Public Types | Public Member Functions | Static Public Attributes | Protected Member Functions | Protected Attributes | Static Private Attributes | List of all members
oomph::NavierStokesEquations< DIM > Class Template Referenceabstract

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#include <navier_stokes_elements.h>

+ Inheritance diagram for oomph::NavierStokesEquations< DIM >:

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...
 
typedef double(* NavierStokesPressureAdvDiffSourceFctPt) (const Vector< double > &x)
 Function pointer to source function fct(x) for the pressure advection diffusion equation (only used during validation!). x is a Vector! More...
 
- Public Types inherited from oomph::FiniteElement
typedef void(* SteadyExactSolutionFctPt) (const Vector< double > &, Vector< double > &)
 Function pointer for function that computes vector-valued steady "exact solution" $ {\bf f}({\bf x}) $ as $ \mbox{\tt fct}({\bf x}, {\bf f}) $. More...
 
typedef void(* UnsteadyExactSolutionFctPt) (const double &, const Vector< double > &, Vector< double > &)
 Function pointer for function that computes Vector-valued time-dependent function $ {\bf f}(t,{\bf x}) $ as $ \mbox{\tt fct}(t, {\bf x}, {\bf f}) $. More...
 

Public Member Functions

 NavierStokesEquations ()
 Constructor: NULL the body force and source function and make sure the ALE terms are included by default. More...
 
const double & re () const
 Reynolds number. More...
 
const double & re_st () const
 Product of Reynolds and Strouhal number (=Womersley number) More...
 
double *& re_pt ()
 Pointer to Reynolds number. More...
 
double *& re_st_pt ()
 Pointer to product of Reynolds and Strouhal number (=Womersley number) More...
 
const double & viscosity_ratio () const
 Viscosity ratio for element: Element's viscosity relative to the viscosity used in the definition of the Reynolds number. More...
 
double *& viscosity_ratio_pt ()
 Pointer to Viscosity Ratio. More...
 
const double & density_ratio () const
 Density ratio for element: Element's density relative to the viscosity used in the definition of the Reynolds number. More...
 
double *& density_ratio_pt ()
 Pointer to Density ratio. More...
 
const double & re_invfr () const
 Global inverse Froude number. More...
 
double *& re_invfr_pt ()
 Pointer to global inverse Froude number. More...
 
const Vector< double > & g () const
 Vector of gravitational components. More...
 
Vector< double > *& g_pt ()
 Pointer to Vector of gravitational components. More...
 
NavierStokesBodyForceFctPtbody_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...
 
NavierStokesSourceFctPtsource_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...
 
NavierStokesPressureAdvDiffSourceFctPtsource_fct_for_pressure_adv_diff ()
 Access function for the source-function pointer for pressure advection diffusion (used for validation only). More...
 
NavierStokesPressureAdvDiffSourceFctPt source_fct_for_pressure_adv_diff () const
 Access function for the source-function pointer for pressure advection diffusion (used for validation only). Const version. More...
 
int & pinned_fp_pressure_eqn ()
 Global eqn number of pressure dof that's pinned in pressure adv diff problem. More...
 
virtual unsigned npres_nst () const =0
 Function to return number of pressure degrees of freedom. More...
 
virtual void pshape_nst (const Vector< double > &s, Shape &psi) const =0
 Compute the pressure shape functions at local coordinate s. More...
 
virtual void pshape_nst (const Vector< double > &s, Shape &psi, Shape &test) const =0
 Compute the pressure shape and test functions at local coordinate s. More...
 
virtual double dpshape_and_dptest_eulerian_nst (const Vector< double > &s, Shape &ppsi, DShape &dppsidx, Shape &ptest, DShape &dptestdx) const =0
 Compute the pressure shape and test functions and derivatives w.r.t. global coords at local coordinate s. Return Jacobian of mapping between local and global coordinates. More...
 
double u_nst (const unsigned &n, const unsigned &i) const
 Velocity i at local node n. Uses suitably interpolated value for hanging nodes. The use of u_index_nst() permits the use of this element as the basis for multi-physics elements. The default is to assume that the i-th velocity component is stored at the i-th location of the node. More...
 
double u_nst (const unsigned &t, const unsigned &n, const unsigned &i) const
 Velocity i at local node n at timestep t (t=0: present; t>0: previous). Uses suitably interpolated value for hanging nodes. More...
 
virtual unsigned u_index_nst (const unsigned &i) const
 Return the index at which the i-th unknown velocity component is stored. The default value, i, is appropriate for single-physics problems. In derived multi-physics elements, this function should be overloaded to reflect the chosen storage scheme. Note that these equations require that the unknowns are always stored at the same indices at each node. More...
 
unsigned n_u_nst () const
 Return the number of velocity components Used in FluidInterfaceElements. More...
 
double du_dt_nst (const unsigned &n, const unsigned &i) const
 i-th component of du/dt at local node n. Uses suitably interpolated value for hanging nodes. More...
 
void disable_ALE ()
 Disable ALE, i.e. assert the mesh is not moving – you do this at your own risk! More...
 
void enable_ALE ()
 (Re-)enable ALE, i.e. take possible mesh motion into account when evaluating the time-derivative. Note: By default, ALE is enabled, at the expense of possibly creating unnecessary work in problems where the mesh is, in fact, stationary. More...
 
virtual double p_nst (const unsigned &n_p) const =0
 Pressure at local pressure "node" n_p Uses suitably interpolated value for hanging nodes. More...
 
virtual double p_nst (const unsigned &t, const unsigned &n_p) const =0
 Pressure at local pressure "node" n_p at time level t. 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_nst () const
 Return the index at which the pressure is stored if it is stored at the nodes. If not stored at the nodes this will return a negative number. More...
 
double pressure_integral () const
 Integral of pressure over element. More...
 
double dissipation () const
 Return integral of dissipation over element. More...
 
double dissipation (const Vector< double > &s) const
 Return dissipation at local coordinate s. More...
 
void get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
 Compute the vorticity vector at local coordinate s. More...
 
void get_vorticity (const Vector< double > &s, double &vorticity) const
 Compute the scalar vorticity at local coordinate s (2D) More...
 
double kin_energy () const
 Get integral of kinetic energy over element. More...
 
double d_kin_energy_dt () const
 Get integral of time derivative of kinetic energy over element. More...
 
void strain_rate (const Vector< double > &s, DenseMatrix< double > &strain_rate) const
 Strain-rate tensor: 1/2 (du_i/dx_j + du_j/dx_i) More...
 
void get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction)
 Compute traction (on the viscous scale) exerted onto the fluid at local coordinate s. N has to be outer unit normal to the fluid. More...
 
void get_traction (const Vector< double > &s, const Vector< double > &N, Vector< double > &traction_p, Vector< double > &traction_visc_n, Vector< double > &traction_visc_t)
 Compute traction (on the viscous scale) exerted onto the fluid at local coordinate s, decomposed into pressure and normal and tangential viscous components. N has to be outer unit normal to the fluid. More...
 
void get_load (const Vector< double > &s, const Vector< double > &N, Vector< double > &load)
 This implements a pure virtual function defined in the FSIFluidElement class. The function computes the traction (on the viscous scale), at the element's local coordinate s, that the fluid element exerts onto an adjacent solid element. The number of arguments is imposed by the interface defined in the FSIFluidElement – only the unit normal N (pointing into the fluid!) is actually used in the computation. More...
 
void get_pressure_and_velocity_mass_matrix_diagonal (Vector< double > &press_mass_diag, Vector< double > &veloc_mass_diag, const unsigned &which_one=0)
 Compute the diagonal of the velocity/pressure mass matrices. If which one=0, both are computed, otherwise only the pressure (which_one=1) or the velocity mass matrix (which_one=2 – the LSC version of the preconditioner only needs that one) More...
 
unsigned nscalar_paraview () const
 Number of scalars/fields output by this element. Reimplements broken virtual function in base class. More...
 
void scalar_value_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot) const
 Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type. More...
 
void scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt) const
 Write values of the i-th scalar field at the plot points. Needs to be implemented for each new specific element type. More...
 
std::string scalar_name_paraview (const unsigned &i) const
 Name of the i-th scalar field. Default implementation returns V1 for the first one, V2 for the second etc. Can (should!) be overloaded with more meaningful names in specific elements. More...
 
void output (std::ostream &outfile)
 Output function: 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_vorticity (std::ostream &outfile, const unsigned &nplot)
 Output function: x,y,[z], [omega_x,omega_y,[and/or omega_z]] in tecplot format. nplot points in each coordinate direction. More...
 
void output_fct (std::ostream &outfile, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt)
 Output exact solution specified via function pointer at a given number of plot points. Function prints as many components as are returned in solution Vector. More...
 
void output_fct (std::ostream &outfile, const unsigned &nplot, const double &time, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt)
 Output exact solution specified via function pointer at a given time and at a given number of plot points. Function prints as many components as are returned in solution Vector. More...
 
void compute_norm (double &norm)
 Compute norm of solution: square of the L2 norm of the velocities. More...
 
void compute_norm (Vector< double > &norm)
 Compute the vector norm of the FEM solution. More...
 
void compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
 Validate against exact solution at given time Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element. More...
 
void compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
 Validate against exact solution. Solution is provided via function pointer. Plot at a given number of plot points and compute L2 error and L2 norm of velocity solution over element. More...
 
void compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, double &error, double &norm)
 Validate against exact solution. Solution is provided via function pointer. Compute L2 error and L2 norm of velocity solution over element. More...
 
void compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error, double &norm)
 Validate against exact solution. Solution is provided via function pointer. Compute L2 error and L2 norm of velocity solution over element. More...
 
void fill_in_contribution_to_residuals (Vector< double > &residuals)
 Compute the element's residual Vector. More...
 
void fill_in_contribution_to_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
 Compute the element's residual Vector and the jacobian matrix Virtual function can be overloaded by hanging-node version. More...
 
void fill_in_contribution_to_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
 Add the element's contribution to its residuals vector, jacobian matrix and mass matrix. More...
 
void fill_in_contribution_to_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
 Compute the element's residual Vector. More...
 
void fill_in_contribution_to_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
 Compute the element's residual Vector and the jacobian matrix Virtual function can be overloaded by hanging-node version. More...
 
void fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
 Add the element's contribution to its residuals vector, jacobian matrix and mass matrix. More...
 
void fill_in_pressure_advection_diffusion_residuals (Vector< double > &residuals)
 Compute the residuals for the associated pressure advection diffusion problem. Used by the Fp preconditioner. More...
 
void fill_in_pressure_advection_diffusion_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
 Compute the residuals and Jacobian for the associated pressure advection diffusion problem. Used by the Fp preconditioner. More...
 
void pin_all_non_pressure_dofs (std::map< Data *, std::vector< int >> &eqn_number_backup)
 Pin all non-pressure dofs and backup eqn numbers. More...
 
virtual void build_fp_press_adv_diff_robin_bc_element (const unsigned &face_index)=0
 Build FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner. More...
 
void output_pressure_advection_diffusion_robin_elements (std::ostream &outfile)
 Output the FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner. More...
 
void delete_pressure_advection_diffusion_robin_elements ()
 Delete the FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner. More...
 
virtual void get_dresidual_dnodal_coordinates (RankThreeTensor< double > &dresidual_dnodal_coordinates)
 Compute derivatives of elemental residual vector with respect to nodal coordinates. Overwrites default implementation in FiniteElement base class. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij}. More...
 
void interpolated_u_nst (const Vector< double > &s, Vector< double > &veloc) const
 Compute vector of FE interpolated velocity u at local coordinate s. More...
 
double interpolated_u_nst (const Vector< double > &s, const unsigned &i) const
 Return FE interpolated velocity u[i] at local coordinate s. More...
 
double interpolated_u_nst (const unsigned &t, const Vector< double > &s, const unsigned &i) const
 Return FE interpolated velocity u[i] at local coordinate s at time level t (t=0: present; t>0: history) More...
 
virtual void dinterpolated_u_nst_ddata (const Vector< double > &s, const unsigned &i, Vector< double > &du_ddata, Vector< unsigned > &global_eqn_number)
 Compute the derivatives of the i-th component of velocity at point s with respect to all data that can affect its value. In addition, return the global equation numbers corresponding to the data. The function is virtual so that it can be overloaded in the refineable version. More...
 
virtual double interpolated_p_nst (const Vector< double > &s) const
 Return FE interpolated pressure at local coordinate s. More...
 
double interpolated_p_nst (const unsigned &t, const Vector< double > &s) const
 Return FE interpolated pressure at local coordinate s at time level t. More...
 
double interpolated_dudx_nst (const Vector< double > &s, const unsigned &i, const unsigned &j) const
 Return FE interpolated derivatives of velocity component u[i] w.r.t spatial global coordinate direction x[j] at local coordinate s. More...
 
void point_output_data (const Vector< double > &s, Vector< double > &data)
 Output solution in data vector at local cordinates s: x,y [,z], u,v,[w], p. More...
 
void get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
 Compute 2D vorticity vector at local coordinate s (return in one and only component of vorticity vector. More...
 
void get_vorticity (const Vector< double > &s, double &vorticity) const
 Compute vorticity vector at local coordinate s and return the one and only component of vorticity vector (only makes sense when solving the 2D N.St. equations) More...
 
void get_vorticity (const Vector< double > &s, Vector< double > &vorticity) const
 Compute 3D vorticity vector at local coordinate s. More...
 
- Public Member Functions inherited from oomph::FSIFluidElement
 FSIFluidElement ()
 Constructor. More...
 
 FSIFluidElement (const FSIFluidElement &)=delete
 Broken copy constructor. More...
 
void operator= (const FSIFluidElement &)=delete
 Broken assignment operator. More...
 
virtual void identify_load_data (std::set< std::pair< Data *, unsigned >> &paired_load_data)=0
 Add to the set paired_load_data pairs containing. More...
 
virtual void identify_pressure_data (std::set< std::pair< Data *, unsigned >> &paired_pressure_data)=0
 Add to the set paired_pressure_data pairs containing. 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...
 
MacroElementmacro_elem_pt ()
 Access function to pointer to macro element. More...
 
void get_x (const Vector< double > &s, Vector< double > &x) const
 Global coordinates as function of local coordinates. Either via FE representation or via macro-element (if Macro_elem_pt!=0) More...
 
void get_x (const unsigned &t, const Vector< double > &s, Vector< double > &x)
 Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). Either via FE representation of QElement or via macro-element (if Macro_elem_pt!=0). More...
 
virtual void get_x_from_macro_element (const Vector< double > &s, Vector< double > &x) const
 Global coordinates as function of local coordinates using macro element representation. (Broken virtual — this must be overloaded in specific geometric element classes) More...
 
virtual void get_x_from_macro_element (const unsigned &t, const Vector< double > &s, Vector< double > &x)
 Global coordinates as function of local coordinates at previous time "level" t (t=0: present; t>0: previous). using macro element representation (Broken virtual – overload in specific geometric element class if you want to use this functionality.) More...
 
virtual void set_integration_scheme (Integral *const &integral_pt)
 Set the spatial integration scheme. More...
 
Integral *const & integral_pt () const
 Return the pointer to the integration scheme (const version) More...
 
virtual void shape (const Vector< double > &s, Shape &psi) const =0
 Calculate the geometric shape functions at local coordinate s. This function must be overloaded for each specific geometric element. More...
 
virtual void shape_at_knot (const unsigned &ipt, Shape &psi) const
 Return the geometric shape function at the ipt-th integration point. More...
 
virtual void dshape_local (const Vector< double > &s, Shape &psi, DShape &dpsids) const
 Function to compute the geometric shape functions and derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element. (Broken virtual function — specifies the interface) More...
 
virtual void dshape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids) const
 Return the geometric shape function and its derivative w.r.t. the local coordinates at the ipt-th integration point. More...
 
virtual void d2shape_local (const Vector< double > &s, Shape &psi, DShape &dpsids, DShape &d2psids) const
 Function to compute the geometric shape functions and also first and second derivatives w.r.t. local coordinates at local coordinate s. This function must be overloaded for each specific geometric element (if required). (Broken virtual function — specifies the interface). Numbering: 1D: d2psids(i,0) = $ d^2 \psi_j / ds^2 $ 2D: d2psids(i,0) = $ \partial^2 \psi_j / \partial s_0^2 $ d2psids(i,1) = $ \partial^2 \psi_j / \partial s_1^2 $ d2psids(i,2) = $ \partial^2 \psi_j / \partial s_0 \partial s_1 $ 3D: d2psids(i,0) = $ \partial^2 \psi_j / \partial s_0^2 $ d2psids(i,1) = $ \partial^2 \psi_j / \partial s_1^2 $ d2psids(i,2) = $ \partial^2 \psi_j / \partial s_2^2 $ d2psids(i,3) = $ \partial^2 \psi_j / \partial s_0 \partial s_1 $ d2psids(i,4) = $ \partial^2 \psi_j / \partial s_0 \partial s_2 $ d2psids(i,5) = $ \partial^2 \psi_j / \partial s_1 \partial s_2 $. More...
 
virtual void d2shape_local_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsids, DShape &d2psids) const
 Return the geometric shape function and its first and second derivatives w.r.t. the local coordinates at the ipt-th integration point. Numbering: 1D: d2psids(i,0) = $ d^2 \psi_j / ds^2 $ 2D: d2psids(i,0) = $ \partial^2 \psi_j / \partial s_0^2 $ d2psids(i,1) = $ \partial^2 \psi_j / \partial s_1^2 $ d2psids(i,2) = $ \partial^2 \psi_j / \partial s_0 \partial s_1 $ 3D: d2psids(i,0) = $ \partial^2 \psi_j / \partial s_0^2 $ d2psids(i,1) = $ \partial^2 \psi_j / \partial s_1^2 $ d2psids(i,2) = $ \partial^2 \psi_j / \partial s_2^2 $ d2psids(i,3) = $ \partial^2 \psi_j / \partial s_0 \partial s_1 $ d2psids(i,4) = $ \partial^2 \psi_j / \partial s_0 \partial s_2 $ d2psids(i,5) = $ \partial^2 \psi_j / \partial s_1 \partial s_2 $. More...
 
virtual double J_eulerian (const Vector< double > &s) const
 Return the Jacobian of mapping from local to global coordinates at local position s. More...
 
virtual double J_eulerian_at_knot (const unsigned &ipt) const
 Return the Jacobian of the mapping from local to global coordinates at the ipt-th integration point. More...
 
void check_J_eulerian_at_knots (bool &passed) const
 Check that Jacobian of mapping between local and Eulerian coordinates at all integration points is positive. More...
 
void check_jacobian (const double &jacobian) const
 Helper function used to check for singular or negative Jacobians in the transform from local to global or Lagrangian coordinates. More...
 
double dshape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx) const
 Compute the geometric shape functions and also first derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. More...
 
virtual double dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx) const
 Return the geometric shape functions and also first derivatives w.r.t. global coordinates at the ipt-th integration point. More...
 
virtual double dshape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsi, DenseMatrix< double > &djacobian_dX, RankFourTensor< double > &d_dpsidx_dX) const
 Compute the geometric shape functions (psi) and first derivatives w.r.t. global coordinates (dpsidx) at the ipt-th integration point. Return the determinant of the jacobian of the mapping (detJ). Additionally calculate the derivatives of both "detJ" and "dpsidx" w.r.t. the nodal coordinates. More...
 
double d2shape_eulerian (const Vector< double > &s, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
 Compute the geometric shape functions and also first and second derivatives w.r.t. global coordinates at local coordinate s; Returns Jacobian of mapping from global to local coordinates. Numbering: 1D: d2psidx(i,0) = $ d^2 \psi_j / d x^2 $ 2D: d2psidx(i,0) = $ \partial^2 \psi_j / \partial x_0^2 $ d2psidx(i,1) = $ \partial^2 \psi_j / \partial x_1^2 $ d2psidx(i,2) = $ \partial^2 \psi_j / \partial x_0 \partial x_1 $ 3D: d2psidx(i,0) = $ \partial^2 \psi_j / \partial x_0^2 $ d2psidx(i,1) = $ \partial^2 \psi_j / \partial x_1^2 $ d2psidx(i,2) = $ \partial^2 \psi_j / \partial x_2^2 $ d2psidx(i,3) = $ \partial^2 \psi_j / \partial x_0 \partial x_1 $ d2psidx(i,4) = $ \partial^2 \psi_j / \partial x_0 \partial x_2 $ d2psidx(i,5) = $ \partial^2 \psi_j / \partial x_1 \partial x_2 $. More...
 
virtual double d2shape_eulerian_at_knot (const unsigned &ipt, Shape &psi, DShape &dpsidx, DShape &d2psidx) const
 Return the geometric shape functions and also first and second derivatives w.r.t. global coordinates at ipt-th integration point. Numbering: 1D: d2psidx(i,0) = $ d^2 \psi_j / d s^2 $ 2D: d2psidx(i,0) = $ \partial^2 \psi_j / \partial x_0^2 $ d2psidx(i,1) = $ \partial^2 \psi_j / \partial x_1^2 $ d2psidx(i,2) = $ \partial^2 \psi_j / \partial x_0 \partial x_1 $ 3D: d2psidx(i,0) = $ \partial^2 \psi_j / \partial x_0^2 $ d2psidx(i,1) = $ \partial^2 \psi_j / \partial x_1^2 $ d2psidx(i,2) = $ \partial^2 \psi_j / \partial x_2^2 $ d2psidx(i,3) = $ \partial^2 \psi_j / \partial x_0 \partial x_1 $ d2psidx(i,4) = $ \partial^2 \psi_j / \partial x_0 \partial x_2 $ d2psidx(i,5) = $ \partial^2 \psi_j / \partial x_1 \partial x_2 $. More...
 
virtual void 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 &current_string) const
 Function to describe the local dofs of the element[s]. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...
 
virtual void describe_nodal_local_dofs (std::ostream &out, const std::string &current_string) const
 Function to describe the local dofs of the element[s]. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...
 
virtual void assign_all_generic_local_eqn_numbers (const bool &store_local_dof_pt)
 Overloaded version of the calculation of the local equation numbers. If the boolean argument is true then pointers to the degrees of freedom associated with each equation number are stored locally in the array Dof_pt. More...
 
Node *& node_pt (const unsigned &n)
 Return a pointer to the local node n. More...
 
Node *const & node_pt (const unsigned &n) const
 Return a pointer to the local node n (const version) More...
 
unsigned nnode () const
 Return the number of nodes. More...
 
virtual unsigned nnode_1d () const
 Return the number of nodes along one edge of the element Default is to return zero — must be overloaded by geometric elements. More...
 
double raw_nodal_position (const unsigned &n, const unsigned &i) const
 Return the i-th coordinate at local node n. Do not use the hanging node representation. NOTE: Moved to cc file because of a possible compiler bug in gcc (yes, really!). The move to the cc file avoids inlining which appears to cause problems (only) when compiled with gcc and -O3; offensive "illegal read" is in optimised-out section of code and data that is allegedly illegal is readily readable (by other means) just before this function is called so I can't really see how we could possibly be responsible for this... More...
 
double raw_nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
 Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level). Do not use the hanging node representation. More...
 
double raw_dnodal_position_dt (const unsigned &n, const unsigned &i) const
 Return the i-th component of nodal velocity: dx/dt at local node n. Do not use the hanging node representation. More...
 
double raw_dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
 Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. Do not use the hanging node representation. More...
 
double raw_nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
 Return the value of the k-th type of the i-th positional variable at the local node n. Do not use the hanging node representation. More...
 
double raw_nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
 Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. Do not use the hanging node representation. More...
 
double raw_dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
 i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...
 
double raw_dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
 i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. Do not use the hanging node representation. More...
 
double nodal_position (const unsigned &n, const unsigned &i) const
 Return the i-th coordinate at local node n. If the node is hanging, the appropriate interpolation is handled by the position function in the Node class. More...
 
double nodal_position (const unsigned &t, const unsigned &n, const unsigned &i) const
 Return the i-th coordinate at local node n, at time level t (t=0: present; t>0: previous time level) Returns suitably interpolated version for hanging nodes. More...
 
double dnodal_position_dt (const unsigned &n, const unsigned &i) const
 Return the i-th component of nodal velocity: dx/dt at local node n. More...
 
double dnodal_position_dt (const unsigned &n, const unsigned &j, const unsigned &i) const
 Return the i-th component of j-th derivative of nodal position: d^jx/dt^j at node n. More...
 
double nodal_position_gen (const unsigned &n, const unsigned &k, const unsigned &i) const
 Return the value of the k-th type of the i-th positional variable at the local node n. More...
 
double nodal_position_gen (const unsigned &t, const unsigned &n, const unsigned &k, const unsigned &i) const
 Return the generalised nodal position (type k, i-th variable) at previous timesteps at local node n. More...
 
double dnodal_position_gen_dt (const unsigned &n, const unsigned &k, const unsigned &i) const
 i-th component of time derivative (velocity) of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...
 
double dnodal_position_gen_dt (const unsigned &j, const unsigned &n, const unsigned &k, const unsigned &i) const
 i-th component of j-th time derivative of the generalised position, dx(k,i)/dt at local node n. ‘Type’: k; Coordinate direction: i. More...
 
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 Nodevertex_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 Nodeconstruct_node (const unsigned &n)
 Construct the local node n and return a pointer to the newly created node object. More...
 
virtual Nodeconstruct_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 Nodeconstruct_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 Nodeconstruct_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 Nodeget_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...
 
Datageom_data_pt (const unsigned &j)
 A standard FiniteElement is fixed, so there are no geometric data when viewed in its GeomObject incarnation. More...
 
void position (const Vector< double > &zeta, Vector< double > &r) const
 Return the parametrised position of the FiniteElement in its incarnation as a GeomObject, r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s). More...
 
void position (const unsigned &t, const Vector< double > &zeta, Vector< double > &r) const
 Return the parametrised position of the FiniteElement in its GeomObject incarnation: r(zeta). The position is given by the Eulerian coordinate and the intrinsic coordinate (zeta) is the local coordinate of the element (s) This version of the function returns the position as a function of time t=0: current time; t>0: previous timestep. Works for t=0 but needs to be overloaded if genuine time-dependence is required. More...
 
void dposition_dt (const Vector< double > &zeta, const unsigned &t, Vector< double > &drdt)
 Return the t-th time derivative of the parametrised position of the FiniteElement in its GeomObject incarnation: $ \frac{d^{t} dr(zeta)}{d t^{t}} $. Call the t-th time derivative of the FE-interpolated Eulerian coordinate. More...
 
virtual double zeta_nodal (const unsigned &n, const unsigned &k, const unsigned &i) const
 Specify the values of the "global" intrinsic coordinate, zeta, of a compound geometric object (a mesh of elements) when the element is viewied as a sub-geometric object. The default assumption is that the element will be treated as a sub-geometric object in a bulk Mesh of other elements (geometric objects). The "global" coordinate of the compound geometric object is simply the Eulerian coordinate, x. The second default assumption is that the coordinate zeta will be stored at the nodes and interpolated using the shape functions of the element. This function returns the value of zeta stored at local node n, where k is the type of coordinate and i is the coordinate direction. The function is virtual so that it can be overloaded by different types of element: FaceElements and SolidFiniteElements. More...
 
void interpolated_zeta (const Vector< double > &s, Vector< double > &zeta) const
 Calculate the interpolated value of zeta, the intrinsic coordinate of the element when viewed as a compound geometric object within a Mesh as a function of the local coordinate of the element, s. The default assumption is the zeta is interpolated using the shape functions of the element with the values given by zeta_nodal(). A MacroElement representation of the intrinsic coordinate parametrised by the local coordinate s is used if available. Choosing the MacroElement representation of zeta (Eulerian x by default) allows a correspondence to be established between elements on different Meshes covering the same curvilinear domain in cases where one element is much coarser than the other. More...
 
void locate_zeta (const Vector< double > &zeta, GeomObject *&geom_object_pt, Vector< double > &s, const bool &use_coordinate_as_initial_guess=false)
 For a given value of zeta, the "global" intrinsic coordinate of a mesh of FiniteElements represented as a compound geometric object, find the local coordinate in this element that corresponds to the requested value of zeta. If zeta cannot be located in this element, geom_object_pt is set to NULL. If zeta is located in this element, we return its "this" pointer. By default don't use any value passed in to the local coordinate s as the initial guess in the Newton method. More...
 
virtual void node_update ()
 Update the positions of all nodes in the element using each node update function. The default implementation may be overloaded so that more efficient versions can be written. More...
 
virtual void identify_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...
 
void point_output (std::ostream &outfile, const Vector< double > &s)
 Output solution (as defined by point_output_data()) at local cordinates s. More...
 
virtual unsigned nplot_points_paraview (const unsigned &nplot) const
 Return the number of actual plot points for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...
 
virtual unsigned nsub_elements_paraview (const unsigned &nplot) const
 Return the number of local sub-elements for paraview plot with parameter nplot. Broken virtual; can be overloaded in specific elements. More...
 
void output_paraview (std::ofstream &file_out, const unsigned &nplot) const
 Paraview output – this outputs the coordinates at the plot points (for parameter nplot) to specified output file. More...
 
virtual void write_paraview_output_offset_information (std::ofstream &file_out, const unsigned &nplot, unsigned &counter) const
 Fill in the offset information for paraview plot. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...
 
virtual void write_paraview_type (std::ofstream &file_out, const unsigned &nplot) const
 Return the paraview element type. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...
 
virtual void write_paraview_offsets (std::ofstream &file_out, const unsigned &nplot, unsigned &offset_sum) const
 Return the offsets for the paraview sub-elements. Broken virtual. Needs to be implemented for each new geometric element type; see http://www.vtk.org/VTK/img/file-formats.pdf. More...
 
virtual void scalar_value_fct_paraview (std::ofstream &file_out, const unsigned &i, const unsigned &nplot, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt) const
 Write values of the i-th scalar field at the plot points. Broken virtual. Needs to be implemented for each new specific element type. More...
 
virtual void output (const unsigned &t, std::ostream &outfile, const unsigned &n_plot) const
 Output the element data at time step t. This is const because it is newly added and so can be done easily. Really all the output(...) functions should be const! More...
 
virtual void output_fct (std::ostream &outfile, const unsigned &n_plot, const double &time, const SolutionFunctorBase &exact_soln) const
 Output a time-dependent exact solution over the element. More...
 
virtual void get_s_plot (const unsigned &i, const unsigned &nplot, Vector< double > &s, const bool &shifted_to_interior=false) const
 Get cector of local coordinates of plot point i (when plotting nplot points in each "coordinate direction"). Generally these plot points will be uniformly spaced across the element. The optional final boolean flag (default: false) allows them to be shifted inwards to avoid duplication of plot point points between elements – useful when they are used in locate_zeta, say. More...
 
virtual std::string tecplot_zone_string (const unsigned &nplot) const
 Return string for tecplot zone header (when plotting nplot points in each "coordinate direction") More...
 
virtual void write_tecplot_zone_footer (std::ostream &outfile, const unsigned &nplot) const
 Add tecplot zone "footer" to output stream (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...
 
virtual void write_tecplot_zone_footer (FILE *file_pt, const unsigned &nplot) const
 Add tecplot zone "footer" to C-style output. (when plotting nplot points in each "coordinate direction"). Empty by default – can be used, e.g., to add FE connectivity lists to elements that need it. More...
 
virtual unsigned nplot_points (const unsigned &nplot) const
 Return total number of plot points (when plotting nplot points in each "coordinate direction") More...
 
virtual void compute_error (FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
 Given the exact solution $ {\bf f}({\bf x}) $ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...
 
virtual void compute_error (FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
 Given the exact solution $ {\bf f}({\bf x}) $ this function calculates the norm of the error and that of the exact solution. Version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...
 
virtual void compute_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, Vector< double > &error, Vector< double > &norm)
 Plot the error when compared against a given exact solution $ {\bf f}({\bf x}) $. Also calculates the norm of the error and that of the exact solution. The version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...
 
virtual void compute_error (std::ostream &outfile, FiniteElement::UnsteadyExactSolutionFctPt exact_soln_pt, const double &time, Vector< double > &error, Vector< double > &norm)
 Plot the error when compared against a given time-dependent exact solution $ {\bf f}(t,{\bf x}) $. Also calculates the norm of the error and that of the exact solution. The version with vectors of norms and errors so that different variables' norms and errors can be returned individually. More...
 
virtual void compute_abs_error (std::ostream &outfile, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt, double &error)
 Plot the error when compared against a given exact solution $ {\bf f}({\bf x}) $. Also calculates the maximum absolute error. More...
 
void integrate_fct (FiniteElement::SteadyExactSolutionFctPt integrand_fct_pt, Vector< double > &integral)
 Evaluate integral of a Vector-valued function $ {\bf f}({\bf x}) $ over the element. More...
 
void integrate_fct (FiniteElement::UnsteadyExactSolutionFctPt integrand_fct_pt, const double &time, Vector< double > &integral)
 Evaluate integral of a Vector-valued, time-dependent function $ {\bf f}(t,{\bf x}) $ over the element. More...
 
virtual void build_face_element (const int &face_index, FaceElement *face_element_pt)
 Function for building a lower dimensional FaceElement on the specified face of the FiniteElement. The arguments are the index of the face, an integer whose value depends on the particular element type, and a pointer to the FaceElement. More...
 
virtual unsigned 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 &current_string) const
 Function to describe the dofs of the element. The ostream specifies the output stream to which the description is written; the string stores the currently assembled output that is ultimately written to the output stream by Data::describe_dofs(...); it is typically built up incrementally as we descend through the call hierarchy of this function when called from Problem::describe_dofs(...) More...
 
void add_internal_value_pt_to_map (std::map< unsigned, double * > &map_of_value_pt)
 Add pointers to the internal data values to map indexed by the global equation number. More...
 
void add_internal_data_values_to_vector (Vector< double > &vector_of_values)
 Add all internal data and time history values to the vector in the internal storage order. More...
 
void read_internal_data_values_from_vector (const Vector< double > &vector_of_values, unsigned &index)
 Read all internal data and time history values from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...
 
void add_internal_eqn_numbers_to_vector (Vector< long > &vector_of_eqn_numbers)
 Add all equation numbers associated with internal data to the vector in the internal storage order. More...
 
void read_internal_eqn_numbers_from_vector (const Vector< long > &vector_of_eqn_numbers, unsigned &index)
 Read all equation numbers associated with internal data from the vector starting from index. On return the index will be set to the value at the end of the data that has been read in. More...
 
virtual void assign_local_eqn_numbers (const bool &store_local_dof_pt)
 Setup the arrays of local equation numbers for the element. If the optional boolean argument is true, then pointers to the associated degrees of freedom are stored locally in the array Dof_pt. More...
 
virtual void complete_setup_of_dependencies ()
 Complete the setup of any additional dependencies that the element may have. Empty virtual function that may be overloaded for specific derived elements. Used, e.g., for elements with algebraic node update functions to determine the "geometric Data", i.e. the Data that affects the element's shape. This function is called (for all elements) at the very beginning of the equation numbering procedure to ensure that all dependencies are accounted for. More...
 
virtual void get_residuals (Vector< double > &residuals)
 Calculate the vector of residuals of the equations in the element. By default initialise the vector to zero and then call the fill_in_contribution_to_residuals() function. Note that this entire function can be overloaded if desired. More...
 
virtual void get_jacobian (Vector< double > &residuals, DenseMatrix< double > &jacobian)
 Calculate the elemental Jacobian matrix "d equation / d variable". More...
 
virtual void get_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
 Calculate the residuals and the elemental "mass" matrix, the matrix that multiplies the time derivative terms in a problem. More...
 
virtual void get_jacobian_and_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &jacobian, DenseMatrix< double > &mass_matrix)
 Calculate the residuals and jacobian and elemental "mass" matrix, the matrix that multiplies the time derivative terms. More...
 
virtual void get_dresiduals_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam)
 Calculate the derivatives of the residuals with respect to a parameter. More...
 
virtual void get_djacobian_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam)
 Calculate the derivatives of the elemental Jacobian matrix and residuals with respect to a parameter. More...
 
virtual void get_djacobian_and_dmass_matrix_dparameter (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam)
 Calculate the derivatives of the elemental Jacobian matrix mass matrix and residuals with respect to a parameter. More...
 
virtual void get_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
 Calculate the product of the Hessian (derivative of Jacobian with respect to all variables) an eigenvector, Y, and other specified vectors, C (d(J_{ij})/d u_{k}) Y_{j} C_{k}. More...
 
virtual void get_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
 Return the vector of inner product of the given pairs of history values. More...
 
virtual void get_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
 Compute the vectors that when taken as a dot product with other history values give the inner product over the element. More...
 
void set_halo (const unsigned &non_halo_proc_ID)
 Label the element as halo and specify processor that holds non-halo counterpart. More...
 
void set_nonhalo ()
 Label the element as not being a halo. More...
 
bool is_halo () const
 Is this element a halo? More...
 
int non_halo_proc_ID ()
 ID of processor ID that holds non-halo counterpart of halo element; negative if not a halo. More...
 
void set_must_be_kept_as_halo ()
 Insist that this element be kept as a halo element during a distribute? More...
 
void unset_must_be_kept_as_halo ()
 Do not insist that this element be kept as a halo element during distribution. More...
 
bool must_be_kept_as_halo () const
 Test whether the element must be kept as a halo element. More...
 
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...
 
TimeSteppertime_stepper_pt () const
 Access function for pointer to time stepper: Null if object is not time-dependent. Const version. More...
 
virtual void position (const double &t, const Vector< double > &zeta, Vector< double > &r) const
 Parametrised position on object: r(zeta). Evaluated at the continuous time value, t. More...
 
virtual void dposition (const Vector< double > &zeta, DenseMatrix< double > &drdzeta) const
 Derivative of position Vector w.r.t. to coordinates: $ \frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). Evaluated at current time. More...
 
virtual void d2position (const Vector< double > &zeta, RankThreeTensor< double > &ddrdzeta) const
 2nd derivative of position Vector w.r.t. to coordinates: $ \frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...
 
virtual void d2position (const Vector< double > &zeta, Vector< double > &r, DenseMatrix< double > &drdzeta, RankThreeTensor< double > &ddrdzeta) const
 Posn Vector and its 1st & 2nd derivatives w.r.t. to coordinates: $ \frac{dR_i}{d \zeta_\alpha}$ = drdzeta(alpha,i). $ \frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}$ = ddrdzeta(alpha,beta,i). Evaluated at current time. More...
 
- Public Member Functions inherited from oomph::TemplateFreeNavierStokesEquationsBase
 TemplateFreeNavierStokesEquationsBase ()
 Constructor (empty) More...
 
virtual ~TemplateFreeNavierStokesEquationsBase ()
 Virtual destructor (empty) More...
 
virtual int p_local_eqn (const unsigned &n) const =0
 Access function for the local equation number information for the pressure. p_local_eqn[n] = local equation number or < 0 if pinned. More...
 
- Public Member Functions inherited from oomph::NavierStokesElementWithDiagonalMassMatrices
 NavierStokesElementWithDiagonalMassMatrices ()
 Empty constructor. More...
 
virtual ~NavierStokesElementWithDiagonalMassMatrices ()
 Virtual destructor. More...
 
 NavierStokesElementWithDiagonalMassMatrices (const NavierStokesElementWithDiagonalMassMatrices &)=delete
 Broken copy constructor. More...
 
void operator= (const NavierStokesElementWithDiagonalMassMatrices &)=delete
 Broken assignment operator. More...
 

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_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 double dshape_and_dtest_eulerian_nst (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_nst (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 double dshape_and_dtest_eulerian_at_knot_nst (const unsigned &ipt, Shape &psi, DShape &dpsidx, RankFourTensor< double > &d_dpsidx_dX, Shape &test, DShape &dtestdx, RankFourTensor< double > &d_dtestdx_dX, DenseMatrix< double > &djacobian_dX) const =0
 Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping (J). Also compute derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates. More...
 
virtual void get_body_force_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, Vector< double > &result)
 Calculate the body force at a given time and local and/or Eulerian position. This function is virtual so that it can be overloaded in multi-physics elements where the body force might depend on another variable. More...
 
virtual void get_body_force_gradient_nst (const double &time, const unsigned &ipt, const Vector< double > &s, const Vector< double > &x, DenseMatrix< double > &d_body_force_dx)
 Get gradient of body force term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations. Computed via function pointer (if set) or by finite differencing (default) More...
 
virtual double get_source_nst (const double &time, const unsigned &ipt, const Vector< double > &x)
 Calculate the source fct at given time and Eulerian position. More...
 
virtual void get_source_gradient_nst (const double &time, const unsigned &ipt, const Vector< double > &x, Vector< double > &gradient)
 Get gradient of source term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations. Computed via function pointer (if set) or by finite differencing (default) More...
 
virtual void fill_in_generic_residual_contribution_nst (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. Flag=2: Fill in mass matrix too. More...
 
virtual void fill_in_generic_pressure_advection_diffusion_contribution_nst (Vector< double > &residuals, DenseMatrix< double > &jacobian, unsigned flag)
 Compute the residuals for the associated pressure advection diffusion problem. Used by the Fp preconditioner. flag=1(or 0): do (or don't) compute the Jacobian as well. More...
 
virtual void fill_in_generic_dresidual_contribution_nst (double *const &parameter_pt, Vector< double > &dres_dparam, DenseMatrix< double > &djac_dparam, DenseMatrix< double > &dmass_matrix_dparam, unsigned flag)
 Compute the derivatives of the residuals for the Navier–Stokes equations with respect to a parameter Flag=1 (or 0): do (or don't) compute the Jacobian as well. Flag=2: Fill in mass matrix too. More...
 
void fill_in_contribution_to_hessian_vector_products (Vector< double > const &Y, DenseMatrix< double > const &C, DenseMatrix< double > &product)
 Compute the hessian tensor vector products required to perform continuation of bifurcations analytically. More...
 
- Protected Member Functions inherited from oomph::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 $ X_{pq} $ of the derivative of the shape functions $ \psi_j $ w.r.t. the global eulerian coordinates $ x_i $. I.e. this function calculates. More...
 
template<unsigned DIM>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 Calculate the derivative w.r.t. the nodal coordinates $ X_{pq} $ of the derivative of the shape functions w.r.t. the global eulerian coordinates $ x_i $, using the determinant of the jacobian mapping, its derivative w.r.t. the nodal coordinates $ X_{pq} $, the inverse jacobian and the derivatives of the shape functions w.r.t. the local coordinates. The result is returned as a tensor of rank four. Numbering: d_dpsidx_dX(p,q,j,i) = $ \frac{\partial}{\partial X_{pq}} \left( \frac{\partial \psi_j}{\partial x_i} \right) $ This function is templated by the dimension of the element. More...
 
virtual void transform_derivatives (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
 Convert derivative w.r.t.local coordinates to derivatives w.r.t the coordinates used to assemble the inverse_jacobian passed in the mapping. On entry, dbasis must contain the basis function derivatives w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates on exit. This is virtual so that it may be overloaded if desired for efficiency reasons. More...
 
void transform_derivatives_diagonal (const DenseMatrix< double > &inverse_jacobian, DShape &dbasis) const
 Convert derivative w.r.t local coordinates to derivatives w.r.t the coordinates used to assemble the inverse jacobian passed in the mapping, assuming that the coordinates are aligned in the direction of the local coordinates. On entry dbasis must contain the derivatives of the basis functions w.r.t. the local coordinates; it will contain the derivatives w.r.t. the new coordinates. are converted into the new using the mapping inverse_jacobian. More...
 
virtual void transform_second_derivatives (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 Convert derivatives and second derivatives w.r.t. local coordiantes to derivatives and second derivatives w.r.t. the coordinates used to assemble the jacobian, inverse jacobian and jacobian2 passed to the function. By default this function will call transform_second_derivatives_template<>(...) using the dimension of the element as the template parameter. It is virtual so that it can be overloaded by a specific element to save using a switch statement. Optionally, the element writer may wish to use the transform_second_derivatives_diagonal<>(...) function On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...
 
template<unsigned DIM>
void transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This is templated by dimension because the method of calculation varies significantly with the dimension. On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...
 
template<unsigned DIM>
void transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 Convert derivatives and second derivatives w.r.t. local coordinates to derivatives and second derivatives w.r.t. the coordinates used to asssmble the jacobian, inverse jacobian and jacobian2 passed in the mapping. This version of the function assumes that the local coordinates are aligned with the global coordinates, i.e. the jacobians are diagonal On entry dbasis and d2basis must contain the derivatives w.r.t. the local coordinates; on exit they will be the derivatives w.r.t. the transformed coordinates. More...
 
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 $ X_{pq} $ of the derivative of the shape functions w.r.t. the global eulerian coordinates $ x_i $. More...
 
template<>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 One-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $ X_{pq} $ of the derivative of the shape functions w.r.t. the global eulerian coordinates $ x_i $. More...
 
template<>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 Two-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $ X_{pq} $ of the derivative of the shape functions w.r.t. the global eulerian coordinates $ x_i $. More...
 
template<>
void d_dshape_eulerian_dnodal_coordinates_templated_helper (const double &det_jacobian, const DenseMatrix< double > &jacobian, const DenseMatrix< double > &djacobian_dX, const DenseMatrix< double > &inverse_jacobian, const DShape &dpsids, RankFourTensor< double > &d_dpsidx_dX) const
 Three-d specialisation of function to calculate the derivative w.r.t. the nodal coordinates $ X_{pq} $ of the derivative of the shape functions w.r.t. the global eulerian coordinates $ x_i $. More...
 
template<>
void transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...
 
template<>
void transform_second_derivatives_template (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly. Specialisation to two spatial dimensions. More...
 
template<>
void transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 Convert derivatives and second derivatives w.r.t local coordinates to derivatives w.r.t. the coordinates used to assemble the jacobian, inverse_jacobian and jacobian 2 passed. This must be specialised for each dimension, otherwise it gets very ugly Specialisation to one dimension. More...
 
template<>
void transform_second_derivatives_diagonal (const DenseMatrix< double > &jacobian, const DenseMatrix< double > &inverse_jacobian, const DenseMatrix< double > &jacobian2, DShape &dbasis, DShape &d2basis) const
 Convert second derivatives w.r.t. local coordinates to second derivatives w.r.t. the coordinates passed in the tensor coordinate. Specialised to two spatial dimension. More...
 
- Protected Member Functions inherited from oomph::GeneralisedElement
unsigned add_internal_data (Data *const &data_pt, const bool &fd=true)
 Add a (pointer to an) internal data object to the element and return the index required to obtain it from the access function internal_data_pt(). The boolean indicates whether the datum should be included in the general finite-difference loop when calculating the jacobian. The default value is true, i.e. the data will be included in the finite differencing. More...
 
bool internal_data_fd (const unsigned &i) const
 Return the status of the boolean flag indicating whether the internal data is included in the finite difference loop. More...
 
void exclude_internal_data_fd (const unsigned &i)
 Set the boolean flag to exclude the internal datum from the finite difference loop when computing the jacobian matrix. More...
 
void include_internal_data_fd (const unsigned &i)
 Set the boolean flag to include the internal datum in the finite difference loop when computing the jacobian matrix. More...
 
void clear_global_eqn_numbers ()
 Clear the storage for the global equation numbers and pointers to dofs (if stored) More...
 
void add_global_eqn_numbers (std::deque< unsigned long > const &global_eqn_numbers, std::deque< double * > const &global_dof_pt)
 Add the contents of the queue global_eqn_numbers to the local storage for the local-to-global translation scheme. It is essential that the entries in the queue are added IN ORDER i.e. from the front. More...
 
virtual void assign_internal_and_external_local_eqn_numbers (const bool &store_local_dof_pt)
 Assign the local equation numbers for the internal and external Data This must be called after the global equation numbers have all been assigned. It is virtual so that it can be overloaded by ElementWithExternalElements so that any external data from the external elements in included in the numbering scheme. If the boolean argument is true then pointers to the dofs will be stored in Dof_pt. More...
 
virtual void assign_additional_local_eqn_numbers ()
 Setup any additional look-up schemes for local equation numbers. Examples of use include using local storage to refer to explicit degrees of freedom. The additional memory cost of such storage may or may not be offset by fast local access. More...
 
int internal_local_eqn (const unsigned &i, const unsigned &j) const
 Return the local equation number corresponding to the j-th value stored at the i-th internal data. More...
 
int external_local_eqn (const unsigned &i, const unsigned &j)
 Return the local equation number corresponding to the j-th value stored at the i-th external data. More...
 
void fill_in_jacobian_from_internal_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
 Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...
 
void fill_in_jacobian_from_internal_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
 Calculate the contributions to the jacobian from the internal degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...
 
void fill_in_jacobian_from_external_by_fd (Vector< double > &residuals, DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
 Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version of the function assumes that the residuals vector has already been calculated. If the boolean argument is true, the finite differencing will be performed for all external data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...
 
void fill_in_jacobian_from_external_by_fd (DenseMatrix< double > &jacobian, const bool &fd_all_data=false)
 Calculate the contributions to the jacobian from the external degrees of freedom using finite differences. This version computes the residuals vector before calculating the jacobian terms. If the boolean argument is true, the finite differencing will be performed for all internal data, irrespective of the information in Data_fd. The default value (false) uses the information in Data_fd to selectively difference only certain data. More...
 
virtual void update_before_internal_fd ()
 Function that is called before the finite differencing of any internal data. This may be overloaded to update any dependent data before finite differencing takes place. More...
 
virtual void reset_after_internal_fd ()
 Function that is call after the finite differencing of the internal data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...
 
virtual void update_in_internal_fd (const unsigned &i)
 Function called within the finite difference loop for internal data after a change in any values in the i-th internal data object. More...
 
virtual void reset_in_internal_fd (const unsigned &i)
 Function called within the finite difference loop for internal data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...
 
virtual void update_before_external_fd ()
 Function that is called before the finite differencing of any external data. This may be overloaded to update any dependent data before finite differencing takes place. More...
 
virtual void reset_after_external_fd ()
 Function that is call after the finite differencing of the external data. This may be overloaded to reset any dependent variables that may have changed during the finite differencing. More...
 
virtual void update_in_external_fd (const unsigned &i)
 Function called within the finite difference loop for external data after a change in any values in the i-th external data object. More...
 
virtual void reset_in_external_fd (const unsigned &i)
 Function called within the finite difference loop for external data after the values in the i-th external data object are reset. The default behaviour is to call the update function. More...
 
virtual void fill_in_contribution_to_mass_matrix (Vector< double > &residuals, DenseMatrix< double > &mass_matrix)
 Add the elemental contribution to the mass matrix matrix. and the residuals vector. Note that this function should NOT initialise the residuals vector or the mass matrix. It must be called after the residuals vector and jacobian matrix have been initialised to zero. The default is deliberately broken. More...
 
virtual void fill_in_contribution_to_inner_products (Vector< std::pair< unsigned, unsigned >> const &history_index, Vector< double > &inner_product)
 Fill in the contribution to the inner products between given pairs of history values. More...
 
virtual void fill_in_contribution_to_inner_product_vectors (Vector< unsigned > const &history_index, Vector< Vector< double >> &inner_product_vector)
 Fill in the contributions to the vectors that when taken as dot product with other history values give the inner product over the element. More...
 

Protected 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 * Re_pt
 Pointer to global Reynolds number. More...
 
double * ReSt_pt
 Pointer to global Reynolds number x Strouhal number (=Womersley) More...
 
double * ReInvFr_pt
 Pointer to global Reynolds number x inverse Froude number (= Bond number / Capillary number) More...
 
Vector< double > * G_pt
 Pointer to global gravity Vector. More...
 
NavierStokesBodyForceFctPt Body_force_fct_pt
 Pointer to body force function. More...
 
NavierStokesSourceFctPt Source_fct_pt
 Pointer to volumetric source function. More...
 
NavierStokesPressureAdvDiffSourceFctPt Press_adv_diff_source_fct_pt
 Pointer to source function pressure advection diffusion equation (only to be used during validation) More...
 
bool ALE_is_disabled
 Boolean flag to indicate if ALE formulation is disabled when time-derivatives are computed. Only set to true if you're sure that the mesh is stationary. More...
 
Vector< FpPressureAdvDiffRobinBCElementBase * > Pressure_advection_diffusion_robin_element_pt
 Storage for FaceElements that apply Robin BC for pressure adv diff equation used in Fp preconditioner. More...
 
int Pinned_fp_pressure_eqn
 Global eqn number of pressure dof that's pinned in pressure advection diffusion problem (defaults to -1) More...
 
- Protected Attributes inherited from oomph::FiniteElement
MacroElementMacro_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...
 
TimeStepperGeom_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...
 

Detailed Description

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

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

A class for elements that solve the cartesian Navier–Stokes equations, templated by the dimension DIM. This contains the generic maths – any concrete implementation must be derived from this.

We're solving:

$ { Re \left( St \frac{\partial u_i}{\partial t} + (u_j - u_j^{M}) \frac{\partial u_i}{\partial x_j} \right) = - \frac{\partial p}{\partial x_i} - R_\rho B_i(x_j) - \frac{Re}{Fr} G_i + \frac{\partial }{\partial x_j} \left[ R_\mu \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i} \right) \right] } $

and

$ { \frac{\partial u_i}{\partial x_i} = Q } $

We also provide all functions required to use this element in FSI problems, by deriving it from the FSIFluidElement base class.

Definition at line 392 of file navier_stokes_elements.h.

Member Typedef Documentation

◆ NavierStokesBodyForceFctPt

template<unsigned DIM>
typedef void(* oomph::NavierStokesEquations< DIM >::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 399 of file navier_stokes_elements.h.

◆ NavierStokesPressureAdvDiffSourceFctPt

template<unsigned DIM>
typedef double(* oomph::NavierStokesEquations< DIM >::NavierStokesPressureAdvDiffSourceFctPt) (const Vector< double > &x)

Function pointer to source function fct(x) for the pressure advection diffusion equation (only used during validation!). x is a Vector!

Definition at line 412 of file navier_stokes_elements.h.

◆ NavierStokesSourceFctPt

template<unsigned DIM>
typedef double(* oomph::NavierStokesEquations< DIM >::NavierStokesSourceFctPt) (const double &time, const Vector< double > &x)

Function pointer to source function fct(t,x) x is a Vector!

Definition at line 405 of file navier_stokes_elements.h.

Constructor & Destructor Documentation

◆ NavierStokesEquations()

template<unsigned DIM>
oomph::NavierStokesEquations< DIM >::NavierStokesEquations ( )
inline

Member Function Documentation

◆ body_force_fct_pt() [1/2]

template<unsigned DIM>
NavierStokesBodyForceFctPt& oomph::NavierStokesEquations< DIM >::body_force_fct_pt ( )
inline

Access function for the body-force pointer.

Definition at line 777 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Body_force_fct_pt.

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

◆ body_force_fct_pt() [2/2]

template<unsigned DIM>
NavierStokesBodyForceFctPt oomph::NavierStokesEquations< DIM >::body_force_fct_pt ( ) const
inline

Access function for the body-force pointer. Const version.

Definition at line 783 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Body_force_fct_pt.

◆ build_fp_press_adv_diff_robin_bc_element()

template<unsigned DIM>
virtual void oomph::NavierStokesEquations< DIM >::build_fp_press_adv_diff_robin_bc_element ( const unsigned &  face_index)
pure virtual

◆ compute_error() [1/4]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::compute_error ( FiniteElement::SteadyExactSolutionFctPt  exact_soln_pt,
double &  error,
double &  norm 
)
virtual

Validate against exact solution. Solution is provided via function pointer. Compute L2 error and L2 norm of velocity solution over element.

Validate against exact velocity solution Solution is provided via a function pointer. Compute L2 error and L2 norm of velocity solution over element.

Reimplemented from oomph::FiniteElement.

Definition at line 508 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

◆ compute_error() [2/4]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::compute_error ( FiniteElement::UnsteadyExactSolutionFctPt  exact_soln_pt,
const double &  time,
double &  error,
double &  norm 
)
virtual

Validate against exact solution. Solution is provided via function pointer. 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. Compute L2 error and L2 norm of velocity solution over element.

Reimplemented from oomph::FiniteElement.

Definition at line 446 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

◆ compute_error() [3/4]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::compute_error ( std::ostream &  outfile,
FiniteElement::SteadyExactSolutionFctPt  exact_soln_pt,
double &  error,
double &  norm 
)
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 368 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

◆ compute_error() [4/4]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::compute_error ( std::ostream &  outfile,
FiniteElement::UnsteadyExactSolutionFctPt  exact_soln_pt,
const double &  time,
double &  error,
double &  norm 
)
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 289 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

◆ compute_norm() [1/2]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::compute_norm ( double &  norm)
virtual

Compute norm of solution: square of the L2 norm of the velocities.

Compute norm of the solution.

Reimplemented from oomph::GeneralisedElement.

Definition at line 186 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

◆ compute_norm() [2/2]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::compute_norm ( Vector< double > &  norm)
virtual

Compute the vector norm of the FEM solution.

Compute the vector norm of FEM solution.

Reimplemented from oomph::GeneralisedElement.

Definition at line 239 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

◆ d_kin_energy_dt()

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::d_kin_energy_dt

Get integral of time derivative of kinetic energy over element.

Get integral of time derivative of kinetic energy over element:

Definition at line 1460 of file navier_stokes_elements.cc.

References i, and s.

◆ delete_pressure_advection_diffusion_robin_elements()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::delete_pressure_advection_diffusion_robin_elements ( )
inlinevirtual

Delete the FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner.

Implements oomph::TemplateFreeNavierStokesEquationsBase.

Definition at line 1486 of file navier_stokes_elements.h.

References e, and oomph::NavierStokesEquations< DIM >::Pressure_advection_diffusion_robin_element_pt.

◆ density_ratio()

template<unsigned DIM>
const double& oomph::NavierStokesEquations< DIM >::density_ratio ( ) const
inline

Density ratio for element: Element's density relative to the viscosity used in the definition of the Reynolds number.

Definition at line 741 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Density_Ratio_pt.

◆ density_ratio_pt()

template<unsigned DIM>
double*& oomph::NavierStokesEquations< DIM >::density_ratio_pt ( )
inline

◆ dinterpolated_u_nst_ddata()

template<unsigned DIM>
virtual void oomph::NavierStokesEquations< DIM >::dinterpolated_u_nst_ddata ( const Vector< double > &  s,
const unsigned &  i,
Vector< double > &  du_ddata,
Vector< unsigned > &  global_eqn_number 
)
inlinevirtual

Compute the derivatives of the i-th component of velocity at point s with respect to all data that can affect its value. In addition, return the global equation numbers corresponding to the data. The function is virtual so that it can be overloaded in the refineable version.

Reimplemented in oomph::RefineableNavierStokesEquations< DIM >.

Definition at line 1587 of file navier_stokes_elements.h.

References oomph::Data::eqn_number(), i, oomph::FiniteElement::nnode(), oomph::FiniteElement::node_pt(), s, oomph::FiniteElement::shape(), and oomph::NavierStokesEquations< DIM >::u_index_nst().

◆ disable_ALE()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::disable_ALE ( )
inlinevirtual

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

Reimplemented from oomph::FiniteElement.

Definition at line 909 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::ALE_is_disabled.

Referenced by oomph::BuoyantQCrouzeixRaviartElement< DIM >::disable_ALE(), and oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::disable_ALE().

◆ dissipation() [1/2]

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::dissipation

Return integral of dissipation over element.

Definition at line 1046 of file navier_stokes_elements.cc.

References i, and s.

◆ dissipation() [2/2]

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::dissipation ( const Vector< double > &  s) const

Return dissipation at local coordinate s.

Definition at line 1162 of file navier_stokes_elements.cc.

References i, and s.

◆ dpshape_and_dptest_eulerian_nst()

template<unsigned DIM>
virtual double oomph::NavierStokesEquations< DIM >::dpshape_and_dptest_eulerian_nst ( const Vector< double > &  s,
Shape ppsi,
DShape dppsidx,
Shape ptest,
DShape dptestdx 
) const
pure virtual

◆ dshape_and_dtest_eulerian_at_knot_nst() [1/2]

template<unsigned DIM>
virtual double oomph::NavierStokesEquations< DIM >::dshape_and_dtest_eulerian_at_knot_nst ( const unsigned &  ipt,
Shape psi,
DShape dpsidx,
RankFourTensor< double > &  d_dpsidx_dX,
Shape test,
DShape dtestdx,
RankFourTensor< double > &  d_dtestdx_dX,
DenseMatrix< double > &  djacobian_dX 
) const
protectedpure virtual

Shape/test functions and derivs w.r.t. to global coords at integration point ipt; return Jacobian of mapping (J). Also compute derivatives of dpsidx, dtestdx and J w.r.t. nodal coordinates.

Implemented in oomph::TTaylorHoodElement< DIM >, oomph::TTaylorHoodElement< DIM >, oomph::TTaylorHoodElement< DIM >, oomph::TCrouzeixRaviartElement< DIM >, oomph::QTaylorHoodElement< DIM >, oomph::QTaylorHoodElement< DIM >, oomph::QTaylorHoodElement< DIM >, oomph::QCrouzeixRaviartElement< DIM >, oomph::QCrouzeixRaviartElement< DIM >, and oomph::QCrouzeixRaviartElement< DIM >.

◆ dshape_and_dtest_eulerian_at_knot_nst() [2/2]

template<unsigned DIM>
virtual double oomph::NavierStokesEquations< DIM >::dshape_and_dtest_eulerian_at_knot_nst ( const unsigned &  ipt,
Shape psi,
DShape dpsidx,
Shape test,
DShape dtestdx 
) const
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::TTaylorHoodElement< DIM >, oomph::TCrouzeixRaviartElement< DIM >, oomph::PRefineableQCrouzeixRaviartElement< DIM >, oomph::PRefineableQCrouzeixRaviartElement< DIM >, oomph::PRefineableQCrouzeixRaviartElement< DIM >, oomph::QTaylorHoodElement< DIM >, and oomph::QCrouzeixRaviartElement< DIM >.

◆ dshape_and_dtest_eulerian_nst()

template<unsigned DIM>
virtual double oomph::NavierStokesEquations< DIM >::dshape_and_dtest_eulerian_nst ( const Vector< double > &  s,
Shape psi,
DShape dpsidx,
Shape test,
DShape dtestdx 
) const
protectedpure virtual

◆ du_dt_nst()

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::du_dt_nst ( const unsigned &  n,
const unsigned &  i 
) const
inline

◆ enable_ALE()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::enable_ALE ( )
inlinevirtual

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

Reimplemented from oomph::FiniteElement.

Definition at line 918 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::ALE_is_disabled.

Referenced by oomph::BuoyantQCrouzeixRaviartElement< DIM >::enable_ALE(), and oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >::enable_ALE().

◆ fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter ( double *const &  parameter_pt,
Vector< double > &  dres_dparam,
DenseMatrix< double > &  djac_dparam,
DenseMatrix< double > &  dmass_matrix_dparam 
)
inlinevirtual

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

Reimplemented from oomph::GeneralisedElement.

Definition at line 1325 of file navier_stokes_elements.h.

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

◆ fill_in_contribution_to_djacobian_dparameter()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_djacobian_dparameter ( double *const &  parameter_pt,
Vector< double > &  dres_dparam,
DenseMatrix< double > &  djac_dparam 
)
inlinevirtual

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

Reimplemented from oomph::GeneralisedElement.

Definition at line 1309 of file navier_stokes_elements.h.

References oomph::GeneralisedElement::Dummy_matrix, and oomph::NavierStokesEquations< DIM >::fill_in_generic_dresidual_contribution_nst().

◆ fill_in_contribution_to_dresiduals_dparameter()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_dresiduals_dparameter ( double *const &  parameter_pt,
Vector< double > &  dres_dparam 
)
inlinevirtual

◆ fill_in_contribution_to_hessian_vector_products()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_hessian_vector_products ( Vector< double > const &  Y,
DenseMatrix< double > const &  C,
DenseMatrix< double > &  product 
)
protectedvirtual

Compute the hessian tensor vector products required to perform continuation of bifurcations analytically.

Reimplemented from oomph::GeneralisedElement.

Definition at line 2104 of file navier_stokes_elements.cc.

◆ fill_in_contribution_to_jacobian()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_jacobian ( Vector< double > &  residuals,
DenseMatrix< double > &  jacobian 
)
inlinevirtual

◆ fill_in_contribution_to_jacobian_and_mass_matrix()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_jacobian_and_mass_matrix ( Vector< double > &  residuals,
DenseMatrix< double > &  jacobian,
DenseMatrix< double > &  mass_matrix 
)
inlinevirtual

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

Reimplemented from oomph::GeneralisedElement.

Definition at line 1283 of file navier_stokes_elements.h.

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

◆ fill_in_contribution_to_residuals()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_residuals ( Vector< double > &  residuals)
inlinevirtual

◆ fill_in_generic_dresidual_contribution_nst()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_generic_dresidual_contribution_nst ( double *const &  parameter_pt,
Vector< double > &  dres_dparam,
DenseMatrix< double > &  djac_dparam,
DenseMatrix< double > &  dmass_matrix_dparam,
unsigned  flag 
)
protectedvirtual

Compute the derivatives of the residuals for the Navier–Stokes equations with respect to a parameter Flag=1 (or 0): do (or don't) compute the Jacobian as well. Flag=2: Fill in mass matrix too.

Compute the derivatives of the residuals for the Navier–Stokes equations with respect to a parameter; flag=2 or 1 or 0: do (or don't) compute the Jacobian and mass matrix as well.

Definition at line 2087 of file navier_stokes_elements.cc.

Referenced by oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_djacobian_and_dmass_matrix_dparameter(), oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_djacobian_dparameter(), and oomph::NavierStokesEquations< DIM >::fill_in_contribution_to_dresiduals_dparameter().

◆ fill_in_generic_pressure_advection_diffusion_contribution_nst()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_generic_pressure_advection_diffusion_contribution_nst ( Vector< double > &  residuals,
DenseMatrix< double > &  jacobian,
unsigned  flag 
)
protectedvirtual

Compute the residuals for the associated pressure advection diffusion problem. Used by the Fp preconditioner. flag=1(or 0): do (or don't) compute the Jacobian as well.

Reimplemented in oomph::RefineableNavierStokesEquations< DIM >.

Definition at line 1604 of file navier_stokes_elements.cc.

References e, i, s, and oomph::QuadTreeNames::W.

Referenced by oomph::NavierStokesEquations< DIM >::fill_in_pressure_advection_diffusion_jacobian(), and oomph::NavierStokesEquations< DIM >::fill_in_pressure_advection_diffusion_residuals().

◆ fill_in_generic_residual_contribution_nst()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_generic_residual_contribution_nst ( Vector< double > &  residuals,
DenseMatrix< double > &  jacobian,
DenseMatrix< double > &  mass_matrix,
unsigned  flag 
)
protectedvirtual

Compute the residuals for the Navier–Stokes equations. Flag=1 (or 0): do (or don't) compute the Jacobian as well. Flag=2: Fill in mass matrix too.

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

Reimplemented in oomph::RefineableNavierStokesEquations< DIM >.

Definition at line 1774 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

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

◆ fill_in_pressure_advection_diffusion_jacobian()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_pressure_advection_diffusion_jacobian ( Vector< double > &  residuals,
DenseMatrix< double > &  jacobian 
)
inlinevirtual

Compute the residuals and Jacobian for the associated pressure advection diffusion problem. Used by the Fp preconditioner.

Implements oomph::TemplateFreeNavierStokesEquationsBase.

Definition at line 1348 of file navier_stokes_elements.h.

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

◆ fill_in_pressure_advection_diffusion_residuals()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::fill_in_pressure_advection_diffusion_residuals ( Vector< double > &  residuals)
inlinevirtual

Compute the residuals for the associated pressure advection diffusion problem. Used by the Fp preconditioner.

Implements oomph::TemplateFreeNavierStokesEquationsBase.

Definition at line 1339 of file navier_stokes_elements.h.

References oomph::GeneralisedElement::Dummy_matrix, and oomph::NavierStokesEquations< DIM >::fill_in_generic_pressure_advection_diffusion_contribution_nst().

◆ fix_pressure()

template<unsigned DIM>
virtual void oomph::NavierStokesEquations< DIM >::fix_pressure ( const unsigned &  p_dof,
const double &  p_value 
)
pure virtual

◆ full_output() [1/2]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::full_output ( std::ostream &  outfile)
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 1180 of file navier_stokes_elements.h.

Referenced by oomph::QCrouzeixRaviartElement< DIM >::full_output(), and oomph::TCrouzeixRaviartElement< DIM >::full_output().

◆ full_output() [2/2]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::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 847 of file navier_stokes_elements.cc.

References i, and s.

◆ g()

template<unsigned DIM>
const Vector<double>& oomph::NavierStokesEquations< DIM >::g ( ) const
inline

◆ g_pt()

template<unsigned DIM>
Vector<double>*& oomph::NavierStokesEquations< DIM >::g_pt ( )
inline

Pointer to Vector of gravitational components.

Definition at line 771 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::G_pt.

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

◆ get_body_force_gradient_nst()

template<unsigned DIM>
virtual void oomph::NavierStokesEquations< DIM >::get_body_force_gradient_nst ( const double &  time,
const unsigned &  ipt,
const Vector< double > &  s,
const Vector< double > &  x,
DenseMatrix< double > &  d_body_force_dx 
)
inlineprotectedvirtual

Get gradient of body force term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations. Computed via function pointer (if set) or by finite differencing (default)

Definition at line 544 of file navier_stokes_elements.h.

References oomph::GeneralisedElement::Default_fd_jacobian_step, oomph::NavierStokesEquations< DIM >::get_body_force_nst(), i, and s.

◆ get_body_force_nst()

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

Calculate the body force at a given time and local and/or Eulerian position. This function is virtual so that it can be overloaded in multi-physics elements where the body force might depend on another variable.

Reimplemented in oomph::RefineableBuoyantQCrouzeixRaviartElement< DIM >, and oomph::BuoyantQCrouzeixRaviartElement< DIM >.

Definition at line 517 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Body_force_fct_pt, and i.

Referenced by oomph::NavierStokesEquations< DIM >::get_body_force_gradient_nst().

◆ get_dresidual_dnodal_coordinates()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::get_dresidual_dnodal_coordinates ( RankThreeTensor< double > &  dresidual_dnodal_coordinates)
virtual

Compute derivatives of elemental residual vector with respect to nodal coordinates. Overwrites default implementation in FiniteElement base class. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij}.

Compute derivatives of elemental residual vector with respect to nodal coordinates. dresidual_dnodal_coordinates(l,i,j) = d res(l) / dX_{ij} Overloads the FD-based version in the FE base class.

Reimplemented from oomph::FiniteElement.

Reimplemented in oomph::RefineableNavierStokesEquations< DIM >.

Definition at line 2123 of file navier_stokes_elements.cc.

References oomph::GeneralisedElement::Default_fd_jacobian_step, oomph::Node::has_auxiliary_node_update_fct_pt(), i, oomph::Node::perform_auxiliary_node_update_fct(), s, oomph::Data::value_pt(), and oomph::Node::x().

◆ get_load()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::get_load ( const Vector< double > &  s,
const Vector< double > &  N,
Vector< double > &  load 
)
inlinevirtual

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

Implements oomph::FSIFluidElement.

Definition at line 992 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::get_traction(), oomph::QuadTreeNames::N, and s.

◆ get_pressure_and_velocity_mass_matrix_diagonal()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::get_pressure_and_velocity_mass_matrix_diagonal ( Vector< double > &  press_mass_diag,
Vector< double > &  veloc_mass_diag,
const unsigned &  which_one = 0 
)
virtual

Compute the diagonal of the velocity/pressure mass matrices. If which one=0, both are computed, otherwise only the pressure (which_one=1) or the velocity mass matrix (which_one=2 – the LSC version of the preconditioner only needs that one)

Implements oomph::TemplateFreeNavierStokesEquationsBase.

Reimplemented in oomph::RefineableNavierStokesEquations< DIM >.

Definition at line 70 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

◆ get_source_gradient_nst()

template<unsigned DIM>
virtual void oomph::NavierStokesEquations< DIM >::get_source_gradient_nst ( const double &  time,
const unsigned &  ipt,
const Vector< double > &  x,
Vector< double > &  gradient 
)
inlineprotectedvirtual

Get gradient of source term at (Eulerian) position x. This function is virtual to allow overloading in multi-physics problems where the strength of the source function might be determined by another system of equations. Computed via function pointer (if set) or by finite differencing (default)

Definition at line 607 of file navier_stokes_elements.h.

References oomph::GeneralisedElement::Default_fd_jacobian_step, oomph::NavierStokesEquations< DIM >::get_source_nst(), and i.

◆ get_source_nst()

template<unsigned DIM>
virtual double oomph::NavierStokesEquations< DIM >::get_source_nst ( const double &  time,
const unsigned &  ipt,
const Vector< double > &  x 
)
inlineprotectedvirtual

Calculate the source fct at given time and Eulerian position.

Definition at line 585 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Source_fct_pt.

Referenced by oomph::NavierStokesEquations< DIM >::get_source_gradient_nst().

◆ get_traction() [1/2]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::get_traction ( const Vector< double > &  s,
const Vector< double > &  N,
Vector< double > &  traction 
)

Compute traction (on the viscous scale) exerted onto the fluid at local coordinate s. N has to be outer unit normal to the fluid.

Definition at line 1098 of file navier_stokes_elements.cc.

References i, oomph::QuadTreeNames::N, and s.

Referenced by oomph::NavierStokesEquations< DIM >::get_load().

◆ get_traction() [2/2]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::get_traction ( const Vector< double > &  s,
const Vector< double > &  N,
Vector< double > &  traction_p,
Vector< double > &  traction_visc_n,
Vector< double > &  traction_visc_t 
)

Compute traction (on the viscous scale) exerted onto the fluid at local coordinate s, decomposed into pressure and normal and tangential viscous components. N has to be outer unit normal to the fluid.

Definition at line 1127 of file navier_stokes_elements.cc.

References i, oomph::QuadTreeNames::N, and s.

◆ get_vorticity() [1/5]

void oomph::NavierStokesEquations< 2 >::get_vorticity ( const Vector< double > &  s,
double &  vorticity 
) const

Compute vorticity vector at local coordinate s and return the one and only component of vorticity vector (only makes sense when solving the 2D N.St. equations)

Definition at line 1325 of file navier_stokes_elements.cc.

References s.

◆ get_vorticity() [2/5]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::get_vorticity ( const Vector< double > &  s,
double &  vorticity 
) const

Compute the scalar vorticity at local coordinate s (2D)

◆ get_vorticity() [3/5]

void oomph::NavierStokesEquations< 2 >::get_vorticity ( const Vector< double > &  s,
Vector< double > &  vorticity 
) const

Compute 2D vorticity vector at local coordinate s (return in one and only component of vorticity vector.

Definition at line 1256 of file navier_stokes_elements.cc.

References i, and s.

◆ get_vorticity() [4/5]

void oomph::NavierStokesEquations< 3 >::get_vorticity ( const Vector< double > &  s,
Vector< double > &  vorticity 
) const

Compute 3D vorticity vector at local coordinate s.

Definition at line 1343 of file navier_stokes_elements.cc.

References i, and s.

◆ get_vorticity() [5/5]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::get_vorticity ( const Vector< double > &  s,
Vector< double > &  vorticity 
) const

Compute the vorticity vector at local coordinate s.

◆ interpolated_dudx_nst()

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::interpolated_dudx_nst ( const Vector< double > &  s,
const unsigned &  i,
const unsigned &  j 
) const
inline

◆ interpolated_p_nst() [1/2]

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::interpolated_p_nst ( const unsigned &  t,
const Vector< double > &  s 
) const
inline

Return FE interpolated pressure at local coordinate s at time level t.

Definition at line 1661 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::npres_nst(), oomph::NavierStokesEquations< DIM >::p_nst(), oomph::NavierStokesEquations< DIM >::pshape_nst(), s, and t.

◆ interpolated_p_nst() [2/2]

template<unsigned DIM>
virtual double oomph::NavierStokesEquations< DIM >::interpolated_p_nst ( const Vector< double > &  s) const
inlinevirtual

◆ interpolated_u_nst() [1/3]

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::interpolated_u_nst ( const unsigned &  t,
const Vector< double > &  s,
const unsigned &  i 
) const
inline

Return FE interpolated velocity u[i] at local coordinate s at time level t (t=0: present; t>0: history)

Definition at line 1555 of file navier_stokes_elements.h.

References i, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), t, and oomph::NavierStokesEquations< DIM >::u_index_nst().

◆ interpolated_u_nst() [2/3]

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::interpolated_u_nst ( const Vector< double > &  s,
const unsigned &  i 
) const
inline

Return FE interpolated velocity u[i] at local coordinate s.

Definition at line 1530 of file navier_stokes_elements.h.

References i, oomph::FiniteElement::nnode(), oomph::FiniteElement::nodal_value(), s, oomph::FiniteElement::shape(), and oomph::NavierStokesEquations< DIM >::u_index_nst().

◆ interpolated_u_nst() [3/3]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::interpolated_u_nst ( const Vector< double > &  s,
Vector< double > &  veloc 
) const
inline

◆ kin_energy()

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::kin_energy

Get integral of kinetic energy over element.

Get integral of kinetic energy over element: Note that this is the "raw" kinetic energy in the sense that the density ratio has not been included. In problems with two or more fluids the user will have to remember to premultiply certain elements by the appropriate density ratio.

Definition at line 1416 of file navier_stokes_elements.cc.

References i, and s.

◆ n_u_nst()

template<unsigned DIM>
unsigned oomph::NavierStokesEquations< DIM >::n_u_nst ( ) const
inline

Return the number of velocity components Used in FluidInterfaceElements.

Definition at line 873 of file navier_stokes_elements.h.

◆ npres_nst()

template<unsigned DIM>
virtual unsigned oomph::NavierStokesEquations< DIM >::npres_nst ( ) const
pure virtual

◆ nscalar_paraview()

template<unsigned DIM>
unsigned oomph::NavierStokesEquations< DIM >::nscalar_paraview ( ) const
inlinevirtual

Number of scalars/fields output by this element. Reimplements broken virtual function in base class.

Reimplemented from oomph::FiniteElement.

Definition at line 1014 of file navier_stokes_elements.h.

◆ output() [1/4]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::output ( FILE *  file_pt)
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::TTaylorHoodElement< DIM >, oomph::TCrouzeixRaviartElement< DIM >, oomph::QTaylorHoodElement< DIM >, and oomph::QCrouzeixRaviartElement< DIM >.

Definition at line 1167 of file navier_stokes_elements.h.

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

◆ output() [2/4]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::output ( FILE *  file_pt,
const unsigned &  nplot 
)
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::QTaylorHoodElement< DIM >, oomph::QCrouzeixRaviartElement< DIM >, oomph::TTaylorHoodElement< DIM >, and oomph::TCrouzeixRaviartElement< DIM >.

Definition at line 803 of file navier_stokes_elements.cc.

References i, and s.

◆ output() [3/4]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::output ( std::ostream &  outfile)
inlinevirtual

◆ output() [4/4]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::output ( std::ostream &  outfile,
const unsigned &  nplot 
)
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::TTaylorHoodElement< DIM >, oomph::TCrouzeixRaviartElement< DIM >, oomph::QTaylorHoodElement< DIM >, and oomph::QCrouzeixRaviartElement< DIM >.

Definition at line 756 of file navier_stokes_elements.cc.

References i, and s.

◆ output_fct() [1/2]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::output_fct ( std::ostream &  outfile,
const unsigned &  nplot,
const double &  time,
FiniteElement::UnsteadyExactSolutionFctPt  exact_soln_pt 
)
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 629 of file navier_stokes_elements.cc.

References i, and s.

◆ output_fct() [2/2]

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::output_fct ( std::ostream &  outfile,
const unsigned &  nplot,
FiniteElement::SteadyExactSolutionFctPt  exact_soln_pt 
)
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 573 of file navier_stokes_elements.cc.

References i, and s.

◆ output_pressure_advection_diffusion_robin_elements()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::output_pressure_advection_diffusion_robin_elements ( std::ostream &  outfile)
inline

Output the FaceElements that apply the Robin boundary condition to the pressure advection diffusion problem required by Fp preconditioner.

Definition at line 1449 of file navier_stokes_elements.h.

References e, i, oomph::FiniteElement::integral_pt(), oomph::FaceElement::interpolated_x(), oomph::Integral::knot(), oomph::Integral::nweight(), oomph::FaceElement::outer_unit_normal(), oomph::NavierStokesEquations< DIM >::Pressure_advection_diffusion_robin_element_pt, and s.

◆ output_veloc()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::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 687 of file navier_stokes_elements.cc.

References i, s, oomph::OneDimLagrange::shape(), and t.

◆ output_vorticity()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::output_vorticity ( std::ostream &  outfile,
const unsigned &  nplot 
)

Output function: x,y,[z], [omega_x,omega_y,[and/or omega_z]] in tecplot format. nplot points in each coordinate direction.

Output function for vorticity. x,y,[z],[omega_x,omega_y,[and/or omega_z]] in tecplot format. Specified number of plot points in each coordinate direction.

Definition at line 978 of file navier_stokes_elements.cc.

References i, s, and oomph::Global_string_for_annotation::string().

◆ p_nodal_index_nst()

template<unsigned DIM>
virtual int oomph::NavierStokesEquations< DIM >::p_nodal_index_nst ( ) const
inlinevirtual

Return the index at which the pressure is stored if it is stored at the nodes. If not stored at the nodes this will return a negative number.

Implements oomph::TemplateFreeNavierStokesEquationsBase.

Reimplemented in oomph::TTaylorHoodElement< DIM >, and oomph::QTaylorHoodElement< DIM >.

Definition at line 936 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Pressure_not_stored_at_node.

Referenced by oomph::NavierStokesEquations< DIM >::pin_all_non_pressure_dofs().

◆ p_nst() [1/2]

template<unsigned DIM>
virtual double oomph::NavierStokesEquations< DIM >::p_nst ( const unsigned &  n_p) const
pure virtual

◆ p_nst() [2/2]

template<unsigned DIM>
virtual double oomph::NavierStokesEquations< DIM >::p_nst ( const unsigned &  t,
const unsigned &  n_p 
) const
pure virtual

◆ pin_all_non_pressure_dofs()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::pin_all_non_pressure_dofs ( std::map< Data *, std::vector< int >> &  eqn_number_backup)
inlinevirtual

◆ pinned_fp_pressure_eqn()

template<unsigned DIM>
int& oomph::NavierStokesEquations< DIM >::pinned_fp_pressure_eqn ( )
inlinevirtual

Global eqn number of pressure dof that's pinned in pressure adv diff problem.

Implements oomph::TemplateFreeNavierStokesEquationsBase.

Definition at line 817 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Pinned_fp_pressure_eqn.

◆ point_output_data()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::point_output_data ( const Vector< double > &  s,
Vector< double > &  data 
)
inlinevirtual

Output solution in data vector at local cordinates s: x,y [,z], u,v,[w], p.

Reimplemented from oomph::FiniteElement.

Definition at line 1717 of file navier_stokes_elements.h.

References oomph::FiniteElement::dim(), i, oomph::NavierStokesEquations< DIM >::interpolated_p_nst(), oomph::NavierStokesEquations< DIM >::interpolated_u_nst(), oomph::FiniteElement::interpolated_x(), and s.

◆ pressure_integral()

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::pressure_integral

Integral of pressure over element.

Return pressure integrated over the element.

Definition at line 1558 of file navier_stokes_elements.cc.

References i, s, and oomph::QuadTreeNames::W.

◆ pshape_nst() [1/2]

template<unsigned DIM>
virtual void oomph::NavierStokesEquations< DIM >::pshape_nst ( const Vector< double > &  s,
Shape psi 
) const
pure virtual

◆ pshape_nst() [2/2]

template<unsigned DIM>
virtual void oomph::NavierStokesEquations< DIM >::pshape_nst ( const Vector< double > &  s,
Shape psi,
Shape test 
) const
pure virtual

◆ re()

template<unsigned DIM>
const double& oomph::NavierStokesEquations< DIM >::re ( ) const
inline

Reynolds number.

Definition at line 703 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Re_pt.

◆ re_invfr()

template<unsigned DIM>
const double& oomph::NavierStokesEquations< DIM >::re_invfr ( ) const
inline

Global inverse Froude number.

Definition at line 753 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::ReInvFr_pt.

◆ re_invfr_pt()

template<unsigned DIM>
double*& oomph::NavierStokesEquations< DIM >::re_invfr_pt ( )
inline

Pointer to global inverse Froude number.

Definition at line 759 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::ReInvFr_pt.

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

◆ re_pt()

template<unsigned DIM>
double*& oomph::NavierStokesEquations< DIM >::re_pt ( )
inline

Pointer to Reynolds number.

Definition at line 715 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Re_pt.

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

◆ re_st()

template<unsigned DIM>
const double& oomph::NavierStokesEquations< DIM >::re_st ( ) const
inline

Product of Reynolds and Strouhal number (=Womersley number)

Definition at line 709 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::ReSt_pt.

◆ re_st_pt()

template<unsigned DIM>
double*& oomph::NavierStokesEquations< DIM >::re_st_pt ( )
inline

Pointer to product of Reynolds and Strouhal number (=Womersley number)

Definition at line 721 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::ReSt_pt.

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

◆ scalar_name_paraview()

template<unsigned DIM>
std::string oomph::NavierStokesEquations< DIM >::scalar_name_paraview ( const unsigned &  i) const
inlinevirtual

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

Reimplemented from oomph::FiniteElement.

Definition at line 1127 of file navier_stokes_elements.h.

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

◆ scalar_value_fct_paraview()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::scalar_value_fct_paraview ( std::ofstream &  file_out,
const unsigned &  i,
const unsigned &  nplot,
const double &  time,
FiniteElement::UnsteadyExactSolutionFctPt  exact_soln_pt 
) const
inlinevirtual

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

Reimplemented from oomph::FiniteElement.

Definition at line 1067 of file navier_stokes_elements.h.

References oomph::FiniteElement::get_s_plot(), i, oomph::FiniteElement::interpolated_x(), oomph::FiniteElement::nplot_points_paraview(), and s.

◆ scalar_value_paraview()

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

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

Reimplemented from oomph::FiniteElement.

Definition at line 1021 of file navier_stokes_elements.h.

References oomph::FiniteElement::get_s_plot(), i, oomph::NavierStokesEquations< DIM >::interpolated_p_nst(), oomph::NavierStokesEquations< DIM >::interpolated_u_nst(), oomph::FiniteElement::nplot_points_paraview(), and s.

◆ source_fct_for_pressure_adv_diff() [1/2]

template<unsigned DIM>
NavierStokesPressureAdvDiffSourceFctPt& oomph::NavierStokesEquations< DIM >::source_fct_for_pressure_adv_diff ( )
inline

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

Definition at line 802 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Press_adv_diff_source_fct_pt.

◆ source_fct_for_pressure_adv_diff() [2/2]

template<unsigned DIM>
NavierStokesPressureAdvDiffSourceFctPt oomph::NavierStokesEquations< DIM >::source_fct_for_pressure_adv_diff ( ) const
inline

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

Definition at line 809 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Press_adv_diff_source_fct_pt.

◆ source_fct_pt() [1/2]

template<unsigned DIM>
NavierStokesSourceFctPt& oomph::NavierStokesEquations< DIM >::source_fct_pt ( )
inline

Access function for the source-function pointer.

Definition at line 789 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Source_fct_pt.

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

◆ source_fct_pt() [2/2]

template<unsigned DIM>
NavierStokesSourceFctPt oomph::NavierStokesEquations< DIM >::source_fct_pt ( ) const
inline

Access function for the source-function pointer. Const version.

Definition at line 795 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Source_fct_pt.

◆ strain_rate()

template<unsigned DIM>
void oomph::NavierStokesEquations< DIM >::strain_rate ( const Vector< double > &  s,
DenseMatrix< double > &  strain_rate 
) const

Strain-rate tensor: 1/2 (du_i/dx_j + du_j/dx_i)

Get strain-rate tensor: 1/2 (du_i/dx_j + du_j/dx_i)

Definition at line 1185 of file navier_stokes_elements.cc.

References i, oomph::DenseMatrix< T >::ncol(), oomph::DenseMatrix< T >::nrow(), and s.

Referenced by oomph::RefineableNavierStokesEquations< DIM >::get_Z2_flux(), oomph::TCrouzeixRaviartElement< DIM >::get_Z2_flux(), and oomph::TTaylorHoodElement< DIM >::get_Z2_flux().

◆ u_index_nst()

template<unsigned DIM>
virtual unsigned oomph::NavierStokesEquations< DIM >::u_index_nst ( const unsigned &  i) const
inlinevirtual

◆ u_nst() [1/2]

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::u_nst ( const unsigned &  n,
const unsigned &  i 
) const
inline

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

Definition at line 848 of file navier_stokes_elements.h.

References i, oomph::FiniteElement::nodal_value(), and oomph::NavierStokesEquations< DIM >::u_index_nst().

◆ u_nst() [2/2]

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::u_nst ( const unsigned &  t,
const unsigned &  n,
const unsigned &  i 
) const
inline

Velocity i at local node n at timestep t (t=0: present; t>0: previous). Uses suitably interpolated value for hanging nodes.

Definition at line 855 of file navier_stokes_elements.h.

References i, oomph::FiniteElement::nodal_value(), t, and oomph::NavierStokesEquations< DIM >::u_index_nst().

◆ viscosity_ratio()

template<unsigned DIM>
const double& oomph::NavierStokesEquations< DIM >::viscosity_ratio ( ) const
inline

Viscosity ratio for element: Element's viscosity relative to the viscosity used in the definition of the Reynolds number.

Definition at line 728 of file navier_stokes_elements.h.

References oomph::NavierStokesEquations< DIM >::Viscosity_Ratio_pt.

◆ viscosity_ratio_pt()

template<unsigned DIM>
double*& oomph::NavierStokesEquations< DIM >::viscosity_ratio_pt ( )
inline

Member Data Documentation

◆ ALE_is_disabled

template<unsigned DIM>
bool oomph::NavierStokesEquations< DIM >::ALE_is_disabled
protected

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

Definition at line 470 of file navier_stokes_elements.h.

Referenced by oomph::NavierStokesEquations< DIM >::disable_ALE(), oomph::NavierStokesEquations< DIM >::enable_ALE(), and oomph::RefineableNavierStokesEquations< DIM >::further_build().

◆ Body_force_fct_pt

template<unsigned DIM>
NavierStokesBodyForceFctPt oomph::NavierStokesEquations< DIM >::Body_force_fct_pt
protected

◆ Default_Gravity_vector

template<unsigned DIM>
Vector< double > oomph::NavierStokesEquations< DIM >::Default_Gravity_vector
staticprivate

Static default value for the gravity vector.

Navier-Stokes equations default gravity vector.

Definition at line 429 of file navier_stokes_elements.h.

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

◆ Default_Physical_Constant_Value

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::Default_Physical_Constant_Value = 0.0
staticprivate

Static default value for the physical constants (all initialised to zero)

Navier–Stokes equations static data.

Definition at line 422 of file navier_stokes_elements.h.

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

◆ Default_Physical_Ratio_Value

template<unsigned DIM>
double oomph::NavierStokesEquations< DIM >::Default_Physical_Ratio_Value = 1.0
staticprivate

Static default value for the physical ratios (all are initialised to one)

Navier–Stokes equations static data.

Definition at line 426 of file navier_stokes_elements.h.

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

◆ Density_Ratio_pt

template<unsigned DIM>
double* oomph::NavierStokesEquations< DIM >::Density_Ratio_pt
protected

◆ G_pt

template<unsigned DIM>
Vector<double>* oomph::NavierStokesEquations< DIM >::G_pt
protected

◆ Gamma

template<unsigned DIM>
Vector< double > oomph::NavierStokesEquations< DIM >::Gamma
static

Vector to decide whether the stress-divergence form is used or not.

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

Navier–Stokes equations static data

Definition at line 698 of file navier_stokes_elements.h.

◆ Pinned_fp_pressure_eqn

template<unsigned DIM>
int oomph::NavierStokesEquations< DIM >::Pinned_fp_pressure_eqn
protected

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

Definition at line 479 of file navier_stokes_elements.h.

Referenced by oomph::NavierStokesEquations< DIM >::pinned_fp_pressure_eqn().

◆ Press_adv_diff_source_fct_pt

template<unsigned DIM>
NavierStokesPressureAdvDiffSourceFctPt oomph::NavierStokesEquations< DIM >::Press_adv_diff_source_fct_pt
protected

Pointer to source function pressure advection diffusion equation (only to be used during validation)

Definition at line 465 of file navier_stokes_elements.h.

Referenced by oomph::NavierStokesEquations< DIM >::source_fct_for_pressure_adv_diff().

◆ Pressure_advection_diffusion_robin_element_pt

template<unsigned DIM>
Vector<FpPressureAdvDiffRobinBCElementBase*> oomph::NavierStokesEquations< DIM >::Pressure_advection_diffusion_robin_element_pt
protected

◆ Pressure_not_stored_at_node

template<unsigned DIM>
int oomph::NavierStokesEquations< DIM >::Pressure_not_stored_at_node = -100
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 418 of file navier_stokes_elements.h.

Referenced by oomph::NavierStokesEquations< DIM >::p_nodal_index_nst().

◆ Re_pt

template<unsigned DIM>
double* oomph::NavierStokesEquations< DIM >::Re_pt
protected

◆ ReInvFr_pt

template<unsigned DIM>
double* oomph::NavierStokesEquations< DIM >::ReInvFr_pt
protected

◆ ReSt_pt

template<unsigned DIM>
double* oomph::NavierStokesEquations< DIM >::ReSt_pt
protected

◆ Source_fct_pt

template<unsigned DIM>
NavierStokesSourceFctPt oomph::NavierStokesEquations< DIM >::Source_fct_pt
protected

◆ Viscosity_Ratio_pt

template<unsigned DIM>
double* oomph::NavierStokesEquations< DIM >::Viscosity_Ratio_pt
protected

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