A class for elements that solve the polar Navier–Stokes equations, This contains the generic maths – any concrete implementation must be derived from this. More...
#include <polar_navier_stokes_elements.h>
Public Types | |
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... | |
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" as . More... | |
typedef void(* | UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &) |
Function pointer for function that computes Vector-valued time-dependent function as . More... | |
Public Member Functions | |
PolarNavierStokesEquations () | |
Constructor: NULL the body force and source function. More... | |
const double & | re () const |
Reynolds number. More... | |
const double & | alpha () const |
Alpha. More... | |
const double & | re_st () const |
Product of Reynolds and Strouhal number (=Womersley number) More... | |
double *& | re_pt () |
Pointer to Reynolds number. More... | |
double *& | alpha_pt () |
Pointer to Alpha. 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... | |
virtual unsigned | npres_pnst () const =0 |
Function to return number of pressure degrees of freedom. More... | |
virtual double | u_pnst (const unsigned &n, const unsigned &i) const =0 |
Velocity i at local node n. Uses suitably interpolated value for hanging nodes. More... | |
virtual double | u_pnst (const unsigned &t, const unsigned &n, const unsigned &i) const =0 |
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_pnst (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... | |
double | du_dt_pnst (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... | |
virtual double | p_pnst (const unsigned &n_p) const =0 |
Pressure at local pressure "node" n_p Uses suitably interpolated value for hanging nodes. More... | |
virtual void | fix_pressure (const unsigned &p_dof, const double &p_value)=0 |
Pin p_dof-th pressure dof and set it to value specified by p_value. More... | |
virtual int | p_nodal_index_pnst () |
Which nodal value represents the pressure? (Default: negative, indicating that pressure is not based on nodal interpolation). 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... | |
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... | |
double | kin_energy () const |
Get integral of kinetic energy over element. More... | |
void | strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate) const |
Strain-rate tensor: Now returns polar strain. More... | |
void | strain_rate_by_r (const Vector< double > &s, DenseMatrix< double > &strain_rate) const |
Function to return polar strain multiplied by r. More... | |
void | get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction) |
Compute traction (on the viscous scale) at local coordinate s for outer unit normal N. More... | |
void | get_load (const Vector< double > &s, const Vector< double > &xi, const Vector< double > &x, const Vector< double > &N, Vector< double > &load) |
The potential loading on an external SolidElement is always provided by the traction function. More... | |
void | output (std::ostream &outfile) |
Output functionget_vels(const Vector<double>& x_to_get, Vector<double>& vels): x,y,[z],u,v,[w],p in tecplot format. Default number of plot points. More... | |
void | output (std::ostream &outfile, const unsigned &nplot) |
Output function: x,y,[z],u,v,[w],p in tecplot format. nplot points in each coordinate direction. More... | |
void | output (FILE *file_pt) |
C-style output function: x,y,[z],u,v,[w],p in tecplot format. Default number of plot points. More... | |
void | output (FILE *file_pt, const unsigned &nplot) |
C-style output function: x,y,[z],u,v,[w],p in tecplot format. nplot points in each coordinate direction. 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_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_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 | 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) |
Compute the element's residual Vector and the jacobian matrix Plus the mass matrix especially for eigenvalue problems. More... | |
virtual void | fill_in_generic_residual_contribution (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix, unsigned flag) |
Compute the residuals for the Navier–Stokes equations; flag=1(or 0): do (or don't) compute the Jacobian as well. More... | |
void | interpolated_u_pnst (const Vector< double > &s, Vector< double > &veloc) const |
Compute vector of FE interpolated velocity u at local coordinate s. More... | |
double | interpolated_u_pnst (const Vector< double > &s, const unsigned &i) const |
Return FE interpolated velocity u[i] at local coordinate s. More... | |
double | interpolated_p_pnst (const Vector< double > &s) const |
Return FE interpolated pressure at local coordinate s. More... | |
double | interpolated_dudx_pnst (const Vector< double > &s, const unsigned &i, const unsigned &j) const |
//////////////////////////////////////////////////////////////// My own work: /// Return FE interpolated velocity derivative du[i]/dx[j] /// at local coordinate s /// 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) = 2D: d2psids(i,0) = d2psids(i,1) = d2psids(i,2) = 3D: d2psids(i,0) = d2psids(i,1) = d2psids(i,2) = d2psids(i,3) = d2psids(i,4) = d2psids(i,5) = . 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) = 2D: d2psids(i,0) = d2psids(i,1) = d2psids(i,2) = 3D: d2psids(i,0) = d2psids(i,1) = d2psids(i,2) = d2psids(i,3) = d2psids(i,4) = d2psids(i,5) = . 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) = 2D: d2psidx(i,0) = d2psidx(i,1) = d2psidx(i,2) = 3D: d2psidx(i,0) = d2psidx(i,1) = d2psidx(i,2) = d2psidx(i,3) = d2psidx(i,4) = d2psidx(i,5) = . 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) = 2D: d2psidx(i,0) = d2psidx(i,1) = d2psidx(i,2) = 3D: d2psidx(i,0) = d2psidx(i,1) = d2psidx(i,2) = d2psidx(i,3) = d2psidx(i,4) = d2psidx(i,5) = . More... | |
virtual void | assign_nodal_local_eqn_numbers (const bool &store_local_dof_pt) |
Assign the local equation numbers for Data stored at the nodes Virtual so that it can be overloaded by RefineableFiniteElements. If the boolean is true then the pointers to the degrees of freedom associated with each equation number are stored in Dof_pt. More... | |
virtual void | describe_local_dofs (std::ostream &out, const std::string ¤t_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 ¤t_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... | |
virtual void | get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates) |
Compute derivatives of elemental residual vector with respect to nodal coordinates. Default implementation by FD can be overwritten for specific elements. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij}. More... | |
virtual void | disable_ALE () |
This is an empty function that establishes a uniform interface for all (derived) elements that involve time-derivatives. Such elements are/should be implemented in ALE form to allow mesh motions. The additional expense associated with the computation of the mesh velocities is, of course, superfluous if the elements are used in problems in which the mesh is stationary. This function should therefore be overloaded in all derived elements that are formulated in ALE form to suppress the computation of the mesh velocities. The user disables the ALE functionality at his/her own risk! If the mesh does move after all, then the results will be wrong. Here we simply issue a warning message stating that the empty function has been called. More... | |
virtual void | enable_ALE () |
(Re-)enable ALE, i.e. take possible mesh motion into account when evaluating the time-derivative. This function is empty and simply establishes a common interface for all derived elements that are formulated in ALE form. More... | |
virtual unsigned | required_nvalue (const unsigned &n) const |
Number of values that must be stored at local node n by the element. The default is 0, until over-ridden by a particular element. For example, a Poisson equation requires only one value to be stored at each node; 2D Navier–Stokes equations require two values (velocity components) to be stored at each Node (provided that the pressure interpolation is discontinuous). 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 unsigned | nvertex_node () const |
Return the number of vertex nodes in this element. Broken virtual function in "pure" finite elements. More... | |
virtual Node * | vertex_node_pt (const unsigned &j) const |
Pointer to the j-th vertex node in the element. Broken virtual function in "pure" finite elements. 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: . 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_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. The information will typically be used in interaction problems in which the FiniteElement provides a forcing term for an ElementWithExternalElement. The Data must be provided as paired_load data containing. 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... | |
virtual void | point_output_data (const Vector< double > &s, Vector< double > &data) |
Virtual function to write the double precision numbers that appear in a single line of output into the data vector. Empty virtual, can be overloaded for specific elements; used e.g. by LineVisualiser. 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 unsigned | nscalar_paraview () const |
Number of scalars/fields output by this element. Broken virtual. Needs to be implemented for each new specific element type. More... | |
virtual 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. 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 | 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. Broken virtual. Needs to be implemented for each new specific element type. More... | |
virtual 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... | |
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, double &error, double &norm) |
Calculate the norm of the error and that of the exact solution. More... | |
virtual void | compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm) |
Calculate the norm of the error and that of the exact solution. More... | |
virtual void | compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm) |
Given the exact solution 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 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 . 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 . 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 . 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 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 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 | self_test () |
Self-test: Check inversion of element & do self-test for GeneralisedElement. Return 0 if OK. 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 ¤t_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 ¶meter_pt, Vector< double > &dres_dparam) |
Calculate the derivatives of the residuals with respect to a parameter. More... | |
virtual void | get_djacobian_dparameter (double *const ¶meter_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 ¶meter_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... | |
virtual void | compute_norm (Vector< double > &norm) |
Compute norm of solution – broken virtual can be overloaded by element writer to implement whatever norm is desired for the specific element. More... | |
virtual void | compute_norm (double &norm) |
Compute norm of solution – broken virtual can be overloaded by element writer to implement whatever norm is desired for the specific 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... | |
virtual unsigned | ndof_types () const |
The number of types of degrees of freedom in this element are sub-divided into. More... | |
virtual void | get_dof_numbers_for_unknowns (std::list< std::pair< unsigned long, unsigned >> &dof_lookup_list) const |
Create a list of pairs for the unknowns that this element is "in charge of" – ignore any unknowns associated with external Data . The first entry in each pair must contain the global equation number of the unknown, while the second one contains the number of the DOF type that this unknown is associated with. (The function can obviously only be called if the equation numbering scheme has been set up.) 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: = 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: = 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: = drdzeta(alpha,i). = ddrdzeta(alpha,beta,i). Evaluated at current time. More... | |
Static Public Attributes | |
static Vector< double > | Gamma |
Vector to decide whether the stress-divergence form is used or not. More... | |
Static Public Attributes inherited from oomph::FiniteElement | |
static double | Tolerance_for_singular_jacobian = 1.0e-16 |
Tolerance below which the jacobian is considered singular. More... | |
static bool | Accept_negative_jacobian = false |
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... | |
Protected Member Functions | |
virtual int | p_local_eqn (const unsigned &n)=0 |
Access function for the local equation number information for the pressure. p_local_eqn[n] = local equation number or < 0 if pinned. More... | |
virtual double | dshape_and_dtest_eulerian_pnst (const Vector< double > &s, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0 |
Compute the shape functions and derivatives w.r.t. global coords at local coordinate s. Return Jacobian of mapping between local and global coordinates. More... | |
virtual double | dshape_and_dtest_eulerian_at_knot_pnst (const unsigned &ipt, Shape &psi, DShape &dpsidx, Shape &test, DShape &dtestdx) const =0 |
Compute the shape functions and derivatives w.r.t. global coords at ipt-th integration point Return Jacobian of mapping between local and global coordinates. More... | |
virtual void | pshape_pnst (const Vector< double > &s, Shape &psi) const =0 |
Compute the pressure shape functions at local coordinate s. More... | |
virtual void | pshape_pnst (const Vector< double > &s, Shape &psi, Shape &test) const =0 |
Compute the pressure shape and test functions at local coordinate s. More... | |
void | get_body_force (double time, const Vector< double > &x, Vector< double > &result) |
Calculate the body force at a given time and Eulerian position. More... | |
double | get_source_fct (double time, const Vector< double > &x) |
Calculate the source fct at given time and Eulerian position. More... | |
Protected Member Functions inherited from oomph::FiniteElement | |
virtual 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. More... | |
virtual 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. More... | |
virtual 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. More... | |
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 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 function returns the determinant of the jacobian, the jacobian and the inverse jacobian. 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 of the derivative of the shape functions 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 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 , 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) = 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... | |
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 of the function assumes that the residuals vector has already been calculated. 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 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 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 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 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_dresiduals_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam) |
Add the elemental contribution to the derivatives of the residuals with respect to a parameter. This function should NOT initialise any entries and must be called after the entries have been initialised to zero The default implementation is to use finite differences to calculate the derivatives. More... | |
virtual void | fill_in_contribution_to_djacobian_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam) |
Add the elemental contribution to the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. This function should NOT initialise any entries and must be called after the entries have been initialised to zero The default implementation is to use finite differences to calculate the derivatives. More... | |
virtual void | fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const ¶meter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam) |
Add the elemental contribution to the derivative of the jacobian matrix, mass matrix and the residuals vector with respect to the passed parameter. Note that this function should NOT initialise any entries. It must be called after the residuals vector and matrices have been initialised to zero. More... | |
virtual void | fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product) |
Fill in contribution to 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 | 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 Attributes | |
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 * | Alpha_pt |
Pointer to the angle alpha. 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... | |
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... | |
Static Private Attributes | |
static int | Pressure_not_stored_at_node = -100 |
Static "magic" number that indicates that the pressure is not stored at a node. More... | |
static double | Default_Physical_Constant_Value = 0.0 |
Static default value for the physical constants (all initialised to zero) More... | |
static double | Default_Physical_Ratio_Value = 1.0 |
Static default value for the physical ratios (all are initialised to one) More... | |
static Vector< double > | Default_Gravity_vector |
Static default value for the gravity vector. More... | |
Additional Inherited Members | |
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... | |
A class for elements that solve the polar Navier–Stokes equations, This contains the generic maths – any concrete implementation must be derived from this.
Definition at line 107 of file polar_navier_stokes_elements.h.
typedef void(* oomph::PolarNavierStokesEquations::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!
Definition at line 112 of file polar_navier_stokes_elements.h.
typedef double(* oomph::PolarNavierStokesEquations::NavierStokesSourceFctPt) (const double &time, const Vector< double > &x) |
Function pointer to source function fct(t,x) x is a Vector!
Definition at line 118 of file polar_navier_stokes_elements.h.
|
inline |
Constructor: NULL the body force and source function.
Definition at line 245 of file polar_navier_stokes_elements.h.
References Default_Gravity_vector, Default_Physical_Constant_Value, Default_Physical_Ratio_Value, Density_Ratio_pt, G_pt, Re_pt, ReInvFr_pt, ReSt_pt, and Viscosity_Ratio_pt.
|
inline |
Alpha.
Definition at line 272 of file polar_navier_stokes_elements.h.
References Alpha_pt.
Referenced by fill_in_generic_residual_contribution(), oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution(), output(), strain_rate(), and strain_rate_by_r().
|
inline |
Pointer to Alpha.
Definition at line 290 of file polar_navier_stokes_elements.h.
References Alpha_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
|
inline |
Access function for the body-force pointer.
Definition at line 352 of file polar_navier_stokes_elements.h.
References Body_force_fct_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
|
inline |
Access function for the body-force pointer. Const version.
Definition at line 358 of file polar_navier_stokes_elements.h.
References Body_force_fct_pt.
|
virtual |
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.
Validate against exact velocity 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.
Reimplemented from oomph::FiniteElement.
Definition at line 139 of file polar_navier_stokes_elements.cc.
References i, oomph::FiniteElement::integral_pt(), interpolated_u_pnst(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::Integral::nweight(), s, oomph::QuadTreeNames::W, and oomph::Integral::weight().
|
virtual |
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.
Validate against exact velocity 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.
Reimplemented from oomph::FiniteElement.
Definition at line 61 of file polar_navier_stokes_elements.cc.
References i, oomph::FiniteElement::integral_pt(), interpolated_u_pnst(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::Integral::nweight(), s, oomph::QuadTreeNames::W, and oomph::Integral::weight().
|
inline |
Density ratio for element: Element's density relative to the viscosity used in the definition of the Reynolds number.
Definition at line 316 of file polar_navier_stokes_elements.h.
References Density_Ratio_pt.
|
inline |
Pointer to Density ratio.
Definition at line 322 of file polar_navier_stokes_elements.h.
References Density_Ratio_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
double oomph::PolarNavierStokesEquations::dissipation | ( | ) | const |
Return integral of dissipation over element.
Definition at line 721 of file polar_navier_stokes_elements.cc.
References i, oomph::FiniteElement::integral_pt(), oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::Integral::nweight(), s, strain_rate(), and oomph::Integral::weight().
Referenced by full_output().
double oomph::PolarNavierStokesEquations::dissipation | ( | const Vector< double > & | s | ) | const |
Return dissipation at local coordinate s.
Definition at line 798 of file polar_navier_stokes_elements.cc.
References i, s, and strain_rate().
|
protectedpure virtual |
Compute the shape functions and derivatives w.r.t. global coords at ipt-th integration point Return Jacobian of mapping between local and global coordinates.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Referenced by fill_in_generic_residual_contribution(), and oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution().
|
protectedpure virtual |
Compute the shape functions and derivatives w.r.t. global coords at local coordinate s. Return Jacobian of mapping between local and global coordinates.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
|
inline |
i-th component of du/dt at local node n. Uses suitably interpolated value for hanging nodes.
Definition at line 401 of file polar_navier_stokes_elements.h.
References i, oomph::FiniteElement::node_pt(), oomph::TimeStepper::ntstorage(), t, oomph::GeomObject::time_stepper_pt(), oomph::Data::time_stepper_pt(), oomph::TimeStepper::type(), u_pnst(), and oomph::TimeStepper::weight().
Referenced by full_output().
|
inlinevirtual |
Compute the element's residual Vector and the jacobian matrix Virtual function can be overloaded by hanging-node version.
Reimplemented from oomph::FiniteElement.
Definition at line 575 of file polar_navier_stokes_elements.h.
References oomph::GeneralisedElement::Dummy_matrix, and fill_in_generic_residual_contribution().
|
inlinevirtual |
Compute the element's residual Vector and the jacobian matrix Plus the mass matrix especially for eigenvalue problems.
Reimplemented from oomph::GeneralisedElement.
Definition at line 643 of file polar_navier_stokes_elements.h.
References fill_in_generic_residual_contribution().
|
inlinevirtual |
Compute the element's residual Vector.
Reimplemented from oomph::GeneralisedElement.
Definition at line 564 of file polar_navier_stokes_elements.h.
References oomph::GeneralisedElement::Dummy_matrix, and fill_in_generic_residual_contribution().
|
virtual |
Compute the residuals for the Navier–Stokes equations; flag=1(or 0): do (or don't) compute the Jacobian as well.
/////////////////////////////////////////////////////////////////// / The finished version of the new equations /////
Compute the residuals for the Navier–Stokes equations; flag=1(or 0): do (or don't) compute the Jacobian as well. flag=2 for Residuals, Jacobian and mass_matrix
This is now my new version with Jacobian and dimensionless phi
Reimplemented in oomph::RefineablePolarNavierStokesEquations.
Definition at line 1100 of file polar_navier_stokes_elements.cc.
References alpha(), dshape_and_dtest_eulerian_at_knot_pnst(), Gamma, i, oomph::FiniteElement::integral_pt(), oomph::FiniteElement::interpolated_x(), oomph::Integral::knot(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_local_eqn(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::nodal_value(), npres_pnst(), oomph::Integral::nweight(), p_local_eqn(), p_pnst(), pshape_pnst(), re(), re_st(), s, u_index_pnst(), oomph::QuadTreeNames::W, and oomph::Integral::weight().
Referenced by fill_in_contribution_to_jacobian(), fill_in_contribution_to_jacobian_and_mass_matrix(), and fill_in_contribution_to_residuals().
|
pure virtual |
Pin p_dof-th pressure dof and set it to value specified by p_value.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
|
inline |
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.
Definition at line 510 of file polar_navier_stokes_elements.h.
Referenced by oomph::PolarCrouzeixRaviartElement::full_output().
void oomph::PolarNavierStokesEquations::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.
Full output function: x,y,[z],u,v,[w],p,du/dt,dv/dt,[dw/dt],dissipation in tecplot format. Specified number of plot points in each coordinate direction.
Definition at line 607 of file polar_navier_stokes_elements.cc.
References dissipation(), oomph::FiniteElement::dnodal_position_dt(), oomph::FiniteElement::dshape_eulerian(), du_dt_pnst(), oomph::FiniteElement::get_s_plot(), i, interpolated_p_pnst(), interpolated_u_pnst(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and u_pnst().
|
inline |
Vector of gravitational components.
Definition at line 340 of file polar_navier_stokes_elements.h.
References G_pt.
|
inline |
Pointer to Vector of gravitational components.
Definition at line 346 of file polar_navier_stokes_elements.h.
References G_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
|
inlineprotected |
Calculate the body force at a given time and Eulerian position.
Definition at line 207 of file polar_navier_stokes_elements.h.
References Body_force_fct_pt, and i.
|
inline |
The potential loading on an external SolidElement is always provided by the traction function.
Definition at line 472 of file polar_navier_stokes_elements.h.
References get_traction(), oomph::QuadTreeNames::N, and s.
|
inlineprotected |
Calculate the source fct at given time and Eulerian position.
Definition at line 229 of file polar_navier_stokes_elements.h.
References Source_fct_pt.
void oomph::PolarNavierStokesEquations::get_traction | ( | const Vector< double > & | s, |
const Vector< double > & | N, | ||
Vector< double > & | traction | ||
) |
Compute traction (on the viscous scale) at local coordinate s for outer unit normal N.
Definition at line 772 of file polar_navier_stokes_elements.cc.
References i, interpolated_p_pnst(), oomph::QuadTreeNames::N, s, and strain_rate().
Referenced by get_load().
|
inline |
//////////////////////////////////////////////////////////////// My own work: /// Return FE interpolated velocity derivative du[i]/dx[j] /// at local coordinate s ///
Definition at line 731 of file polar_navier_stokes_elements.h.
References oomph::FiniteElement::dshape_eulerian(), i, oomph::FiniteElement::nnode(), s, and u_pnst().
|
inline |
Return FE interpolated pressure at local coordinate s.
Definition at line 706 of file polar_navier_stokes_elements.h.
References npres_pnst(), p_pnst(), pshape_pnst(), and s.
Referenced by full_output(), oomph::RefineablePolarCrouzeixRaviartElement::further_build(), oomph::RefineablePolarTaylorHoodElement::get_interpolated_values(), get_traction(), output(), and pressure_integral().
|
inline |
Return FE interpolated velocity u[i] at local coordinate s.
Definition at line 685 of file polar_navier_stokes_elements.h.
References i, oomph::FiniteElement::nnode(), s, oomph::FiniteElement::shape(), and u_pnst().
|
inline |
Compute vector of FE interpolated velocity u at local coordinate s.
Definition at line 662 of file polar_navier_stokes_elements.h.
References i, oomph::FiniteElement::nnode(), s, oomph::FiniteElement::shape(), and u_pnst().
Referenced by compute_error(), full_output(), oomph::RefineablePolarTaylorHoodElement::get_interpolated_values(), oomph::RefineablePolarCrouzeixRaviartElement::get_interpolated_values(), kin_energy(), and output().
double oomph::PolarNavierStokesEquations::kin_energy | ( | ) | const |
Get integral of kinetic energy over element.
Get integral of kinetic energy over element:
Definition at line 1006 of file polar_navier_stokes_elements.cc.
References i, oomph::FiniteElement::integral_pt(), interpolated_u_pnst(), oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::Integral::nweight(), s, and oomph::Integral::weight().
|
pure virtual |
Function to return number of pressure degrees of freedom.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Referenced by fill_in_generic_residual_contribution(), oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution(), and interpolated_p_pnst().
|
inlinevirtual |
C-style output function: x,y,[z],u,v,[w],p in tecplot format. Default number of plot points.
Reimplemented from oomph::FiniteElement.
Reimplemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Definition at line 497 of file polar_navier_stokes_elements.h.
References output().
|
virtual |
C-style output function: x,y,[z],u,v,[w],p in tecplot format. nplot points in each coordinate direction.
C-style output function: x,y,[z],u,v,[w],p in tecplot format. Specified number of plot points in each coordinate direction.
Reimplemented from oomph::FiniteElement.
Reimplemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Definition at line 563 of file polar_navier_stokes_elements.cc.
References oomph::FiniteElement::get_s_plot(), i, interpolated_p_pnst(), interpolated_u_pnst(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, and oomph::FiniteElement::tecplot_zone_string().
|
inlinevirtual |
Output functionget_vels(const Vector<double>& x_to_get, Vector<double>& vels): x,y,[z],u,v,[w],p in tecplot format. Default number of plot points.
Reimplemented from oomph::FiniteElement.
Reimplemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Definition at line 485 of file polar_navier_stokes_elements.h.
Referenced by output(), oomph::PolarCrouzeixRaviartElement::output(), and oomph::PolarTaylorHoodElement::output().
|
virtual |
Output function: x,y,[z],u,v,[w],p in tecplot format. nplot points in each coordinate direction.
Output function: x,y,[z],u,v,[w],p in tecplot format. Specified number of plot points in each coordinate direction.
Reimplemented from oomph::FiniteElement.
Reimplemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Definition at line 394 of file polar_navier_stokes_elements.cc.
References alpha(), oomph::FiniteElement::get_s_plot(), interpolated_p_pnst(), interpolated_u_pnst(), oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, and oomph::FiniteElement::tecplot_zone_string().
|
virtual |
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.
Output "exact" solution at a given time Solution is provided via function pointer. Plot at a given number of plot points. Function prints as many components as are returned in solution Vector.
Reimplemented from oomph::FiniteElement.
Definition at line 271 of file polar_navier_stokes_elements.cc.
References oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().
|
virtual |
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.
Output "exact" solution Solution is provided via function pointer. Plot at a given number of plot points. Function prints as many components as are returned in solution Vector.
Reimplemented from oomph::FiniteElement.
Definition at line 216 of file polar_navier_stokes_elements.cc.
References oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::tecplot_zone_string(), and oomph::FiniteElement::write_tecplot_zone_footer().
void oomph::PolarNavierStokesEquations::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)
Output function: Velocities only x,y,[z],u,v,[w] in tecplot format at specified previous timestep (t=0: present; t>0: previous timestep). Specified number of plot points in each coordinate direction.
Definition at line 328 of file polar_navier_stokes_elements.cc.
References oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::nplot_points(), s, oomph::FiniteElement::shape(), t, oomph::FiniteElement::tecplot_zone_string(), u_pnst(), and oomph::FiniteElement::write_tecplot_zone_footer().
|
protectedpure virtual |
Access function for the local equation number information for the pressure. p_local_eqn[n] = local equation number or < 0 if pinned.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Referenced by fill_in_generic_residual_contribution(), and oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution().
|
inlinevirtual |
Which nodal value represents the pressure? (Default: negative, indicating that pressure is not based on nodal interpolation).
Reimplemented in oomph::PolarTaylorHoodElement.
Definition at line 432 of file polar_navier_stokes_elements.h.
References Pressure_not_stored_at_node.
Referenced by oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution().
|
pure virtual |
Pressure at local pressure "node" n_p Uses suitably interpolated value for hanging nodes.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Referenced by fill_in_generic_residual_contribution(), oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution(), and interpolated_p_pnst().
double oomph::PolarNavierStokesEquations::pressure_integral | ( | ) | const |
Integral of pressure over element.
Return pressure integrated over the element.
Definition at line 1048 of file polar_navier_stokes_elements.cc.
References i, oomph::FiniteElement::integral_pt(), interpolated_p_pnst(), oomph::FiniteElement::J_eulerian(), oomph::Integral::knot(), oomph::Integral::nweight(), s, oomph::QuadTreeNames::W, and oomph::Integral::weight().
|
inlinevirtual |
Pointer to n_p-th pressure node (Default: NULL, indicating that pressure is not based on nodal interpolation).
Reimplemented in oomph::RefineablePolarTaylorHoodElement, oomph::RefineablePolarNavierStokesEquations, and oomph::PolarTaylorHoodElement.
Definition at line 439 of file polar_navier_stokes_elements.h.
|
protectedpure virtual |
Compute the pressure shape functions at local coordinate s.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Referenced by fill_in_generic_residual_contribution(), oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution(), and interpolated_p_pnst().
|
protectedpure virtual |
Compute the pressure shape and test functions at local coordinate s.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
|
inline |
Reynolds number.
Definition at line 266 of file polar_navier_stokes_elements.h.
References Re_pt.
Referenced by fill_in_generic_residual_contribution(), and oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution().
|
inline |
Global inverse Froude number.
Definition at line 328 of file polar_navier_stokes_elements.h.
References ReInvFr_pt.
|
inline |
Pointer to global inverse Froude number.
Definition at line 334 of file polar_navier_stokes_elements.h.
References ReInvFr_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
|
inline |
Pointer to Reynolds number.
Definition at line 284 of file polar_navier_stokes_elements.h.
References Re_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
|
inline |
Product of Reynolds and Strouhal number (=Womersley number)
Definition at line 278 of file polar_navier_stokes_elements.h.
References ReSt_pt.
Referenced by fill_in_generic_residual_contribution(), and oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution().
|
inline |
Pointer to product of Reynolds and Strouhal number (=Womersley number)
Definition at line 296 of file polar_navier_stokes_elements.h.
References ReSt_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
|
inline |
Access function for the source-function pointer.
Definition at line 364 of file polar_navier_stokes_elements.h.
References Source_fct_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
|
inline |
Access function for the source-function pointer. Const version.
Definition at line 370 of file polar_navier_stokes_elements.h.
References Source_fct_pt.
void oomph::PolarNavierStokesEquations::strain_rate | ( | const Vector< double > & | s, |
DenseMatrix< double > & | strain_rate | ||
) | const |
Strain-rate tensor: Now returns polar strain.
Get strain-rate tensor: Slightly more complicated in polar coordinates (see eg. Aris)
Definition at line 822 of file polar_navier_stokes_elements.cc.
References alpha(), oomph::FiniteElement::dshape_eulerian(), i, oomph::FiniteElement::interpolated_x(), oomph::DenseMatrix< T >::ncol(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::nodal_value(), oomph::DenseMatrix< T >::nrow(), s, and u_index_pnst().
Referenced by dissipation(), and get_traction().
void oomph::PolarNavierStokesEquations::strain_rate_by_r | ( | const Vector< double > & | s, |
DenseMatrix< double > & | strain_rate | ||
) | const |
Function to return polar strain multiplied by r.
Return polar strain-rate tensor multiplied by r Slightly more complicated in polar coordinates (see eg. Aris)
Definition at line 909 of file polar_navier_stokes_elements.cc.
References alpha(), oomph::FiniteElement::dshape_eulerian(), i, oomph::FiniteElement::interpolated_x(), oomph::DenseMatrix< T >::ncol(), oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_position(), oomph::FiniteElement::nodal_value(), oomph::DenseMatrix< T >::nrow(), s, and u_index_pnst().
Referenced by oomph::RefineablePolarNavierStokesEquations::get_Z2_flux().
|
inlinevirtual |
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.
Definition at line 394 of file polar_navier_stokes_elements.h.
References i.
Referenced by fill_in_generic_residual_contribution(), oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution(), oomph::RefineablePolarTaylorHoodElement::get_interpolated_values(), oomph::RefineablePolarCrouzeixRaviartElement::get_interpolated_values(), oomph::RefineablePolarTaylorHoodElement::insert_load_data(), oomph::RefineablePolarCrouzeixRaviartElement::insert_load_data(), strain_rate(), and strain_rate_by_r().
|
pure virtual |
Velocity i at local node n. Uses suitably interpolated value for hanging nodes.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
Referenced by du_dt_pnst(), full_output(), interpolated_dudx_pnst(), interpolated_u_pnst(), and output_veloc().
|
pure virtual |
Velocity i at local node n at timestep t (t=0: present; t>0: previous). Uses suitably interpolated value for hanging nodes.
Implemented in oomph::PolarTaylorHoodElement, and oomph::PolarCrouzeixRaviartElement.
|
inline |
Viscosity ratio for element: Element's viscosity relative to the viscosity used in the definition of the Reynolds number.
Definition at line 303 of file polar_navier_stokes_elements.h.
References Viscosity_Ratio_pt.
|
inline |
Pointer to Viscosity Ratio.
Definition at line 309 of file polar_navier_stokes_elements.h.
References Viscosity_Ratio_pt.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build().
|
protected |
Pointer to the angle alpha.
Definition at line 151 of file polar_navier_stokes_elements.h.
Referenced by alpha(), alpha_pt(), and oomph::RefineablePolarNavierStokesEquations::further_build().
|
protected |
Pointer to body force function.
Definition at line 167 of file polar_navier_stokes_elements.h.
Referenced by body_force_fct_pt(), oomph::RefineablePolarNavierStokesEquations::further_build(), and get_body_force().
|
staticprivate |
Static default value for the gravity vector.
Navier-Stokes equations default gravity vector.
Definition at line 135 of file polar_navier_stokes_elements.h.
Referenced by PolarNavierStokesEquations().
|
staticprivate |
Static default value for the physical constants (all initialised to zero)
Navier–Stokes equations static data.
Definition at line 128 of file polar_navier_stokes_elements.h.
Referenced by PolarNavierStokesEquations().
|
staticprivate |
Static default value for the physical ratios (all are initialised to one)
Navier–Stokes equations static data.
Definition at line 132 of file polar_navier_stokes_elements.h.
Referenced by PolarNavierStokesEquations().
|
protected |
Pointer to the density ratio (relative to the density used in the definition of the Reynolds number)
Definition at line 146 of file polar_navier_stokes_elements.h.
Referenced by density_ratio(), density_ratio_pt(), oomph::RefineablePolarNavierStokesEquations::further_build(), and PolarNavierStokesEquations().
|
protected |
Pointer to global gravity Vector.
Definition at line 164 of file polar_navier_stokes_elements.h.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build(), g(), g_pt(), and PolarNavierStokesEquations().
|
static |
Vector to decide whether the stress-divergence form is used or not.
Start of what would've been navier_stokes_elements.cc //.
Navier–Stokes equations static data
Definition at line 261 of file polar_navier_stokes_elements.h.
Referenced by fill_in_generic_residual_contribution(), and oomph::RefineablePolarNavierStokesEquations::fill_in_generic_residual_contribution().
|
staticprivate |
Static "magic" number that indicates that the pressure is not stored at a node.
"Magic" negative number that indicates that the pressure is not stored at a node. This cannot be -1 because that represents the positional hanging scheme in the hanging_pt object of nodes
Definition at line 124 of file polar_navier_stokes_elements.h.
Referenced by p_nodal_index_pnst().
|
protected |
Pointer to global Reynolds number.
Definition at line 154 of file polar_navier_stokes_elements.h.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build(), PolarNavierStokesEquations(), re(), and re_pt().
|
protected |
Pointer to global Reynolds number x inverse Froude number (= Bond number / Capillary number)
Definition at line 161 of file polar_navier_stokes_elements.h.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build(), PolarNavierStokesEquations(), re_invfr(), and re_invfr_pt().
|
protected |
Pointer to global Reynolds number x Strouhal number (=Womersley)
Definition at line 157 of file polar_navier_stokes_elements.h.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build(), PolarNavierStokesEquations(), re_st(), and re_st_pt().
|
protected |
Pointer to volumetric source function.
Definition at line 170 of file polar_navier_stokes_elements.h.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build(), get_source_fct(), and source_fct_pt().
|
protected |
Pointer to the viscosity ratio (relative to the viscosity used in the definition of the Reynolds number)
Definition at line 142 of file polar_navier_stokes_elements.h.
Referenced by oomph::RefineablePolarNavierStokesEquations::further_build(), PolarNavierStokesEquations(), viscosity_ratio(), and viscosity_ratio_pt().