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#include <boussinesq_elements.h>

Inheritance diagram for oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >:

Public Member Functions
	RefineableBuoyantQCrouzeixRaviartElement ()
	Constructor: call the underlying constructors and initialise the pointer to the Rayleigh number to address the default value of 0.0. More...

unsigned	required_nvalue (const unsigned &n) const
	The required number of values stored at the nodes is the sum of the required values of the two single-physics elements. This step is generic for any composed element of this type. More...

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

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

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

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

unsigned	nscalar_paraview () const
	Number of scalars/fields output by this element. Broken virtual. Needs to be implemented for each new specific element type. Temporary dummy. More...

void	scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. Temporary dummy. More...

std::string	scalar_name_paraview (const unsigned &i) const
	Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names. More...

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

void	output (std::ostream &outfile, const unsigned &nplot)
	Output function: x,y,u or x,y,z,u at Nplot^DIM plot points. More...

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

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

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

void	output_fct (std::ostream &outfile, const unsigned &Nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
	Output function for a time-dependent exact solution. Broken default. More...

unsigned	u_index_adv_diff () const
	Overload the index at which the temperature variable is stored. We choose to store is after the fluid velocities. More...

unsigned	nvertex_node () const
	Number of vertex nodes in the element is obtained from the geometric element. More...

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element, Call the geometric element's function. More...

unsigned	ncont_interpolated_values () const
	The total number of continously interpolated values is DIM+1 (DIM fluid velocities and one temperature). More...

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)
	Get the continuously interpolated values at the local coordinate s. We choose to put the fluid velocities first, followed by the temperature. More...

void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)
	Get all continuously interpolated values at the local coordinate s at time level t (t=0: present; t>0: previous). We choose to put the fluid velocities first, followed by the temperature. More...

void	further_setup_hanging_nodes ()
	The additional hanging node information must be set up for both single-physics elements. More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Call the rebuild_from_sons functions for each of the constituent multi-physics elements. More...

void	further_build ()
	Call the underlying single-physics element's further_build() functions and make sure that the pointer to the Rayleigh number is passed to the sons. More...

unsigned	nrecovery_order ()
	The recovery order is that of the NavierStokes elements. More...

unsigned	num_Z2_flux_terms ()
	The number of Z2 flux terms is the same as that in the fluid element plus that in the advection-diffusion element. More...

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)
	Get the Z2 flux by concatenating the fluxes from the fluid and the advection diffusion elements. More...

unsigned	ncompound_fluxes ()
	The number of compound fluxes is two (one for the fluid and one for the temperature) More...

void	get_Z2_compound_flux_indices (Vector< unsigned > &flux_index)
	Fill in which flux components are associated with the fluid measure and which are associated with the temperature measure. More...

void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Validate against exact solution at given time Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element Overload to broken default. More...

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Validate against exact solution. Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element Overload to broken default. More...

void	get_wind_adv_diff (const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &wind) const
	Overload the wind function in the advection-diffusion equations. This provides the coupling from the Navier–Stokes equations to the advection-diffusion equations because the wind is the fluid velocity. More...

void	get_body_force_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &result)
	Overload the body force in the navier-stokes equations This provides the coupling from the advection-diffusion equations to the Navier–Stokes equations, the body force is the temperature multiplied by the Rayleigh number acting in the direction opposite to gravity. More...

void	fill_in_contribution_to_residuals (Vector< double > &residuals)
	Fill in the constituent elements' contribution to the residual vector. More...

void	fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Compute the element's residual Vector and the jacobian matrix using full finite differences, the default implementation. More...

void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Add the element's contribution to its residuals vector, jacobian matrix and mass matrix. More...

void	fill_in_off_diagonal_jacobian_blocks_analytic (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Compute the contribution of the off-diagonal blocks analytically. More...

Public Member Functions inherited from oomph::RefineableQAdvectionDiffusionElement< DIM, 3 >
	RefineableQAdvectionDiffusionElement ()
	Empty Constructor: More...

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

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

unsigned	ncont_interpolated_values () const
	Number of continuously interpolated values: 1. More...

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

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: empty. More...

unsigned	nrecovery_order ()
	Order of recovery shape functions for Z2 error estimation: Same order as shape functions. More...

void	further_setup_hanging_nodes ()
	Perform additional hanging node procedures for variables that are not interpolated by all nodes. Empty. More...

Public Member Functions inherited from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >
	QAdvectionDiffusionElement ()
	Constructor: Call constructors for QElement and Advection Diffusion equations. More...

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

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

Public Member Functions inherited from oomph::AdvectionDiffusionEquations< DIM >
	AdvectionDiffusionEquations ()
	Constructor: Initialise the Source_fct_pt and Wind_fct_pt to null and set (pointer to) Peclet number to default. More...

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

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

double	du_dt_adv_diff (const unsigned &n) const
	du/dt at local node n. Uses suitably interpolated value for hanging nodes. More...

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

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

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

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

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

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

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

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

virtual void	get_source_adv_diff (const unsigned &ipt, const Vector< double > &x, double &source) const
	Get source term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations. More...

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

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

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

Public Member Functions inherited from oomph::FiniteElement
void	set_dimension (const unsigned &dim)
	Set the dimension of the element and initially set the dimension of the nodes to be the same as the dimension of the element. More...

void	set_nodal_dimension (const unsigned &nodal_dim)
	Set the dimension of the nodes in the element. This will typically only be required when constructing FaceElements or in beam and shell type elements where a lower dimensional surface is embedded in a higher dimensional space. More...

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)
	Set the number of nodes in the element to n, by resizing the storage for pointers to the Node objects. More...

int	nodal_local_eqn (const unsigned &n, const unsigned &i) const
	Return the local equation number corresponding to the i-th value at the n-th local node. More...

double	dJ_eulerian_at_knot (const unsigned &ipt, Shape &psi, DenseMatrix< double > &djacobian_dX) const
	Compute the geometric shape functions (psi) at integration point ipt. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of "detJ" w.r.t. the nodal coordinates. More...

	FiniteElement ()
	Constructor. More...

virtual	~FiniteElement ()
	The destructor cleans up the static memory allocated for shape function storage. Internal and external data get wiped by the GeneralisedElement destructor; nodes get killed in mesh destructor. More...

	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
	Adjust local coordinates so that they're located inside the element. More...

void	get_centre_of_gravity_and_max_radius_in_terms_of_zeta (Vector< double > &cog, double &max_radius) const
	Compute centre of gravity of all nodes and radius of node that is furthest from it. Used to assess approximately if a point is likely to be contained with an element in locate_zeta-like operations. More...

virtual void	local_coordinate_of_node (const unsigned &j, Vector< double > &s) const
	Get local coordinates of node j in the element; vector sets its own size (broken virtual) More...

virtual void	local_fraction_of_node (const unsigned &j, Vector< double > &s_fraction)
	Get the local fraction of the node j in the element A dumb, but correct default implementation is provided. More...

virtual double	local_one_d_fraction_of_node (const unsigned &n1d, const unsigned &i)
	Get the local fraction of any node in the n-th position in a one dimensional expansion along the i-th local coordinate. More...

virtual void	set_macro_elem_pt (MacroElement *macro_elem_pt)
	Set pointer to macro element – can be overloaded in derived elements to perform additional tasks. More...

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

void	get_x (const Vector< double > &s, Vector< double > &x) const
	Global coordinates as function of local coordinates. Either via FE representation or via macro-element (if Macro_elem_pt!=0) More...

void	get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x)
	Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). Either via FE representation of QElement or via macro-element (if Macro_elem_pt!=0). More...

virtual void	get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const
	Global coordinates as function of local coordinates using macro element representation. (Broken virtual — this must be overloaded in specific geometric element classes) More...

virtual void	get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)
	Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). using macro element representation (Broken virtual – overload in specific geometric element class if you want to use this functionality.) More...

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
	Calculate the geometric shape functions at local coordinate s. This function must be overloaded for each specific geometric element. More...

virtual void	shape_at_knot (const unsigned &ipt, Shape &psi) const
	Return the geometric shape function at the ipt-th integration point. More...

virtual void	dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
	Function to compute the geometric shape functions and derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element. (Broken virtual function — specifies the interface) More...

virtual void	dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const
	Return the geometric shape function and its derivative w.r.t. the local coordinates at the ipt-th integration point. More...

virtual void	d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const
	Function to compute the geometric shape functions and also first and second derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element (if required). (Broken virtual function — specifies the interface). Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / ds^2$ 2D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ 3D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_2^2$ d2psids(i,3) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ d2psids(i,4) = $\partial^2 \psi_j / \partial s_0 \partial s_2$ d2psids(i,5) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ . More...

virtual void	d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const
	Return the geometric shape function and its first and second derivatives w.r.t. the local coordinates at the ipt-th integration point. Numbering: 1D: d2psids(i,0) = $d^2 \psi_j / ds^2$ 2D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ 3D: d2psids(i,0) = $\partial^2 \psi_j / \partial s_0^2$ d2psids(i,1) = $\partial^2 \psi_j / \partial s_1^2$ d2psids(i,2) = $\partial^2 \psi_j / \partial s_2^2$ d2psids(i,3) = $\partial^2 \psi_j / \partial s_0 \partial s_1$ d2psids(i,4) = $\partial^2 \psi_j / \partial s_0 \partial s_2$ d2psids(i,5) = $\partial^2 \psi_j / \partial s_1 \partial s_2$ . More...

virtual double	J_eulerian (const Vector< double > &s) const
	Return the Jacobian of mapping from local to global coordinates at local position s. More...

virtual double	J_eulerian_at_knot (const unsigned &ipt) const
	Return the Jacobian of the mapping from local to global coordinates at the ipt-th integration point. More...

void	check_J_eulerian_at_knots (bool &passed) const
	Check that Jacobian of mapping between local and Eulerian coordinates at all integration points is positive. More...

void	check_jacobian (const double &jacobian) const
	Helper function used to check for singular or negative Jacobians in the transform from local to global or Lagrangian coordinates. More...

double	dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const
	Compute the geometric shape functions and also first derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. More...

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const
	Return the geometric shape functions and also first derivatives w.r.t. global coordinates at the ipt-th integration point. More...

virtual double	dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const
	Compute the geometric shape functions (psi) and first derivatives w.r.t. global coordinates (dpsidx) at the ipt-th integration point. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of both "detJ" and "dpsidx" w.r.t. the nodal coordinates. More...

double	d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
	Compute the geometric shape functions and also first and second derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. Numbering: 1D: d2psidx(i,0) = $d^2 \psi_j / d x^2$ 2D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ 3D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_2^2$ d2psidx(i,3) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ d2psidx(i,4) = $\partial^2 \psi_j / \partial x_0 \partial x_2$ d2psidx(i,5) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ . More...

virtual double	d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
	Return the geometric shape functions and also first and second derivatives w.r.t. global coordinates at ipt-th integration point. Numbering: 1D: d2psidx(i,0) = $d^2 \psi_j / d s^2$ 2D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ 3D: d2psidx(i,0) = $\partial^2 \psi_j / \partial x_0^2$ d2psidx(i,1) = $\partial^2 \psi_j / \partial x_1^2$ d2psidx(i,2) = $\partial^2 \psi_j / \partial x_2^2$ d2psidx(i,3) = $\partial^2 \psi_j / \partial x_0 \partial x_1$ d2psidx(i,4) = $\partial^2 \psi_j / \partial x_0 \partial x_2$ d2psidx(i,5) = $\partial^2 \psi_j / \partial x_1 \partial x_2$ . More...

virtual void	describe_local_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the local dofs of the element[s]. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

virtual void	describe_nodal_local_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the local dofs of the element[s]. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

virtual void	assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)
	Overloaded version of the calculation of the local equation numbers. If the boolean argument is true then pointers to the degrees of freedom associated with each equation number are stored locally in the array Dof_pt. More...

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
	Return the number of nodes along one edge of the element Default is to return zero — must be overloaded by geometric elements. More...

double	raw_nodal_position (const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n. Do not use the hanging node representation. NOTE: Moved to cc file because of a possible compiler bug in gcc (yes, really!). The move to the cc file avoids inlining which appears to cause problems (only) when compiled with gcc and -O3; offensive "illegal read" is in optimised-out section of code and data that is allegedly illegal is readily readable (by other means) just before this function is called so I can't really see how we could possibly be responsible for this... More...

double	raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level). Do not use the hanging node representation. More...

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const
	Return the i-th component of nodal velocity: dx/dt at local node n. Do not use the hanging node representation. More...

double	raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
	Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. Do not use the hanging node representation. More...

double	raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the value of the k-th type of the i-th positional variable at the local node n. Do not use the hanging node representation. More...

double	raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. Do not use the hanging node representation. More...

double	raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...

double	raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...

double	nodal_position (const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n. If the node is hanging, the appropriate interpolation is handled by the position function in the Node class. More...

double	nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level) Returns suitably interpolated version for hanging nodes. More...

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
	Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. More...

double	nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the value of the k-th type of the i-th positional variable at the local node n. More...

double	nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
	Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. More...

double	dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...

double	dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
	i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...

unsigned	nnodal_position_type () const
	Return the number of coordinate types that the element requires to interpolate the geometry between the nodes. For Lagrange elements it is 1. More...

bool	has_hanging_nodes () const
	Return boolean to indicate if any of the element's nodes are geometrically hanging. More...

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

virtual Node *	construct_node (const unsigned &n)
	Construct the local node n and return a pointer to the newly created node object. More...

virtual Node *	construct_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n, including storage for history values required by timestepper, and return a pointer to the newly created node object. More...

virtual Node *	construct_boundary_node (const unsigned &n)
	Construct the local node n as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object. More...

virtual Node *	construct_boundary_node (const unsigned &n, TimeStepper *const &time_stepper_pt)
	Construct the local node n, including storage for history values required by timestepper, as a boundary node; that is a node that MAY be placed on a mesh boundary and return a pointer to the newly created node object. More...

int	get_node_number (Node *const &node_pt) const
	Return the number of the node *node_pt if this node is in the element, else return -1;. More...

virtual Node *	get_node_at_local_coordinate (const Vector< double > &s) const
	If there is a node at this local coordinate, return the pointer to the node. More...

double	raw_nodal_value (const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n but do NOT take hanging nodes into account. More...

double	raw_nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n, at time level t (t=0: present; t>0 previous timesteps), but do NOT take hanging nodes into account. More...

double	nodal_value (const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n. Produces suitably interpolated values for hanging nodes. More...

double	nodal_value (const unsigned &t, const unsigned &n, const unsigned &i) const
	Return the i-th value stored at local node n, at time level t (t=0: present; t>0 previous timesteps). Produces suitably interpolated values for hanging nodes. More...

unsigned	dim () const
	Return the spatial dimension of the element, i.e. the number of local coordinates required to parametrise its geometry. More...

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
	Return FE interpolated coordinate x[i] at local coordinate s at previous timestep t (t=0: present; t>0: previous timestep) More...

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
	Return FE interpolated position x[] at local coordinate s at previous timestep t as Vector (t=0: present; t>0: previous timestep) More...

virtual double	interpolated_dxdt (const Vector< double > &s, const unsigned &i, const unsigned &t)
	Return t-th time-derivative of the i-th FE-interpolated Eulerian coordinate at local coordinate s. More...

virtual void	interpolated_dxdt (const Vector< double > &s, const unsigned &t, Vector< double > &dxdt)
	Compte t-th time-derivative of the FE-interpolated Eulerian coordinate vector at local coordinate s. More...

unsigned	ngeom_data () const
	A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. More...

Data *	geom_data_pt (const unsigned &j)
	A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. More...

void	position (const Vector< double > &zeta, Vector< double > &r) const
	Return the parametrised position of the FiniteElement in its incarnation as a GeomObject, r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s). More...

void	position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const
	Return the parametrised position of the FiniteElement in its GeomObject incarnation: r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s) This version of the function returns the position as a function of time t=0: current time; t>0: previous timestep. Works for t=0 but needs to be overloaded if genuine time-dependence is required. More...

void	dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt)
	Return the t-th time derivative of the parametrised position of the FiniteElement in its GeomObject incarnation: $\frac{d^{t} dr(zeta)}{d t^{t}}$ . Call the t-th time derivative of the FE-interpolated Eulerian coordinate. More...

virtual double	zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const
	Specify the values of the "global" intrinsic coordinate, zeta, of a compound geometric object (a mesh of elements) when the element is viewied as a sub-geometric object. The default assumption is that the element will be treated as a sub-geometric object in a bulk Mesh of other elements (geometric objects). The "global" coordinate of the compound geometric object is simply the Eulerian coordinate, x. The second default assumption is that the coordinate zeta will be stored at the nodes and interpolated using the shape functions of the element. This function returns the value of zeta stored at local node n, where k is the type of coordinate and i is the coordinate direction. The function is virtual so that it can be overloaded by different types of element: FaceElements and SolidFiniteElements. More...

void	interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const
	Calculate the interpolated value of zeta, the intrinsic coordinate of the element when viewed as a compound geometric object within a Mesh as a function of the local coordinate of the element, s. The default assumption is the zeta is interpolated using the shape functions of the element with the values given by zeta_nodal(). A MacroElement representation of the intrinsic coordinate parametrised by the local coordinate s is used if available. Choosing the MacroElement representation of zeta (Eulerian x by default) allows a correspondence to be established between elements on different Meshes covering the same curvilinear domain in cases where one element is much coarser than the other. More...

void	locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false)
	For a given value of zeta, the "global" intrinsic coordinate of a mesh of FiniteElements represented as a compound geometric object, find the local coordinate in this element that corresponds to the requested value of zeta. If zeta cannot be located in this element, geom_object_pt is set to NULL. If zeta is located in this element, we return its "this" pointer. By default don't use any value passed in to the local coordinate s as the initial guess in the Newton method. More...

virtual void	node_update ()
	Update the positions of all nodes in the element using each node update function. The default implementation may be overloaded so that more efficient versions can be written. More...

virtual void	identify_geometric_data (std::set< Data * > &geometric_data_pt)
	The purpose of this function is to identify all `Data` objects that affect the elements' geometry. This function is implemented as an empty virtual function since it can only be implemented in conjunction with a node-update strategy. A specific implementation is provided in the ElementWithMovingNodes class. More...

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
	Calculate the size of the element (length, area, volume,...) in Eulerian computational coordinates. Use suitably overloaded compute_physical_size() function to compute the actual size (taking into account factors such as 2pi or radii the integrand) – such function can only be implemented on an equation-by-equation basis. More...

virtual double	compute_physical_size () const
	Broken virtual function to compute the actual size (taking into account factors such as 2pi or radii the integrand) – such function can only be implemented on an equation-by-equation basis. More...

void	point_output (std::ostream &outfile, const Vector< double > &s)
	Output solution (as defined by point_output_data()) at local cordinates s. More...

virtual unsigned	nplot_points_paraview (const unsigned &nplot) const
	Return the number of actual plot points for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...

virtual unsigned	nsub_elements_paraview (const unsigned &nplot) const
	Return the number of local sub-elements for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...

void	output_paraview (std::ofstream &file_out, const unsigned &nplot) const
	Paraview output – this outputs the coordinates at the plot points (for parameter nplot) to specified output file. More...

virtual void	write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const
	Fill in the offset information for paraview plot. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const
	Return the paraview element type. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const
	Return the offsets for the paraview sub-elements. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...

virtual void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const
	Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...

virtual void	output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const
	Output the element data at time step t. This is const because it is newly added and so can be done easily. Really all the output(...) functions should be const! 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
	Get cector of local coordinates of plot point i (when plotting nplot points in each "coordinate direction"). Generally these plot points will be uniformly spaced across the element. The optional final boolean flag (default: false) allows them to be shifted inwards to avoid duplication of plot point points between elements – useful when they are used in locate_zeta, say. More...

virtual std::string	tecplot_zone_string (const unsigned &nplot) const
	Return string for tecplot zone header (when plotting nplot points in each "coordinate direction") More...

virtual void	write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const
	Add tecplot zone "footer" to output stream (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...

virtual void	write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const
	Add tecplot zone "footer" to C-style output. (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...

virtual unsigned	nplot_points (const unsigned &nplot) const
	Return total number of plot points (when plotting nplot points in each "coordinate direction") More...

virtual void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
	Given the exact solution ${\bf f}({\bf x})$ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
	Given the exact solution ${\bf f}({\bf x})$ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the norm of the error and that of the exact solution. The version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
	Plot the error when compared against a given time-dependent exact solution ${\bf f}(t,{\bf x})$ . Also calculates the norm of the error and that of the exact solution. The version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...

virtual void	compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error)
	Plot the error when compared against a given exact solution ${\bf f}({\bf x})$ . Also calculates the maximum absolute error. More...

void	integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
	Evaluate integral of a Vector-valued function ${\bf f}({\bf x})$ over the element. More...

void	integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
	Evaluate integral of a Vector-valued, time-dependent function ${\bf f}(t,{\bf x})$ over the element. More...

virtual void	build_face_element (const int &face_index, FaceElement *face_element_pt)
	Function for building a lower dimensional FaceElement on the specified face of the FiniteElement. The arguments are the index of the face, an integer whose value depends on the particular element type, and a pointer to the FaceElement. More...

virtual unsigned	get_bulk_node_number (const int &face_index, const unsigned &i) const
	Get the number of the ith node on face face_index (in the bulk node vector). More...

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
	Get a pointer to the function mapping face coordinates to bulk coordinates. More...

virtual BulkCoordinateDerivativesFctPt	bulk_coordinate_derivatives_fct_pt (const int &face_index) const
	Get a pointer to the derivative of the mapping from face to bulk coordinates. More...

Public Member Functions inherited from oomph::GeneralisedElement
GeneralisedElement()	GeneralisedElement (const GeneralisedElement &)=delete
	Constructor: Initialise all pointers and all values to zero. 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
	Return the global equation number corresponding to the ieqn_local-th local equation number. More...

int	local_eqn_number (const unsigned long &ieqn_global) const
	Return the local equation number corresponding to the ieqn_global-th global equation number. Returns minus one (-1) if there is no local degree of freedom corresponding to the chosen global equation number. More...

unsigned	add_external_data (Data *const &data_pt, const bool &fd=true)
	Add a (pointer to an) external data object to the element and return its index (i.e. the index required to obtain it from the access function `external_data_pt(...)`. The optional boolean flag indicates whether the data should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite-differencing. More...

bool	external_data_fd (const unsigned &i) const
	Return the status of the boolean flag indicating whether the external data is included in the finite difference loop. More...

void	exclude_external_data_fd (const unsigned &i)
	Set the boolean flag to exclude the external datum from the the finite difference loop when computing the jacobian matrix. More...

void	include_external_data_fd (const unsigned &i)
	Set the boolean flag to include the external datum in the the finite difference loop when computing the jacobian matrix. More...

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)
	Set the timestepper associated with the i-th internal data object. More...

void	assign_internal_eqn_numbers (unsigned long &global_number, Vector< double * > &Dof_pt)
	Assign the global equation numbers to the internal Data. The arguments are the current highest global equation number (which will be incremented) and a Vector of pointers to the global variables (to which any unpinned values in the internal Data are added). More...

void	describe_dofs (std::ostream &out, const std::string &current_string) const
	Function to describe the dofs of the element. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...

void	add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)
	Add pointers to the internal data values to map indexed by the global equation number. More...

void	add_internal_data_values_to_vector (Vector< double > &vector_of_values)
	Add all internal data and time history values to the vector in the internal storage order. More...

void	read_internal_data_values_from_vector (const Vector< double > &vector_of_values, unsigned &index)
	Read all internal data and time history values from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...

void	add_internal_eqn_numbers_to_vector (Vector< long > &vector_of_eqn_numbers)
	Add all equation numbers associated with internal data to the vector in the internal storage order. More...

void	read_internal_eqn_numbers_from_vector (const Vector< long > &vector_of_eqn_numbers, unsigned &index)
	Read all equation numbers associated with internal data from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...

virtual void	assign_local_eqn_numbers (const bool &store_local_dof_pt)
	Setup the arrays of local equation numbers for the element. If the optional boolean argument is true, then pointers to the associated degrees of freedom are stored locally in the array Dof_pt. More...

virtual void	complete_setup_of_dependencies ()
	Complete the setup of any additional dependencies that the element may have. Empty virtual function that may be overloaded for specific derived elements. Used, e.g., for elements with algebraic node update functions to determine the "geometric Data", i.e. the Data that affects the element's shape. This function is called (for all elements) at the very beginning of the equation numbering procedure to ensure that all dependencies are accounted for. More...

virtual void	get_residuals (Vector< double > &residuals)
	Calculate the vector of residuals of the equations in the element. By default initialise the vector to zero and then call the fill_in_contribution_to_residuals() function. Note that this entire function can be overloaded if desired. More...

virtual void	get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the elemental Jacobian matrix "d equation / d variable". More...

virtual void	get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Calculate the residuals and the elemental "mass" matrix, the matrix that multiplies the time derivative terms in a problem. More...

virtual void	get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Calculate the residuals and jacobian and elemental "mass" matrix, the matrix that multiplies the time derivative terms. More...

virtual void	get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
	Calculate the derivatives of the residuals with respect to a parameter. More...

virtual void	get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Calculate the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. More...

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)
	Calculate the derivatives of the elemental Jacobian matrix mass matrix and residuals with respect to a parameter. More...

virtual void	get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Calculate the product of the Hessian (derivative of Jacobian with respect to all variables) an eigenvector, Y, and other specified vectors, C (d(J_{ij})/d u_{k}) Y_{j} C_{k}. More...

virtual void	get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Return the vector of inner product of the given pairs of history values. More...

virtual void	get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Compute the vectors that when taken as a dot product with other history values give the inner product over the element. More...

void	set_halo (const unsigned &non_halo_proc_ID)
	Label the element as halo and specify processor that holds non-halo counterpart. More...

void	set_nonhalo ()
	Label the element as not being a halo. More...

bool	is_halo () const
	Is this element a halo? More...

int	non_halo_proc_ID ()
	ID of processor ID that holds non-halo counterpart of halo element; negative if not a halo. More...

void	set_must_be_kept_as_halo ()
	Insist that this element be kept as a halo element during a distribute? More...

void	unset_must_be_kept_as_halo ()
	Do not insist that this element be kept as a halo element during distribution. More...

bool	must_be_kept_as_halo () const
	Test whether the element must be kept as a halo element. More...

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

	GeomObject (const unsigned &ndim)
	Constructor: Pass dimension of geometric object (# of Eulerian coords = # of Lagrangian coords; no time history available/needed) More...

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim)
	Constructor: pass # of Eulerian and Lagrangian coordinates. No time history available/needed. More...

	GeomObject (const unsigned &nlagrangian, const unsigned &ndim, TimeStepper *time_stepper_pt)
	Constructor: pass # of Eulerian and Lagrangian coordinates and pointer to time-stepper which is used to handle the position at previous timesteps and allows the evaluation of veloc/acceleration etc. in cases where the GeomData varies with time. More...

	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 ()
	Access function for pointer to time stepper: Null if object is not time-dependent. More...

TimeStepper *	time_stepper_pt () const
	Access function for pointer to time stepper: Null if object is not time-dependent. Const version. More...

virtual void	position (const double &t, const Vector< double > &zeta, Vector< double > &r) const
	Parametrised position on object: r(zeta). Evaluated at the continuous time value, t. More...

virtual void	dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const
	Derivative of position Vector w.r.t. to coordinates: $\frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). Evaluated at current time. More...

virtual void	d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const
	2nd derivative of position Vector w.r.t. to coordinates: $\frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...

virtual void	d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const
	Posn Vector and its 1st & 2nd derivatives w.r.t. to coordinates: $\frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). $\frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...

Public Member Functions inherited from oomph::RefineableAdvectionDiffusionEquations< DIM >
	RefineableAdvectionDiffusionEquations ()
	Empty Constructor. More...

	RefineableAdvectionDiffusionEquations (const RefineableAdvectionDiffusionEquations< DIM > &dummy)=delete
	Broken copy constructor. More...

void	operator= (const RefineableAdvectionDiffusionEquations< DIM > &)=delete
	Broken assignment operator. More...

void	dinterpolated_u_adv_diff_ddata (const Vector< double > &s, Vector< double > &du_ddata, Vector< unsigned > &global_eqn_number)
	Compute the derivatives of the i-th component of velocity at point s with respect to all data that can affect its value. In addition, return the global equation numbers corresponding to the data. Overload the non-refineable version to take account of hanging node information. More...

Public Member Functions inherited from oomph::RefineableElement
	RefineableElement ()
	Constructor, calls the FiniteElement constructor and initialises the member data. More...

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

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

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

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

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

virtual unsigned	required_nsons () const
	Set the number of sons that can be constructed by the element The default is none. More...

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

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

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

template<class ELEMENT >
void	split (Vector< ELEMENT * > &son_pt) const
	Split the element into the number of sons to be constructed and return a vector of pointers to the sons. Elements are allocated, but they are not given any properties. The refinement level of the sons is one higher than that of the father elemern. More...

int	local_hang_eqn (Node *const &node_pt, const unsigned &i)
	Access function that returns the local equation number for the hanging node variables (values stored at master nodes). The local equation number corresponds to the i-th unknown stored at the node addressed by node_pt. More...

virtual void	build (Mesh &mesh_pt, Vector< Node > &new_node_pt, bool &was_already_built, std::ofstream &new_nodes_file)=0
	Interface to function that builds the element: i.e. construct the nodes, assign their positions, apply boundary conditions, etc. The required procedures depend on the geometrical type of the element and must be implemented in specific refineable elements. Any new nodes created during the build process are returned in the vector new_node_pt. More...

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

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

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

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

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

void	deselect_sons_for_unrefinement ()
	No unrefinement will be performed by merging the four sons of this element. More...

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

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

virtual void	unbuild ()
	Unbuild the element, i.e. mark the nodes that were created during its creation for possible deletion. More...

virtual void	deactivate_element ()
	Final operations that must be performed when the element is no longer active in the mesh, but still resident in the QuadTree. More...

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

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

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

virtual Node *	interpolating_node_pt (const unsigned &n, const int &value_id)
	In mixed elements, different sets of nodes are used to interpolate different unknowns. This function returns the n-th node that interpolates the value_id-th unknown. Default implementation is that all variables use the positional nodes, i.e. isoparametric elements. Note that any overloaded versions of this function MUST provide a set of nodes for the position, which always has the value_id -1. More...

virtual double	local_one_d_fraction_of_interpolating_node (const unsigned &n1d, const unsigned &i, const int &value_id)
	Return the local one dimensional fraction of the n1d-th node in the direction of the local coordinate s[i] that is used to interpolate the value_id-th continuously interpolated unknown. Default assumes isoparametric interpolation for all unknowns. More...

virtual Node *	get_interpolating_node_at_local_coordinate (const Vector< double > &s, const int &value_id)
	Return a pointer to the node that interpolates the value-id-th unknown at local coordinate s. If there is not a node at that position, then return 0. More...

virtual unsigned	ninterpolating_node (const int &value_id)
	Return the number of nodes that are used to interpolate the value_id-th unknown. Default is to assume isoparametric elements. More...

virtual unsigned	ninterpolating_node_1d (const int &value_id)
	Return the number of nodes in a one_d direction that are used to interpolate the value_id-th unknown. Default is to assume an isoparametric mapping. More...

virtual void	interpolating_basis (const Vector< double > &s, Shape &psi, const int &value_id) const
	Return the basis functions that are used to interpolate the value_id-th unknown. By default assume isoparameteric interpolation. More...

virtual void	check_integrity (double &max_error)=0
	Check the integrity of the element: Continuity of positions values, etc. Essentially, check that the approximation of the functions is consistent when viewed from both sides of the element boundaries Must be overloaded for each different geometric element. More...

void	identify_field_data_for_interactions (std::set< std::pair< Data *, unsigned >> &paired_field_data)
	The purpose of this function is to identify all possible Data that can affect the fields interpolated by the FiniteElement. This must be overloaded to include data from any hanging nodes correctly. More...

void	assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt)
	Overload the function that assigns local equation numbers for the Data stored at the nodes so that hanging data is taken into account. More...

virtual RefineableElement *	root_element_pt ()
	Pointer to the root element in refinement hierarchy (must be implemented in specific elements that do refinement via tree-like refinement structure. Here we provide a default implementation that is appropriate for cases where tree-like refinement doesn't exist or if the element doesn't have root in that tree (i.e. if it's a root itself): We return "this". More...

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

void	get_father_at_refinement_level (unsigned &refinement_level, RefineableElement *&father_at_reflevel_pt)
	Return a pointer to the "father" element at the specified refinement level. More...

virtual void	initial_setup (Tree *const &adopted_father_pt=0, const unsigned &initial_p_order=0)
	Initial setup of the element: e.g. set the appropriate internal p-order. If an adopted father is specified, information from this is used instead of using the father found from the tree. More...

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

virtual void	setup_hanging_nodes (Vector< std::ofstream * > &output_stream)
	Mark up any hanging nodes that arise as a result of non-uniform refinement. Any hanging nodes will be documented in files addressed by the streams in the vector output_stream, if the streams are open. More...

unsigned	nshape_controlling_nodes ()
	Number of shape-controlling nodes = the number of non-hanging nodes plus the number of master nodes associated with hanging nodes. More...

std::map< Node *, unsigned >	shape_controlling_node_lookup ()
	Return lookup scheme for unique number associated with any of the nodes that actively control the shape of the element (i.e. they are either non-hanging nodes of this element or master nodes of hanging nodes. More...

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

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

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

virtual void	compute_exact_Z2_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_flux_pt, double &error, double &norm)
	Plot the error when compared against a given exact flux. Also calculates the norm of the error and that of the exact flux. More...

virtual double	geometric_jacobian (const Vector< double > &x)
	Return the geometric jacobian (should be overloaded in cylindrical and spherical geometries). Default value one is suitable for Cartesian coordinates. More...

Public Member Functions inherited from oomph::RefineableQElement< DIM >
	RefineableQElement ()
	Empty constuctor. More...

Public Member Functions inherited from oomph::RefineableQCrouzeixRaviartElement< DIM >
	RefineableQCrouzeixRaviartElement ()
	Constructor. More...

	RefineableQCrouzeixRaviartElement (const RefineableQCrouzeixRaviartElement< DIM > &dummy)=delete
	Broken copy constructor. More...

unsigned	ncont_interpolated_values () const
	Broken assignment operator. More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	Rebuild from sons: Reconstruct pressure from the (merged) sons This must be specialised for each dimension. More...

unsigned	nrecovery_order ()
	Order of recovery shape functions for Z2 error estimation: Same order as shape functions. More...

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

Node *	vertex_node_pt (const unsigned &j) const
	Pointer to the j-th vertex node in the element. More...

void	get_interpolated_values (const Vector< double > &s, Vector< double > &values)
	Get the function value u in Vector. Note: Given the generality of the interface (this function is usually called from black-box documentation or interpolation routines), the values Vector sets its own size in here. More...

void	get_interpolated_values (const unsigned &t, const Vector< double > &s, Vector< double > &values)
	Get all function values [u,v..,p] at previous timestep t (t=0: present; t>0: previous timestep). More...

void	further_setup_hanging_nodes ()
	Perform additional hanging node procedures for variables that are not interpolated by all nodes. Empty. More...

void	further_build ()
	Further build for Crouzeix_Raviart interpolates the internal pressure dofs from father element: Make sure pressure values and dp/ds agree between fathers and sons at the midpoints of the son elements. This must be specialised for each dimension. More...

void	build_fp_press_adv_diff_robin_bc_element (const unsigned &face_index)
	Build FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner. More...

void	identify_load_data (std::set< std::pair< Data *, unsigned >> &paired_load_data)
	Add to the set `paired_load_data` pairs containing. More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	2D Rebuild from sons: Reconstruct pressure from the (merged) sons More...

void	rebuild_from_sons (Mesh *&mesh_pt)
	3D Rebuild from sons: Reconstruct pressure from the (merged) sons More...

void	further_build ()
	2D Further build for Crouzeix_Raviart interpolates the internal pressure dofs from father element: Make sure pressure values and dp/ds agree between fathers and sons at the midpoints of the son elements. More...

void	further_build ()
	3D Further build for Crouzeix_Raviart interpolates the internal pressure dofs from father element: Make sure pressure values and dp/ds agree between fathers and sons at the midpoints of the son elements. More...

Public Member Functions inherited from oomph::QCrouzeixRaviartElement< DIM >
	QCrouzeixRaviartElement ()
	Constructor, there are DIM+1 internal values (for the pressure) More...

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

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

double	p_nst (const unsigned &i) const
	Return the i-th pressure value (Discontinous pressure interpolation – no need to cater for hanging nodes). More...

double	p_nst (const unsigned &t, const unsigned &i) const
	Return the i-th pressure value (Discontinous pressure interpolation – no need to cater for hanging nodes). More...

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

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const
	Pressure shape and test functions and their derivs w.r.t. to global coords at local coordinate s (taken from geometry) Return Jacobian of mapping between local and global coordinates. More...

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

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

void	identify_pressure_data (std::set< std::pair< Data *, unsigned >> &paired_pressure_data)
	Add to the set `paired_pressure_data` pairs containing. More...

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

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

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

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

void	full_output (std::ostream &outfile)
	Full output function: x,y,[z],u,v,[w],p,du/dt,dv/dt,[dw/dt],dissipation in tecplot format. Default number of plot points. More...

void	full_output (std::ostream &outfile, const unsigned &nplot)
	Full output function: x,y,[z],u,v,[w],p,du/dt,dv/dt,[dw/dt],dissipation in tecplot format. nplot points in each coordinate direction. More...

unsigned	ndof_types () const
	The number of "DOF types" that degrees of freedom in this element are sub-divided into: Velocity and pressure. More...

void	get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const
	Create a list of pairs for all unknowns in this element, so that the first entry in each pair contains the global equation number of the unknown, while the second one contains the number of the "DOF type" that this unknown is associated with. (Function can obviously only be called if the equation numbering scheme has been set up.) Velocity=0; Pressure=1. More...

void	pshape_nst (const Vector< double > &s, Shape &psi) const
	2D : Pressure shape functions More...

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const
	2D : Pressure shape and test functions and derivs w.r.t. to Eulerian coords. Return Jacobian of mapping between local and global coordinates. More...

void	pshape_nst (const Vector< double > &s, Shape &psi) const
	3D : Pressure shape functions More...

double	dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const
	3D : Pressure shape and test functions and derivs w.r.t. to Eulerian coords. Return Jacobian of mapping between local and global coordinates. More...

Public Member Functions inherited from oomph::NavierStokesEquations< DIM >
	NavierStokesEquations ()
	Constructor: NULL the body force and source function and make sure the ALE terms are included by default. More...

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

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

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

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

const double &	viscosity_ratio () const
	Viscosity ratio for element: Element's viscosity relative to the viscosity used in the definition of the Reynolds number. More...

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

const double &	density_ratio () const
	Density ratio for element: Element's density relative to the viscosity used in the definition of the Reynolds number. More...

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

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

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

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

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

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

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

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

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

NavierStokesPressureAdvDiffSourceFctPt &	source_fct_for_pressure_adv_diff ()
	Access function for the source-function pointer for pressure advection diffusion (used for validation only). More...

NavierStokesPressureAdvDiffSourceFctPt	source_fct_for_pressure_adv_diff () const
	Access function for the source-function pointer for pressure advection diffusion (used for validation only). Const version. More...

int &	pinned_fp_pressure_eqn ()
	Global eqn number of pressure dof that's pinned in pressure adv diff problem. More...

double	u_nst (const unsigned &n, const unsigned &i) const
	Velocity i at local node n. Uses suitably interpolated value for hanging nodes. The use of u_index_nst() permits the use of this element as the basis for multi-physics elements. The default is to assume that the i-th velocity component is stored at the i-th location of the node. More...

double	u_nst (const unsigned &t, const unsigned &n, const unsigned &i) const
	Velocity i at local node n at timestep t (t=0: present; t>0: previous). Uses suitably interpolated value for hanging nodes. More...

virtual unsigned	u_index_nst (const unsigned &i) const
	Return the index at which the i-th unknown velocity component 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. More...

unsigned	n_u_nst () const
	Return the number of velocity components Used in FluidInterfaceElements. More...

double	du_dt_nst (const unsigned &n, const unsigned &i) const
	i-th component of du/dt at local node n. Uses suitably interpolated value for hanging nodes. More...

void	disable_ALE ()
	Disable ALE, i.e. assert the mesh is not moving – you do this at your own risk! More...

void	enable_ALE ()
	(Re-)enable ALE, i.e. take possible mesh motion into account when evaluating the time-derivative. Note: By default, ALE is enabled, at the expense of possibly creating unnecessary work in problems where the mesh is, in fact, stationary. More...

virtual int	p_nodal_index_nst () const
	Return the index at which the pressure is stored if it is stored at the nodes. If not stored at the nodes this will return a negative number. More...

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

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

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

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

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

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

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

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

void	get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction)
	Compute traction (on the viscous scale) exerted onto the fluid at local coordinate s. N has to be outer unit normal to the fluid. More...

void	get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction_p, Vector< double > &traction_visc_n, Vector< double > &traction_visc_t)
	Compute traction (on the viscous scale) exerted onto the fluid at local coordinate s, decomposed into pressure and normal and tangential viscous components. N has to be outer unit normal to the fluid. More...

void	get_load (const Vector< double > &s, const Vector< double > &N, Vector< double > &load)
	This implements a pure virtual function defined in the FSIFluidElement class. The function computes the traction (on the viscous scale), at the element's local coordinate s, that the fluid element exerts onto an adjacent solid element. The number of arguments is imposed by the interface defined in the FSIFluidElement – only the unit normal N (pointing into the fluid!) is actually used in the computation. More...

unsigned	nscalar_paraview () const
	Number of scalars/fields output by this element. Reimplements broken virtual function in base class. More...

void	scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const
	Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type. More...

void	scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const
	Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type. More...

std::string	scalar_name_paraview (const unsigned &i) const
	Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names in specific elements. More...

void	full_output (std::ostream &outfile)
	Full output function: x,y,[z],u,v,[w],p,du/dt,dv/dt,[dw/dt],dissipation in tecplot format. Default number of plot points. More...

void	full_output (std::ostream &outfile, const unsigned &nplot)
	Full output function: x,y,[z],u,v,[w],p,du/dt,dv/dt,[dw/dt],dissipation in tecplot format. nplot points in each coordinate direction. More...

void	output_veloc (std::ostream &outfile, const unsigned &nplot, const unsigned &t)
	Output function: x,y,[z],u,v,[w] in tecplot format. nplot points in each coordinate direction at timestep t (t=0: present; t>0: previous timestep) More...

void	output_vorticity (std::ostream &outfile, const unsigned &nplot)
	Output function: x,y,[z], [omega_x,omega_y,[and/or omega_z]] in tecplot format. nplot points in each coordinate direction. More...

void	output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
	Output exact solution specified via function pointer at a given number of plot points. Function prints as many components as are returned in solution Vector. More...

void	output_fct (std::ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
	Output exact solution specified via function pointer at a given time and at a given number of plot points. Function prints as many components as are returned in solution Vector. More...

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

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

void	compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Validate against exact solution at given time Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element. More...

void	compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Validate against exact solution. Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element. More...

void	compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
	Validate against exact solution. Solution is provided via function pointer. Compute L2 error and L2 norm of velocity solution over element. More...

void	compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
	Validate against exact solution. Solution is provided via function pointer. Compute L2 error and L2 norm of velocity solution over element. 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)
	Compute the element's residual Vector and the jacobian matrix Virtual function can be overloaded by hanging-node version. More...

void	fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
	Add the element's contribution to its residuals vector, jacobian matrix and mass matrix. More...

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

void	fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
	Compute the element's residual Vector and the jacobian matrix Virtual function can be overloaded by hanging-node version. More...

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

void	fill_in_pressure_advection_diffusion_residuals (Vector< double > &residuals)
	Compute the residuals for the associated pressure advection diffusion problem. Used by the Fp preconditioner. More...

void	fill_in_pressure_advection_diffusion_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Compute the residuals and Jacobian for the associated pressure advection diffusion problem. Used by the Fp preconditioner. More...

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

void	output_pressure_advection_diffusion_robin_elements (std::ostream &outfile)
	Output the FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner. More...

void	delete_pressure_advection_diffusion_robin_elements ()
	Delete the FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner. More...

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

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

double	interpolated_u_nst (const unsigned &t, const Vector< double > &s, const unsigned &i) const
	Return FE interpolated velocity u[i] at local coordinate s at time level t (t=0: present; t>0: history) More...

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

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

double	interpolated_dudx_nst (const Vector< double > &s, const unsigned &i, const unsigned &j) const
	Return FE interpolated derivatives of velocity component u[i] w.r.t spatial global coordinate direction x[j] at local coordinate s. More...

void	point_output_data (const Vector< double > &s, Vector< double > &data)
	Output solution in data vector at local cordinates s: x,y [,z], u,v,[w], p. More...

void	get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
	Compute 2D vorticity vector at local coordinate s (return in one and only component of vorticity vector. More...

void	get_vorticity (const Vector< double > &s, double &vorticity) const
	Compute vorticity vector at local coordinate s and return the one and only component of vorticity vector (only makes sense when solving the 2D N.St. equations) More...

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

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

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

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

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

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

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

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

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

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

Public Member Functions inherited from oomph::RefineableNavierStokesEquations< DIM >
	RefineableNavierStokesEquations ()
	Constructor. More...

virtual Node *	pressure_node_pt (const unsigned &n_p)
	Pointer to n_p-th pressure node (Default: NULL, indicating that pressure is not based on nodal interpolation). More...

void	get_pressure_and_velocity_mass_matrix_diagonal (Vector< double > &press_mass_diag, Vector< double > &veloc_mass_diag, const unsigned &which_one=0)
	Compute the diagonal of the velocity/pressure mass matrices. If which one=0, both are computed, otherwise only the pressure (which_one=1) or the velocity mass matrix (which_one=2 – the LSC version of the preconditioner only needs that one) More...

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

void	get_Z2_flux (const Vector< double > &s, Vector< double > &flux)
	Get 'flux' for Z2 error recovery: Upper triangular entries in strain rate tensor. More...

void	dinterpolated_u_nst_ddata (const Vector< double > &s, const unsigned &i, Vector< double > &du_ddata, Vector< unsigned > &global_eqn_number)
	Compute the derivatives of the i-th component of velocity at point s with respect to all data that can affect its value. In addition, return the global equation numbers corresponding to the data. Overload the non-refineable version to take account of hanging node information. More...

Private Member Functions
double	Default_Physical_Constant_Value
	Set the default value of the Rayleigh number to be zero. More...

double	Default_Physical_Constant_Value

Private Attributes
double *	Ra_pt
	Pointer to a new physical variable, the Rayleigh number. More...

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

Additional Inherited Members
Public Types inherited from oomph::AdvectionDiffusionEquations< DIM >
typedef void(*	AdvectionDiffusionSourceFctPt) (const Vector< double > &x, double &f)
	Function pointer to source function fct(x,f(x)) – x is a Vector! More...

typedef void(*	AdvectionDiffusionWindFctPt) (const Vector< double > &x, Vector< double > &wind)
	Function pointer to wind function fct(x,w(x)) – x is a Vector! More...

Public Types inherited from oomph::FiniteElement
typedef void(*	SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)
	Function pointer for function that computes vector-valued steady "exact solution" ${\bf f}({\bf x})$ as $\mbox{\tt fct}({\bf x}, {\bf f})$ . More...

typedef void(*	UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)
	Function pointer for function that computes Vector-valued time-dependent function ${\bf f}(t,{\bf x})$ as $\mbox{\tt fct}(t, {\bf x}, {\bf f})$ . More...

Public Types inherited from oomph::NavierStokesEquations< DIM >
typedef void(*	NavierStokesBodyForceFctPt) (const double &time, const Vector< double > &x, Vector< double > &body_force)
	Function pointer to body force function fct(t,x,f(x)) x is a Vector! More...

typedef double(*	NavierStokesSourceFctPt) (const double &time, const Vector< double > &x)
	Function pointer to source function fct(t,x) x is a Vector! More...

typedef double(*	NavierStokesPressureAdvDiffSourceFctPt) (const Vector< double > &x)
	Function pointer to source function fct(x) for the pressure advection diffusion equation (only used during validation!). x is a Vector! More...

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

Static Public Member Functions inherited from oomph::RefineableNavierStokesEquations< DIM >
static void	pin_redundant_nodal_pressures (const Vector< GeneralisedElement * > &element_pt)
	Loop over all elements in Vector (which typically contains all the elements in a fluid mesh) and pin the nodal pressure degrees of freedom that are not being used. Function uses the member function. More...

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

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

static bool	Accept_negative_jacobian = false
	Boolean that if set to true allows a negative jacobian in the transform between global and local coordinates (negative surface area = left-handed coordinate system). More...

static bool	Suppress_output_while_checking_for_inverted_elements
	Static boolean to suppress output while checking for inverted elements. More...

Static Public Attributes inherited from oomph::GeneralisedElement
static bool	Suppress_warning_about_any_repeated_data = false
	Static boolean to suppress warnings about repeated data. Defaults to false. More...

static bool	Suppress_warning_about_repeated_internal_data
	Static boolean to suppress warnings about repeated internal data. Defaults to false. More...

static bool	Suppress_warning_about_repeated_external_data = true
	Static boolean to suppress warnings about repeated external data. Defaults to true. More...

static double	Default_fd_jacobian_step = 1.0e-8
	Double used for the default finite difference step in elemental jacobian calculations. More...

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

Protected Member Functions inherited from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >
double	dshape_and_dtest_eulerian_adv_diff (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
	Shape, test functions & derivs. w.r.t. to global coords. Return Jacobian. More...

double	dshape_and_dtest_eulerian_at_knot_adv_diff (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
	Shape, test functions & derivs. w.r.t. to global coords. at integration point ipt. Return Jacobian. More...

Protected Member Functions inherited from oomph::FiniteElement
template<unsigned DIM>
double	invert_jacobian (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Take the matrix passed as jacobian and return its inverse in inverse_jacobian. This function is templated by the dimension of the element because matrix inversion cannot be written efficiently in a generic manner. More...

virtual double	invert_jacobian_mapping (const DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	A template-free interface that takes the matrix passed as jacobian and return its inverse in inverse_jacobian. By default the function will use the dimension of the element to call the correct invert_jacobian(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements. More...

virtual double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates, given the derivatives of the shape functions w.r.t. local coordinates. Returns the determinant of the jacobian, the jacobian and inverse jacobian. More...

double	local_to_eulerian_mapping (const DShape &dpsids, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates, given the derivatives of the shape functions w.r.t. local coordinates, Return only the determinant of the jacobian and the inverse of the mapping (ds/dx). More...

virtual void	dJ_eulerian_dnodal_coordinates (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	A template-free interface that calculates the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. To do this it requires the jacobian matrix and the derivatives of the shape functions w.r.t. the local coordinates. By default the function will use the dimension of the element to call the correct dJ_eulerian_dnodal_coordinates_templated_helper(..) function. This should be overloaded for efficiency (removal of a switch statement) in specific elements. More...

template<unsigned DIM>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij using the jacobian matrix and the derivatives of the shape functions w.r.t. the local coordinates. This function is templated by the dimension of the element. More...

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
	A template-free interface that calculates the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions $\psi_j$ w.r.t. the global eulerian coordinates . I.e. this function calculates. More...

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
	Calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates , using the determinant of the jacobian mapping, its derivative w.r.t. the nodal coordinates $X_{pq}$ , the inverse jacobian and the derivatives of the shape functions w.r.t. the local coordinates. The result is returned as a tensor of rank four. Numbering: d_dpsidx_dX(p,q,j,i) = $\frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right)$ This function is templated by the dimension of the element. More...

virtual void	transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
	Convert derivative w.r.t.local coordinates to derivatives w.r.t the coordinates used to assemble the inverse_jacobian passed in the mapping. On entry, dbasis must contain the basis function derivatives w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates on exit. This is virtual so that it may be overloaded if desired for efficiency reasons. More...

void	transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
	Convert derivative w.r.t local coordinates to derivatives w.r.t the coordinates used to assemble the inverse jacobian passed in the mapping, assuming that the coordinates are aligned in the direction of the local coordinates. On entry dbasis must contain the derivatives of the basis functions w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates. are converted into the new using the mapping inverse_jacobian. More...

virtual void	transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t. local coordiantes to derivatives and second derivatives w.r.t. the coordinates used to assemble the jacobian, inverse jacobian and jacobian2 passed to the function. By default this function will call transform_second_derivatives_template<>(...) using the dimension of the element as the template parameter. It is virtual so that it can be overloaded by a specific element to save using a switch statement. Optionally, the element writer may wish to use the transform_second_derivatives_diagonal<>(...) function On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

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
	Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This is templated by dimension because the method of calculation varies significantly with the dimension. On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

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
	Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This version of the function assumes that the local coordinates are aligned with the global coordinates, i.e. the jacobians are diagonal On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...

void	fill_in_jacobian_from_nodal_by_fd (DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. More...

virtual void	update_before_nodal_fd ()
	Function that is called before the finite differencing of any nodal data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_nodal_fd ()
	Function that is call after the finite differencing of the nodal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_nodal_fd (const unsigned &i)
	Function called within the finite difference loop for nodal data after a change in the i-th nodal value. More...

virtual void	reset_in_nodal_fd (const unsigned &i)
	Function called within the finite difference loop for nodal data after the i-th nodal values is reset. The default behaviour is to call the update function. More...

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
	Three-d specialisation of function to calculate inverse of jacobian mapping. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Zero-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	One-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Two-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

template<>
void	dJ_eulerian_dnodal_coordinates_templated_helper (const DenseMatrix< double > &jacobian, const DShape &dpsids, DenseMatrix< double > &djacobian_dX) const
	Three-d specialisation of function to calculate the derivative of the jacobian of a mapping with respect to the nodal coordinates X_ij. More...

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
	Zero-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

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
	One-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

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
	Two-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

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
	Three-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $X_{pq}$ of the derivative of the shape functions w.r.t. the global eulerian coordinates . More...

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...

template<>
void	transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly. Specialisation to two spatial dimensions. More...

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...

template<>
void	transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
	Convert second derivatives w.r.t. local coordinates to second derivatives w.r.t. the coordinates passed in the tensor coordinate. Specialised to two spatial dimension. More...

Protected Member Functions inherited from oomph::GeneralisedElement
unsigned	add_internal_data (Data *const &data_pt, const bool &fd=true)
	Add a (pointer to an) internal data object to the element and return the index required to obtain it from the access function `internal_data_pt()`. The boolean indicates whether the datum should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite differencing. More...

bool	internal_data_fd (const unsigned &i) const
	Return the status of the boolean flag indicating whether the internal data is included in the finite difference loop. More...

void	exclude_internal_data_fd (const unsigned &i)
	Set the boolean flag to exclude the internal datum from the finite difference loop when computing the jacobian matrix. More...

void	include_internal_data_fd (const unsigned &i)
	Set the boolean flag to include the internal datum in the finite difference loop when computing the jacobian matrix. More...

void	clear_global_eqn_numbers ()
	Clear the storage for the global equation numbers and pointers to dofs (if stored) More...

void	add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)
	Add the contents of the queue global_eqn_numbers to the local storage for the local-to-global translation scheme. It is essential that the entries in the queue are added IN ORDER i.e. from the front. More...

virtual void	assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)
	Assign the local equation numbers for the internal and external Data This must be called after the global equation numbers have all been assigned. It is virtual so that it can be overloaded by ElementWithExternalElements so that any external data from the external elements in included in the numbering scheme. If the boolean argument is true then pointers to the dofs will be stored in Dof_pt. More...

virtual void	assign_additional_local_eqn_numbers ()
	Setup any additional look-up schemes for local equation numbers. Examples of use include using local storage to refer to explicit degrees of freedom. The additional memory cost of such storage may or may not be offset by fast local access. More...

int	internal_local_eqn (const unsigned &i, const unsigned &j) const
	Return the local equation number corresponding to the j-th value stored at the i-th internal data. More...

int	external_local_eqn (const unsigned &i, const unsigned &j)
	Return the local equation number corresponding to the j-th value stored at the i-th external data. More...

void	fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all external data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

void	fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
	Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...

virtual void	update_before_internal_fd ()
	Function that is called before the finite differencing of any internal data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_internal_fd ()
	Function that is call after the finite differencing of the internal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_internal_fd (const unsigned &i)
	Function called within the finite difference loop for internal data after a change in any values in the i-th internal data object. More...

virtual void	reset_in_internal_fd (const unsigned &i)
	Function called within the finite difference loop for internal data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...

virtual void	update_before_external_fd ()
	Function that is called before the finite differencing of any external data. This may be overloaded to update any dependent data before finite differencing takes place. More...

virtual void	reset_after_external_fd ()
	Function that is call after the finite differencing of the external data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...

virtual void	update_in_external_fd (const unsigned &i)
	Function called within the finite difference loop for external data after a change in any values in the i-th external data object. More...

virtual void	reset_in_external_fd (const unsigned &i)
	Function called within the finite difference loop for external data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...

virtual void	fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
	Add the elemental contribution to the mass matrix matrix. and the residuals vector. Note that this function should NOT initialise the residuals vector or the mass matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is deliberately broken. More...

virtual void	fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
	Fill in the contribution to the inner products between given pairs of history values. More...

virtual void	fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
	Fill in the contributions to the vectors that when taken as dot product with other history values give the inner product over the element. More...

Protected Member Functions inherited from oomph::RefineableAdvectionDiffusionEquations< DIM >
void	fill_in_generic_residual_contribution_adv_diff (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag)
	Add the element's contribution to the elemental residual vector and/or Jacobian matrix flag=1: compute both flag=0: compute only residual vector. More...

Protected Member Functions inherited from oomph::RefineableElement
void	assemble_local_to_eulerian_jacobian (const DShape &dpsids, DenseMatrix< double > &jacobian) const
	Assemble the jacobian matrix for the mapping from local to Eulerian coordinates, given the derivatives of the shape function w.r.t the local coordinates. Overload the standard version to use the hanging information for the Eulerian coordinates. More...

void	assemble_local_to_eulerian_jacobian2 (const DShape &d2psids, DenseMatrix< double > &jacobian2) const
	Assemble the the "jacobian" matrix of second derivatives of the mapping from local to Eulerian coordinates, given the second derivatives of the shape functions w.r.t. local coordinates. Overload the standard version to use the hanging information for the Eulerian coordinates. More...

void	assemble_eulerian_base_vectors (const DShape &dpsids, DenseMatrix< double > &interpolated_G) const
	Assemble the covariant Eulerian base vectors, assuming that the derivatives of the shape functions with respect to the local coordinates have already been constructed. Overload the standard version to account for hanging nodes. More...

double	local_to_eulerian_mapping_diagonal (const DShape &dpsids, DenseMatrix< double > &jacobian, DenseMatrix< double > &inverse_jacobian) const
	Calculate the mapping from local to Eulerian coordinates given the derivatives of the shape functions w.r.t the local coordinates. assuming that the coordinates are aligned in the direction of the local coordinates, i.e. there are no cross terms and the jacobian is diagonal. This funciton returns the determinant of the jacobian, the jacobian and the inverse jacobian. Overload the standard version to take hanging info into account. More...

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

virtual void	fill_in_jacobian_from_nodal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian)
	Calculate the contributions to the jacobian from the nodal degrees of freedom using finite differences. This version is overloaded to take hanging node information into account. More...

Protected Member Functions inherited from oomph::QCrouzeixRaviartElement< DIM >
double	dshape_and_dtest_eulerian_nst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
	Velocity shape and test functions and their derivs w.r.t. to global coords at local coordinate s (taken from geometry) Return Jacobian of mapping between local and global coordinates. More...

double	dshape_and_dtest_eulerian_at_knot_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const
	Velocity shape and test functions and their derivs w.r.t. to global coords at ipt-th integation point (taken from geometry) Return Jacobian of mapping between local and global coordinates. More...

double	dshape_and_dtest_eulerian_at_knot_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const
	Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping (J). Also compute derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates. More...

double	dshape_and_dtest_eulerian_at_knot_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const
	2D Define the shape functions (psi) and test functions (test) and their derivatives w.r.t. global coordinates (dpsidx and dtestdx) and return Jacobian of mapping (J). Additionally compute the derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates. More...

double	dshape_and_dtest_eulerian_at_knot_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const
	3D Define the shape functions (psi) and test functions (test) and their derivatives w.r.t. global coordinates (dpsidx and dtestdx) and return Jacobian of mapping (J). Additionally compute the derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates. More...

Protected Member Functions inherited from oomph::NavierStokesEquations< DIM >
virtual void	get_body_force_gradient_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, DenseMatrix< double > &d_body_force_dx)
	Get gradient of body force term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations. Computed via function pointer (if set) or by finite differencing (default) More...

virtual double	get_source_nst (const double &time, const unsigned &ipt, const Vector< double > &x)
	Calculate the source fct at given time and Eulerian position. More...

virtual void	get_source_gradient_nst (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &gradient)
	Get gradient of source term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations. Computed via function pointer (if set) or by finite differencing (default) More...

virtual void	fill_in_generic_dresidual_contribution_nst (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam, unsigned flag)
	Compute the derivatives of the residuals for the Navier–Stokes equations with respect to a parameter Flag=1 (or 0): do (or don't) compute the Jacobian as well. Flag=2: Fill in mass matrix too. More...

void	fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
	Compute the hessian tensor vector products required to perform continuation of bifurcations analytically. More...

Protected Member Functions inherited from oomph::RefineableNavierStokesEquations< DIM >
virtual void	pin_elemental_redundant_nodal_pressure_dofs ()
	Pin unused nodal pressure dofs (empty by default, because by default pressure dofs are not associated with nodes) More...

void	fill_in_generic_residual_contribution_nst (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag)
	Add element's contribution to elemental residual vector and/or Jacobian matrix flag=1: compute both flag=0: compute only residual vector. More...

void	fill_in_generic_pressure_advection_diffusion_contribution_nst (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)
	Compute the residuals for the associated pressure advection diffusion problem. Used by the Fp preconditioner. flag=1(or 0): do (or don't) compute the Jacobian as well. More...

virtual void	get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)
	Compute derivatives of elemental residual vector with respect to nodal coordinates. Overwrites default implementation in FiniteElement base class. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij}. More...

Static Protected Member Functions inherited from oomph::RefineableElement
static void	check_value_id (const int &n_continuously_interpolated_values, const int &value_id)
	Static helper function that is used to check that the value_id is in range. More...

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

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

AdvectionDiffusionSourceFctPt	Source_fct_pt
	Pointer to source function: More...

AdvectionDiffusionWindFctPt	Wind_fct_pt
	Pointer to wind function: More...

bool	ALE_is_disabled
	Boolean flag to indicate if ALE formulation is disabled when time-derivatives are computed. Only set to true if you're sure that the mesh is stationary. More...

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::GeneralisedElement
int	Non_halo_proc_ID
	Non-halo processor ID for Data; -1 if it's not a halo. More...

bool	Must_be_kept_as_halo
	Does this element need to be kept as a halo element during a distribute? 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
	Timestepper (used to handle access to geometry at previous timesteps) More...

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

unsigned	Refine_level
	Refinement level. More...

bool	To_be_refined
	Flag for refinement. More...

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

bool	Sons_to_be_unrefined
	Flag for unrefinement. More...

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

Protected Attributes inherited from oomph::QCrouzeixRaviartElement< DIM >
unsigned	P_nst_internal_index
	Internal index that indicates at which internal data the pressure is stored. More...

Protected Attributes inherited from oomph::NavierStokesEquations< DIM >
double *	Viscosity_Ratio_pt
	Pointer to the viscosity ratio (relative to the viscosity used in the definition of the Reynolds number) More...

double *	Density_Ratio_pt
	Pointer to the density ratio (relative to the density used in the definition of the Reynolds number) More...

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

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

double *	ReInvFr_pt
	Pointer to global Reynolds number x inverse Froude number (= Bond number / Capillary number) More...

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

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

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

NavierStokesPressureAdvDiffSourceFctPt	Press_adv_diff_source_fct_pt
	Pointer to source function pressure advection diffusion equation (only to be used during validation) More...

bool	ALE_is_disabled
	Boolean flag to indicate if ALE formulation is disabled when time-derivatives are computed. Only set to true if you're sure that the mesh is stationary. More...

Vector< FpPressureAdvDiffRobinBCElementBase * >	Pressure_advection_diffusion_robin_element_pt
	Storage for FaceElements that apply Robin BC for pressure adv diff equation used in Fp preconditioner. More...

int	Pinned_fp_pressure_eqn
	Global eqn number of pressure dof that's pinned in pressure advection diffusion problem (defaults to -1) More...

Static Protected Attributes inherited from oomph::FiniteElement
static const unsigned	Default_Initial_Nvalue = 0
	Default return value for required_nvalue(n) which gives the number of "data" values required by the element at node n; for example, solving a Poisson equation would required only one "data" value at each node. The defaults is set to zero, because a general element is problem-less. More...

static const double	Node_location_tolerance = 1.0e-14
	Default value for the tolerance to be used when locating nodes via local coordinates. More...

static const unsigned	N2deriv [] = {0, 1, 3, 6}
	Static array that holds the number of second derivatives as a function of the dimension of the element. More...

Static Protected Attributes inherited from oomph::GeneralisedElement
static DenseMatrix< double >	Dummy_matrix
	Empty dense matrix used as a dummy argument to combined residual and jacobian functions in the case when only the residuals are being assembled. More...

static std::deque< double * >	Dof_pt_deque
	Static storage for deque used to add_global_equation_numbers when pointers to the dofs in each element are not required. More...

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

Detailed Description

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

////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////

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

Definition at line 800 of file boussinesq_elements.h.

Constructor & Destructor Documentation

◆ RefineableBuoyantQCrouzeixRaviartElement()

template<unsigned DIM>

oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::RefineableBuoyantQCrouzeixRaviartElement ( )

inline

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

Definition at line 815 of file boussinesq_elements.h.

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

Member Function Documentation

◆ compute_error() [1/2]

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 1205 of file boussinesq_elements.h.

References oomph::FiniteElement::compute_error().

◆ compute_error() [2/2]

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 1191 of file boussinesq_elements.h.

References oomph::FiniteElement::compute_error().

◆ Default_Physical_Constant_Value() [1/2]

double oomph::RefineableBuoyantQCrouzeixRaviartElement< 2 >::Default_Physical_Constant_Value

private

Set the default value of the Rayleigh number to be zero.

Definition at line 1589 of file boussinesq_elements.h.

◆ Default_Physical_Constant_Value() [2/2]

double oomph::RefineableBuoyantQCrouzeixRaviartElement< 3 >::Default_Physical_Constant_Value

private

Definition at line 1593 of file boussinesq_elements.h.

◆ disable_ALE()

template<unsigned DIM>

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

inlinevirtual

Final override for disable ALE.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 845 of file boussinesq_elements.h.

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

◆ enable_ALE()

template<unsigned DIM>

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

inlinevirtual

Final override for enable ALE.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 853 of file boussinesq_elements.h.

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

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>

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

inlinevirtual

Compute the element's residual Vector and the jacobian matrix using full finite differences, the default implementation.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 1266 of file boussinesq_elements.h.

References oomph::FiniteElement::fill_in_contribution_to_jacobian(), oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_jacobian(), and oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::fill_in_off_diagonal_jacobian_blocks_analytic().

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 1289 of file boussinesq_elements.h.

References oomph::GeneralisedElement::fill_in_contribution_to_jacobian_and_mass_matrix().

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>

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

inlinevirtual

Fill in the constituent elements' contribution to the residual vector.

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 1252 of file boussinesq_elements.h.

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

◆ fill_in_off_diagonal_jacobian_blocks_analytic()

template<unsigned DIM>

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

inline

Compute the contribution of the off-diagonal blocks analytically.

Definition at line 1301 of file boussinesq_elements.h.

References oomph::QCrouzeixRaviartElement< DIM >::dshape_and_dtest_eulerian_at_knot_nst(), oomph::NavierStokesEquations< DIM >::g(), oomph::Node::hanging_pt(), i, oomph::FiniteElement::integral_pt(), oomph::Node::is_hanging(), oomph::RefineableElement::local_hang_eqn(), oomph::HangInfo::master_node_pt(), oomph::HangInfo::master_weight(), oomph::HangInfo::nmaster(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::nodal_value(), oomph::FiniteElement::node_pt(), oomph::Integral::nweight(), oomph::AdvectionDiffusionEquations< DIM >::pe(), oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::ra(), oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::u_index_adv_diff(), oomph::NavierStokesEquations< DIM >::u_index_nst(), oomph::QuadTreeNames::W, and oomph::Integral::weight().

Referenced by oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::fill_in_contribution_to_jacobian().

◆ further_build()

template<unsigned DIM>

void oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::further_build ( )

inlinevirtual

Call the underlying single-physics element's further_build() functions and make sure that the pointer to the Rayleigh number is passed to the sons.

Reimplemented from oomph::RefineableAdvectionDiffusionEquations< DIM >.

Definition at line 1091 of file boussinesq_elements.h.

References oomph::RefineableElement::father_element_pt(), oomph::RefineableAdvectionDiffusionEquations< DIM >::further_build(), oomph::RefineableQCrouzeixRaviartElement< DIM >::further_build(), and oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::ra_pt().

◆ further_setup_hanging_nodes()

template<unsigned DIM>

void oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::further_setup_hanging_nodes ( )

inlinevirtual

The additional hanging node information must be set up for both single-physics elements.

Reimplemented from oomph::RefineableElement.

Definition at line 1071 of file boussinesq_elements.h.

References oomph::RefineableQCrouzeixRaviartElement< DIM >::further_setup_hanging_nodes().

◆ get_body_force_nst()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::NavierStokesEquations< DIM >.

Definition at line 1231 of file boussinesq_elements.h.

References i, oomph::AdvectionDiffusionEquations< DIM >::interpolated_u_adv_diff(), and oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::ra().

◆ get_interpolated_values() [1/2]

template<unsigned DIM>

void oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::get_interpolated_values	(	const unsigned &	t,
		const Vector< double > &	s,
		Vector< double > &	values
	)

inlinevirtual

Get all continuously interpolated values at the local coordinate s at time level t (t=0: present; t>0: previous). We choose to put the fluid velocities first, followed by the temperature.

Reimplemented from oomph::RefineableAdvectionDiffusionEquations< DIM >.

Definition at line 1039 of file boussinesq_elements.h.

References oomph::RefineableAdvectionDiffusionEquations< DIM >::get_interpolated_values(), oomph::RefineableQCrouzeixRaviartElement< DIM >::get_interpolated_values(), i, s, and t.

◆ get_interpolated_values() [2/2]

template<unsigned DIM>

void oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::get_interpolated_values	(	const Vector< double > &	s,
		Vector< double > &	values
	)

inlinevirtual

Get the continuously interpolated values at the local coordinate s. We choose to put the fluid velocities first, followed by the temperature.

Reimplemented from oomph::RefineableAdvectionDiffusionEquations< DIM >.

Definition at line 1007 of file boussinesq_elements.h.

References oomph::RefineableAdvectionDiffusionEquations< DIM >::get_interpolated_values(), oomph::RefineableQCrouzeixRaviartElement< DIM >::get_interpolated_values(), i, and s.

◆ get_wind_adv_diff()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 1216 of file boussinesq_elements.h.

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

◆ get_Z2_compound_flux_indices()

template<unsigned DIM>

void oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::get_Z2_compound_flux_indices ( Vector< unsigned > & flux_index )

inlinevirtual

Fill in which flux components are associated with the fluid measure and which are associated with the temperature measure.

Reimplemented from oomph::ElementWithZ2ErrorEstimator.

Definition at line 1160 of file boussinesq_elements.h.

References i, oomph::RefineableAdvectionDiffusionEquations< DIM >::num_Z2_flux_terms(), and oomph::RefineableNavierStokesEquations< DIM >::num_Z2_flux_terms().

◆ get_Z2_flux()

template<unsigned DIM>

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

inlinevirtual

Get the Z2 flux by concatenating the fluxes from the fluid and the advection diffusion elements.

Reimplemented from oomph::RefineableAdvectionDiffusionEquations< DIM >.

Definition at line 1126 of file boussinesq_elements.h.

References oomph::RefineableAdvectionDiffusionEquations< DIM >::get_Z2_flux(), oomph::RefineableNavierStokesEquations< DIM >::get_Z2_flux(), i, oomph::RefineableAdvectionDiffusionEquations< DIM >::num_Z2_flux_terms(), oomph::RefineableNavierStokesEquations< DIM >::num_Z2_flux_terms(), and s.

◆ ncompound_fluxes()

template<unsigned DIM>

unsigned oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::ncompound_fluxes ( )

inlinevirtual

The number of compound fluxes is two (one for the fluid and one for the temperature)

Reimplemented from oomph::ElementWithZ2ErrorEstimator.

Definition at line 1153 of file boussinesq_elements.h.

◆ ncont_interpolated_values()

template<unsigned DIM>

unsigned oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::ncont_interpolated_values ( ) const

inlinevirtual

The total number of continously interpolated values is DIM+1 (DIM fluid velocities and one temperature).

Implements oomph::RefineableElement.

Definition at line 998 of file boussinesq_elements.h.

◆ nrecovery_order()

template<unsigned DIM>

unsigned oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::nrecovery_order ( )

inlinevirtual

The recovery order is that of the NavierStokes elements.

Implements oomph::ElementWithZ2ErrorEstimator.

Definition at line 1109 of file boussinesq_elements.h.

References oomph::RefineableQCrouzeixRaviartElement< DIM >::nrecovery_order().

◆ nscalar_paraview()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 864 of file boussinesq_elements.h.

◆ num_Z2_flux_terms()

template<unsigned DIM>

unsigned oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::num_Z2_flux_terms ( )

inlinevirtual

The number of Z2 flux terms is the same as that in the fluid element plus that in the advection-diffusion element.

Reimplemented from oomph::RefineableAdvectionDiffusionEquations< DIM >.

Definition at line 1116 of file boussinesq_elements.h.

◆ nvertex_node()

template<unsigned DIM>

unsigned oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::nvertex_node ( ) const

inlinevirtual

Number of vertex nodes in the element is obtained from the geometric element.

Reimplemented from oomph::FiniteElement.

Definition at line 984 of file boussinesq_elements.h.

◆ output() [1/4]

template<unsigned DIM>

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

inlinevirtual

C-style output function: Broken default.

Reimplemented from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >.

Definition at line 945 of file boussinesq_elements.h.

References oomph::FiniteElement::output().

◆ output() [2/4]

template<unsigned DIM>

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

inlinevirtual

C-style output function: Broken default.

Reimplemented from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >.

Definition at line 951 of file boussinesq_elements.h.

References oomph::FiniteElement::output().

◆ output() [3/4]

template<unsigned DIM>

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

inlinevirtual

Overload the standard output function with the broken default.

Reimplemented from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >.

Definition at line 898 of file boussinesq_elements.h.

References oomph::FiniteElement::output().

◆ output() [4/4]

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >.

Definition at line 905 of file boussinesq_elements.h.

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

◆ output_fct() [1/2]

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >.

Definition at line 967 of file boussinesq_elements.h.

References oomph::FiniteElement::output_fct().

◆ output_fct() [2/2]

template<unsigned DIM>

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

inlinevirtual

Output function for an exact solution: Broken default.

Reimplemented from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >.

Definition at line 957 of file boussinesq_elements.h.

References oomph::FiniteElement::output_fct().

◆ ra()

template<unsigned DIM>

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

inline

Access function for the Rayleigh number (const version)

Definition at line 832 of file boussinesq_elements.h.

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

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

◆ ra_pt()

template<unsigned DIM>

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

inline

Access function for the pointer to the Rayleigh number.

Definition at line 838 of file boussinesq_elements.h.

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

Referenced by oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::further_build().

◆ rebuild_from_sons()

template<unsigned DIM>

void oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::rebuild_from_sons ( Mesh *& mesh_pt )

inlinevirtual

Call the rebuild_from_sons functions for each of the constituent multi-physics elements.

Implements oomph::RefineableElement.

Definition at line 1081 of file boussinesq_elements.h.

References oomph::RefineableQAdvectionDiffusionElement< DIM, NNODE_1D >::rebuild_from_sons(), and oomph::RefineableQCrouzeixRaviartElement< DIM >::rebuild_from_sons().

◆ required_nvalue()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::QAdvectionDiffusionElement< DIM, NNODE_1D >.

Definition at line 825 of file boussinesq_elements.h.

◆ scalar_name_paraview()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 892 of file boussinesq_elements.h.

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

◆ scalar_value_paraview()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 878 of file boussinesq_elements.h.

◆ u_index_adv_diff()

template<unsigned DIM>

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

inlinevirtual

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

Reimplemented from oomph::AdvectionDiffusionEquations< DIM >.

Definition at line 977 of file boussinesq_elements.h.

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

◆ vertex_node_pt()

template<unsigned DIM>

Node* oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::vertex_node_pt ( const unsigned & j ) const

inlinevirtual

Pointer to the j-th vertex node in the element, Call the geometric element's function.

Reimplemented from oomph::FiniteElement.

Definition at line 991 of file boussinesq_elements.h.

Member Data Documentation

◆ Default_Physical_Constant_Value

template<unsigned DIM>

double oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::Default_Physical_Constant_Value

staticprivate

The static default value of the Rayleigh number.

Definition at line 809 of file boussinesq_elements.h.

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

◆ Ra_pt

template<unsigned DIM>

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

private

Pointer to a new physical variable, the Rayleigh number.

Definition at line 806 of file boussinesq_elements.h.

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

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

boussinesq_elements.h

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

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

Constructor & Destructor Documentation

◆ RefineableBuoyantQCrouzeixRaviartElement()

Member Function Documentation

◆ compute_error() [1/2]

◆ compute_error() [2/2]

◆ Default_Physical_Constant_Value() [1/2]

◆ Default_Physical_Constant_Value() [2/2]

◆ disable_ALE()

◆ enable_ALE()

◆ fill_in_contribution_to_jacobian()

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

◆ fill_in_contribution_to_residuals()

◆ fill_in_off_diagonal_jacobian_blocks_analytic()

◆ further_build()

◆ further_setup_hanging_nodes()

◆ get_body_force_nst()

◆ get_interpolated_values() [1/2]

◆ get_interpolated_values() [2/2]

◆ get_wind_adv_diff()

◆ get_Z2_compound_flux_indices()

◆ get_Z2_flux()

◆ ncompound_fluxes()

◆ ncont_interpolated_values()

◆ nrecovery_order()

◆ nscalar_paraview()

◆ num_Z2_flux_terms()

◆ nvertex_node()

◆ output() [1/4]

◆ output() [2/4]

◆ output() [3/4]

◆ output() [4/4]

◆ output_fct() [1/2]

◆ output_fct() [2/2]

◆ ra()

◆ ra_pt()

◆ rebuild_from_sons()

◆ required_nvalue()

◆ scalar_name_paraview()

◆ scalar_value_paraview()

◆ u_index_adv_diff()

◆ vertex_node_pt()

Member Data Documentation

◆ Default_Physical_Constant_Value

◆ Ra_pt

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