, and oomph::Integral::weight().

◆ Default_Gamma_Value() [1/3]

double oomph::EulerEquations< 1 >::Default_Gamma_Value

private

Set the default value of Gamma to be 1.4 in all three dimension specialisations. This form seems to be required for gcc 4.4.4, rather than a more general templated version.

◆ Default_Gamma_Value() [2/3]

double oomph::EulerEquations< 2 >::Default_Gamma_Value

private

◆ Default_Gamma_Value() [3/3]

double oomph::EulerEquations< 3 >::Default_Gamma_Value

private

◆ flux()

template<unsigned DIM>

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

protectedvirtual

Return the flux as a function of the unknown.

Return the flux as a function of the unknowns The unknowns are stored as density, energy and then the velocity components

Reimplemented from oomph::FluxTransportEquations< DIM >.

   {
     // The density flux is the momentum
     for (unsigned j = 0; j < DIM; j++)
     {
       f(0, j) = u[2 + j];
     }
     // The energy flux is given by the velocity component multiplied by
     // E + p
     // Find the pressure
     double p = pressure(u);
  
     // The we can do the energy fluxes
     for (unsigned j = 0; j < DIM; j++)
     {
       f(1, j) = u[2 + j] * (u[1] + p) / u[0];
     }
  
     // Now the momentum fluxes
     for (unsigned i = 0; i < DIM; i++)
     {
       for (unsigned j = 0; j < DIM; j++)
       {
         f(2 + i, j) = u[2 + j] * u[2 + i] / u[0];
       }
       // Add the additional diagonal terms
       f(2 + i, i) += p;
     }
   }

References DIM, f(), i, j, and p.

◆ gamma()

template<unsigned DIM>

double oomph::EulerEquations< DIM >::gamma ( ) const

inline

Return the value of gamma.

     {
       return *Gamma_pt;
     }

References oomph::EulerEquations< DIM >::Gamma_pt.

◆ gamma_pt() [1/2]

template<unsigned DIM>

double*& oomph::EulerEquations< DIM >::gamma_pt ( )

inline

Access function for the pointer to gamma.

     {
       return Gamma_pt;
     }

References oomph::EulerEquations< DIM >::Gamma_pt.

◆ gamma_pt() [2/2]

template<unsigned DIM>

double* const& oomph::EulerEquations< DIM >::gamma_pt ( ) const

inline

Access function for the pointer to gamma (const version)

     {
       return Gamma_pt;
     }

References oomph::EulerEquations< DIM >::Gamma_pt.

◆ nflux()

template<unsigned DIM>

unsigned oomph::EulerEquations< DIM >::nflux ( ) const

inlineprotectedvirtual

DIM momentum-components, a density and an energy are transported.

Reimplemented from oomph::FluxTransportEquations< DIM >.

     {
       return DIM + 2;
     }

References DIM.

Referenced by oomph::EulerEquations< DIM >::allocate_memory_for_averages(), and oomph::EulerEquations< DIM >::compute_error().

◆ output() [1/2]

template<unsigned DIM>

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

inlinevirtual

Output function: x,y,u or x,y,z,u

Reimplemented from oomph::FiniteElement.

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

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

Referenced by oomph::QSpectralEulerElement< DIM, NNODE_1D >::output().

◆ output() [2/2]

template<unsigned DIM>

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

virtual

Output function, print the values of all unknowns.

Output function: x,y,u or x,y,z,u at n_plot^DIM plot points

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::QSpectralEulerElement< DIM, 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);
     // Vector of values
     Vector<double> u(n_flux, 0.0);
  
     // 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);
  
       // Coordinates
       for (unsigned i = 0; i < DIM; i++)
       {
         outfile << this->interpolated_x(s, i) << " ";
       }
  
       // Values
       for (unsigned i = 0; i < n_flux; i++)
       {
         u[i] = this->interpolated_u_flux_transport(s, i);
         outfile << u[i] << " ";
       }
  
       // Now output the velocity
       for (unsigned j = 0; j < DIM; j++)
       {
         outfile << u[2 + j] / u[0] << " ";
       }
  
       // Also the pressure
       outfile << pressure(u);
  
       outfile << std::endl;
     }
     outfile << std::endl;
  
     // Write tecplot footer (e.g. FE connectivity lists)
     this->write_tecplot_zone_footer(outfile, nplot);
   }

References DIM, i, j, and s.

◆ pressure()

template<unsigned DIM>

double oomph::EulerEquations< DIM >::pressure ( const Vector< double > & u ) const

Calculate the pressure from the unknowns.

Calculate the pressure value from the unknowns.

   {
     // Initialise the pressure to zero
     double p = 0.0;
     // Subtract off the momentum components
     for (unsigned j = 0; j < DIM; j++)
     {
       p -= u[2 + j] * u[2 + j];
     }
     // Multiply by half and divide by the extra density component
     p *= 0.5 / u[0];
     // Now add on the energy
     p += u[1];
     // Finaly multiply by gamma minus 1
     p *= (this->gamma() - 1);
  
     // return the pressure
     return p;
   }

References DIM, mathsFunc::gamma(), j, and p.

◆ required_nvalue()

template<unsigned DIM>

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

inlinevirtual

The number of unknowns at each node is the number of flux components

Reimplemented from oomph::FiniteElement.

     {
       return DIM + 2;
     }

References DIM.

Member Data Documentation

◆ Average_gradient

template<unsigned DIM>

double* oomph::EulerEquations< DIM >::Average_gradient

private

Storage for the approximated gradients.

Referenced by oomph::EulerEquations< DIM >::average_gradient(), and oomph::EulerEquations< DIM >::~EulerEquations().

◆ Average_prim_value

template<unsigned DIM>

double* oomph::EulerEquations< DIM >::Average_prim_value

private

Storage for the average primitive values.

Referenced by oomph::EulerEquations< DIM >::average_prim_value(), and oomph::EulerEquations< DIM >::~EulerEquations().

◆ Default_Gamma_Value

template<unsigned DIM>

double oomph::EulerEquations< DIM >::Default_Gamma_Value

staticprivate

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

◆ Gamma_pt

template<unsigned DIM>

double* oomph::EulerEquations< DIM >::Gamma_pt

private

Referenced by oomph::EulerEquations< DIM >::EulerEquations(), oomph::EulerEquations< DIM >::gamma(), and oomph::EulerEquations< DIM >::gamma_pt().

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

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ EulerEquations()

◆ ~EulerEquations()

Member Function Documentation

◆ allocate_memory_for_averages()

◆ average_gradient()

◆ average_prim_value()

◆ compute_error()

◆ Default_Gamma_Value() [1/3]

◆ Default_Gamma_Value() [2/3]

◆ Default_Gamma_Value() [3/3]

◆ flux()

◆ gamma()

◆ gamma_pt() [1/2]

◆ gamma_pt() [2/2]

◆ nflux()

◆ output() [1/2]

◆ output() [2/2]

◆ pressure()

◆ required_nvalue()

Member Data Documentation

◆ Average_gradient

◆ Average_prim_value

◆ Default_Gamma_Value

◆ Gamma_pt

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