#include <biharmonic_problem.h>

Inheritance diagram for oomph::BiharmonicFluidProblem< DIM >:

Public Types
typedef void(*	FluidBCFctPt) (const double &s, Vector< double > &u)

Public Types inherited from oomph::Problem
typedef void(*	SpatialErrorEstimatorFctPt) (Mesh *&mesh_pt, Vector< double > &elemental_error)
	Function pointer for spatial error estimator. More...

typedef void(*	SpatialErrorEstimatorWithDocFctPt) (Mesh *&mesh_pt, Vector< double > &elemental_error, DocInfo &doc_info)
	Function pointer for spatial error estimator with doc. More...

Public Member Functions
	BiharmonicFluidProblem ()
	constructor More...

void	actions_before_newton_solve ()
	actions before solve, performs self test More...

void	actions_after_newton_solve ()
	action after solve More...

void	doc_solution (DocInfo &doc_info, FiniteElement::SteadyExactSolutionFctPt exact_soln_pt=0)

Public Member Functions inherited from oomph::Problem
virtual void	debug_hook_fct (const unsigned &i)

void	set_analytic_dparameter (double *const &parameter_pt)

void	unset_analytic_dparameter (double *const &parameter_pt)

bool	is_dparameter_calculated_analytically (double *const &parameter_pt)

void	set_analytic_hessian_products ()

void	unset_analytic_hessian_products ()

bool	are_hessian_products_calculated_analytically ()

void	set_pinned_values_to_zero ()

bool	distributed () const

virtual void	actions_before_adapt ()

virtual void	actions_after_adapt ()
	Actions that are to be performed after a mesh adaptation. More...

OomphCommunicator *	communicator_pt ()
	access function to the oomph-lib communicator More...

const OomphCommunicator *	communicator_pt () const
	access function to the oomph-lib communicator, const version More...

	Problem ()

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

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

virtual	~Problem ()
	Virtual destructor to clean up memory. More...

Mesh *&	mesh_pt ()
	Return a pointer to the global mesh. More...

Mesh *const &	mesh_pt () const
	Return a pointer to the global mesh (const version) More...

Mesh *&	mesh_pt (const unsigned &imesh)

Mesh *const &	mesh_pt (const unsigned &imesh) const
	Return a pointer to the i-th submesh (const version) More...

unsigned	nsub_mesh () const
	Return number of submeshes. More...

unsigned	add_sub_mesh (Mesh *const &mesh_pt)

void	flush_sub_meshes ()

void	build_global_mesh ()

void	rebuild_global_mesh ()

LinearSolver *&	linear_solver_pt ()
	Return a pointer to the linear solver object. More...

LinearSolver *const &	linear_solver_pt () const
	Return a pointer to the linear solver object (const version) More...

LinearSolver *&	mass_matrix_solver_for_explicit_timestepper_pt ()

LinearSolver *	mass_matrix_solver_for_explicit_timestepper_pt () const

EigenSolver *&	eigen_solver_pt ()
	Return a pointer to the eigen solver object. More...

EigenSolver *const &	eigen_solver_pt () const
	Return a pointer to the eigen solver object (const version) More...

Time *&	time_pt ()
	Return a pointer to the global time object. More...

Time *	time_pt () const
	Return a pointer to the global time object (const version). More...

double &	time ()
	Return the current value of continuous time. More...

double	time () const
	Return the current value of continuous time (const version) More...

TimeStepper *&	time_stepper_pt ()

const TimeStepper *	time_stepper_pt () const

TimeStepper *&	time_stepper_pt (const unsigned &i)
	Return a pointer to the i-th timestepper. More...

ExplicitTimeStepper *&	explicit_time_stepper_pt ()
	Return a pointer to the explicit timestepper. More...

unsigned long	set_timestepper_for_all_data (TimeStepper *const &time_stepper_pt, const bool &preserve_existing_data=false)

virtual void	shift_time_values ()
	Shift all values along to prepare for next timestep. More...

AssemblyHandler *&	assembly_handler_pt ()
	Return a pointer to the assembly handler object. More...

AssemblyHandler *const &	assembly_handler_pt () const
	Return a pointer to the assembly handler object (const version) More...

double &	minimum_dt ()
	Access function to min timestep in adaptive timestepping. More...

double &	maximum_dt ()
	Access function to max timestep in adaptive timestepping. More...

unsigned &	max_newton_iterations ()
	Access function to max Newton iterations before giving up. More...

void	problem_is_nonlinear (const bool &prob_lin)
	Access function to Problem_is_nonlinear. More...

double &	max_residuals ()

bool &	time_adaptive_newton_crash_on_solve_fail ()
	Access function for Time_adaptive_newton_crash_on_solve_fail. More...

double &	newton_solver_tolerance ()

void	add_time_stepper_pt (TimeStepper *const &time_stepper_pt)

void	set_explicit_time_stepper_pt (ExplicitTimeStepper *const &explicit_time_stepper_pt)

void	initialise_dt (const double &dt)

void	initialise_dt (const Vector< double > &dt)

Data *&	global_data_pt (const unsigned &i)
	Return a pointer to the the i-th global data object. More...

void	add_global_data (Data *const &global_data_pt)

void	flush_global_data ()

LinearAlgebraDistribution *const &	dof_distribution_pt () const
	Return the pointer to the dof distribution (read-only) More...

unsigned long	ndof () const
	Return the number of dofs. More...

unsigned	ntime_stepper () const
	Return the number of time steppers. More...

unsigned	nglobal_data () const
	Return the number of global data values. More...

unsigned	self_test ()
	Self-test: Check meshes and global data. Return 0 for OK. More...

void	enable_store_local_dof_pt_in_elements ()

void	disable_store_local_dof_pt_in_elements ()

unsigned long	assign_eqn_numbers (const bool &assign_local_eqn_numbers=true)

void	describe_dofs (std::ostream &out= *(oomph_info.stream_pt())) const

void	enable_discontinuous_formulation ()

void	disable_discontinuous_formulation ()

void	get_dofs (DoubleVector &dofs) const

void	get_dofs (const unsigned &t, DoubleVector &dofs) const
	Return vector of the t'th history value of all dofs. More...

void	set_dofs (const DoubleVector &dofs)
	Set the values of the dofs. More...

void	set_dofs (const unsigned &t, DoubleVector &dofs)
	Set the history values of the dofs. More...

void	set_dofs (const unsigned &t, Vector< double * > &dof_pt)

void	add_to_dofs (const double &lambda, const DoubleVector &increment_dofs)
	Add lambda x incremenet_dofs[l] to the l-th dof. More...

double *	global_dof_pt (const unsigned &i)

double &	dof (const unsigned &i)
	i-th dof in the problem More...

double	dof (const unsigned &i) const
	i-th dof in the problem (const version) More...

double *&	dof_pt (const unsigned &i)
	Pointer to i-th dof in the problem. More...

double *	dof_pt (const unsigned &i) const
	Pointer to i-th dof in the problem (const version) More...

virtual void	get_inverse_mass_matrix_times_residuals (DoubleVector &Mres)

virtual void	get_dvaluesdt (DoubleVector &f)

virtual void	get_residuals (DoubleVector &residuals)
	Get the total residuals Vector for the problem. More...

virtual void	get_jacobian (DoubleVector &residuals, DenseDoubleMatrix &jacobian)

virtual void	get_jacobian (DoubleVector &residuals, CRDoubleMatrix &jacobian)

virtual void	get_jacobian (DoubleVector &residuals, CCDoubleMatrix &jacobian)

virtual void	get_jacobian (DoubleVector &residuals, SumOfMatrices &jacobian)

void	get_fd_jacobian (DoubleVector &residuals, DenseMatrix< double > &jacobian)
	Get the full Jacobian by finite differencing. More...

void	get_derivative_wrt_global_parameter (double *const &parameter_pt, DoubleVector &result)

void	get_hessian_vector_products (DoubleVectorWithHaloEntries const &Y, Vector< DoubleVectorWithHaloEntries > const &C, Vector< DoubleVectorWithHaloEntries > &product)

void	solve_eigenproblem (const unsigned &n_eval, Vector< std::complex< double >> &eigenvalue, Vector< DoubleVector > &eigenvector, const bool &steady=true)
	Solve the eigenproblem. More...

void	solve_eigenproblem (const unsigned &n_eval, Vector< std::complex< double >> &eigenvalue, const bool &steady=true)

virtual void	get_eigenproblem_matrices (CRDoubleMatrix &mass_matrix, CRDoubleMatrix &main_matrix, const double &shift=0.0)

void	assign_eigenvector_to_dofs (DoubleVector &eigenvector)
	Assign the eigenvector passed to the function to the dofs. More...

void	add_eigenvector_to_dofs (const double &epsilon, const DoubleVector &eigenvector)

void	store_current_dof_values ()
	Store the current values of the degrees of freedom. More...

void	restore_dof_values ()
	Restore the stored values of the degrees of freedom. More...

void	enable_jacobian_reuse ()

void	disable_jacobian_reuse ()
	Disable recycling of Jacobian in Newton iteration. More...

bool	jacobian_reuse_is_enabled ()
	Is recycling of Jacobian in Newton iteration enabled? More...

bool &	use_predictor_values_as_initial_guess ()

void	newton_solve ()
	Use Newton method to solve the problem. More...

void	enable_globally_convergent_newton_method ()
	enable globally convergent Newton method More...

void	disable_globally_convergent_newton_method ()
	disable globally convergent Newton method More...

void	newton_solve (unsigned const &max_adapt)

void	steady_newton_solve (unsigned const &max_adapt=0)

void	copy (Problem *orig_problem_pt)

virtual Problem *	make_copy ()

virtual void	read (std::ifstream &restart_file, bool &unsteady_restart)

virtual void	read (std::ifstream &restart_file)

virtual void	dump (std::ofstream &dump_file) const

void	dump (const std::string &dump_file_name) const

void	delete_all_external_storage ()

virtual void	symmetrise_eigenfunction_for_adaptive_pitchfork_tracking ()

double *	bifurcation_parameter_pt () const

void	get_bifurcation_eigenfunction (Vector< DoubleVector > &eigenfunction)

void	activate_fold_tracking (double *const &parameter_pt, const bool &block_solve=true)

void	activate_bifurcation_tracking (double *const &parameter_pt, const DoubleVector &eigenvector, const bool &block_solve=true)

void	activate_bifurcation_tracking (double *const &parameter_pt, const DoubleVector &eigenvector, const DoubleVector &normalisation, const bool &block_solve=true)

void	activate_pitchfork_tracking (double *const &parameter_pt, const DoubleVector &symmetry_vector, const bool &block_solve=true)

void	activate_hopf_tracking (double *const &parameter_pt, const bool &block_solve=true)

void	activate_hopf_tracking (double *const &parameter_pt, const double &omega, const DoubleVector &null_real, const DoubleVector &null_imag, const bool &block_solve=true)

void	deactivate_bifurcation_tracking ()

void	reset_assembly_handler_to_default ()
	Reset the system to the standard non-augemented state. More...

double	arc_length_step_solve (double *const &parameter_pt, const double &ds, const unsigned &max_adapt=0)

double	arc_length_step_solve (Data *const &data_pt, const unsigned &data_index, const double &ds, const unsigned &max_adapt=0)

void	reset_arc_length_parameters ()

int &	sign_of_jacobian ()

void	explicit_timestep (const double &dt, const bool &shift_values=true)
	Take an explicit timestep of size dt. More...

void	unsteady_newton_solve (const double &dt)

void	unsteady_newton_solve (const double &dt, const bool &shift_values)

void	unsteady_newton_solve (const double &dt, const unsigned &max_adapt, const bool &first, const bool &shift=true)

double	doubly_adaptive_unsteady_newton_solve (const double &dt, const double &epsilon, const unsigned &max_adapt, const bool &first, const bool &shift=true)

double	doubly_adaptive_unsteady_newton_solve (const double &dt, const double &epsilon, const unsigned &max_adapt, const unsigned &suppress_resolve_after_spatial_adapt_flag, const bool &first, const bool &shift=true)

double	adaptive_unsteady_newton_solve (const double &dt_desired, const double &epsilon)

double	adaptive_unsteady_newton_solve (const double &dt_desired, const double &epsilon, const bool &shift_values)

void	assign_initial_values_impulsive ()

void	assign_initial_values_impulsive (const double &dt)

void	calculate_predictions ()
	Calculate predictions. More...

void	enable_mass_matrix_reuse ()

void	disable_mass_matrix_reuse ()

bool	mass_matrix_reuse_is_enabled ()
	Return whether the mass matrix is being reused. More...

void	refine_uniformly (const Vector< unsigned > &nrefine_for_mesh)

void	refine_uniformly (const Vector< unsigned > &nrefine_for_mesh, DocInfo &doc_info)

void	refine_uniformly_and_prune (const Vector< unsigned > &nrefine_for_mesh)

void	refine_uniformly_and_prune (const Vector< unsigned > &nrefine_for_mesh, DocInfo &doc_info)

void	refine_uniformly (DocInfo &doc_info)

void	refine_uniformly_and_prune (DocInfo &doc_info)

void	refine_uniformly ()

void	refine_uniformly (const unsigned &i_mesh, DocInfo &doc_info)
	Do uniform refinement for submesh i_mesh with documentation. More...

void	refine_uniformly (const unsigned &i_mesh)
	Do uniform refinement for submesh i_mesh without documentation. More...

void	p_refine_uniformly (const Vector< unsigned > &nrefine_for_mesh)

void	p_refine_uniformly (const Vector< unsigned > &nrefine_for_mesh, DocInfo &doc_info)

void	p_refine_uniformly_and_prune (const Vector< unsigned > &nrefine_for_mesh)

void	p_refine_uniformly_and_prune (const Vector< unsigned > &nrefine_for_mesh, DocInfo &doc_info)

void	p_refine_uniformly (DocInfo &doc_info)

void	p_refine_uniformly_and_prune (DocInfo &doc_info)

void	p_refine_uniformly ()

void	p_refine_uniformly (const unsigned &i_mesh, DocInfo &doc_info)
	Do uniform p-refinement for submesh i_mesh with documentation. More...

void	p_refine_uniformly (const unsigned &i_mesh)
	Do uniform p-refinement for submesh i_mesh without documentation. More...

void	refine_selected_elements (const Vector< unsigned > &elements_to_be_refined)

void	refine_selected_elements (const Vector< RefineableElement * > &elements_to_be_refined_pt)

void	refine_selected_elements (const unsigned &i_mesh, const Vector< unsigned > &elements_to_be_refined)

void	refine_selected_elements (const unsigned &i_mesh, const Vector< RefineableElement * > &elements_to_be_refined_pt)

void	refine_selected_elements (const Vector< Vector< unsigned >> &elements_to_be_refined)

void	refine_selected_elements (const Vector< Vector< RefineableElement * >> &elements_to_be_refined_pt)

void	p_refine_selected_elements (const Vector< unsigned > &elements_to_be_refined)

void	p_refine_selected_elements (const Vector< PRefineableElement * > &elements_to_be_refined_pt)

void	p_refine_selected_elements (const unsigned &i_mesh, const Vector< unsigned > &elements_to_be_refined)

void	p_refine_selected_elements (const unsigned &i_mesh, const Vector< PRefineableElement * > &elements_to_be_refined_pt)

void	p_refine_selected_elements (const Vector< Vector< unsigned >> &elements_to_be_refined)

void	p_refine_selected_elements (const Vector< Vector< PRefineableElement * >> &elements_to_be_refined_pt)

unsigned	unrefine_uniformly ()

unsigned	unrefine_uniformly (const unsigned &i_mesh)

void	p_unrefine_uniformly (DocInfo &doc_info)

void	p_unrefine_uniformly (const unsigned &i_mesh, DocInfo &doc_info)
	Do uniform p-unrefinement for submesh i_mesh without documentation. More...

void	adapt (unsigned &n_refined, unsigned &n_unrefined)

void	adapt ()

void	p_adapt (unsigned &n_refined, unsigned &n_unrefined)

void	p_adapt ()

void	adapt_based_on_error_estimates (unsigned &n_refined, unsigned &n_unrefined, Vector< Vector< double >> &elemental_error)

void	adapt_based_on_error_estimates (Vector< Vector< double >> &elemental_error)

void	get_all_error_estimates (Vector< Vector< double >> &elemental_error)

void	doc_errors (DocInfo &doc_info)
	Get max and min error for all elements in submeshes. More...

void	doc_errors ()
	Get max and min error for all elements in submeshes. More...

void	enable_info_in_newton_solve ()

void	disable_info_in_newton_solve ()
	Disable the output of information when in the newton solver. More...

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

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

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

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

virtual void	actions_before_explicit_stage ()

virtual void	actions_after_explicit_stage ()

Protected Member Functions
void	impose_solid_boundary_on_edge (const unsigned &b, const double &psi=0)

void	impose_traction_free_edge (const unsigned &b)

void	impose_fluid_flow_on_edge (const unsigned &b, FluidBCFctPt u_imposed_fn)

Protected Member Functions inherited from oomph::Problem
unsigned	setup_element_count_per_dof ()

virtual void	sparse_assemble_row_or_column_compressed (Vector< int * > &column_or_row_index, Vector< int * > &row_or_column_start, Vector< double * > &value, Vector< unsigned > &nnz, Vector< double * > &residual, bool compressed_row_flag)

virtual void	actions_before_newton_convergence_check ()

virtual void	actions_before_newton_step ()

virtual void	actions_after_newton_step ()

virtual void	actions_before_implicit_timestep ()

virtual void	actions_after_implicit_timestep ()

virtual void	actions_after_implicit_timestep_and_error_estimation ()

virtual void	actions_before_explicit_timestep ()
	Actions that should be performed before each explicit time step. More...

virtual void	actions_after_explicit_timestep ()
	Actions that should be performed after each explicit time step. More...

virtual void	actions_before_read_unstructured_meshes ()

virtual void	actions_after_read_unstructured_meshes ()

virtual void	actions_after_change_in_global_parameter (double *const &parameter_pt)

virtual void	actions_after_change_in_bifurcation_parameter ()

virtual void	actions_after_parameter_increase (double *const &parameter_pt)

double &	dof_derivative (const unsigned &i)

double &	dof_current (const unsigned &i)

virtual void	set_initial_condition ()

virtual double	global_temporal_error_norm ()

unsigned	newton_solve_continuation (double *const &parameter_pt)

unsigned	newton_solve_continuation (double *const &parameter_pt, DoubleVector &z)

void	calculate_continuation_derivatives (double *const &parameter_pt)

void	calculate_continuation_derivatives (const DoubleVector &z)

void	calculate_continuation_derivatives_fd (double *const &parameter_pt)

bool	does_pointer_correspond_to_problem_data (double *const &parameter_pt)

void	set_consistent_pinned_values_for_continuation ()

Private Attributes
unsigned	Npoint_element

Additional Inherited Members
Public Attributes inherited from oomph::Problem
bool	Shut_up_in_newton_solve

Static Public Attributes inherited from oomph::Problem
static bool	Suppress_warning_about_actions_before_read_unstructured_meshes

Protected Types inherited from oomph::Problem
enum	Assembly_method { Perform_assembly_using_vectors_of_pairs , Perform_assembly_using_two_vectors , Perform_assembly_using_maps , Perform_assembly_using_lists , Perform_assembly_using_two_arrays }
	Enumerated flags to determine which sparse assembly method is used. More...

Protected Attributes inherited from oomph::Problem
Vector< Problem * >	Copy_of_problem_pt

std::map< double *, bool >	Calculate_dparameter_analytic

bool	Calculate_hessian_products_analytic

LinearAlgebraDistribution *	Dof_distribution_pt

Vector< double * >	Dof_pt
	Vector of pointers to dofs. More...

DoubleVectorWithHaloEntries	Element_count_per_dof

double	Relaxation_factor

double	Newton_solver_tolerance

unsigned	Max_newton_iterations
	Maximum number of Newton iterations. More...

unsigned	Nnewton_iter_taken

Vector< double >	Max_res
	Maximum residuals at start and after each newton iteration. More...

double	Max_residuals

bool	Time_adaptive_newton_crash_on_solve_fail

bool	Jacobian_reuse_is_enabled
	Is re-use of Jacobian in Newton iteration enabled? Default: false. More...

bool	Jacobian_has_been_computed

bool	Problem_is_nonlinear

bool	Pause_at_end_of_sparse_assembly

bool	Doc_time_in_distribute

unsigned	Sparse_assembly_method

unsigned	Sparse_assemble_with_arrays_initial_allocation

unsigned	Sparse_assemble_with_arrays_allocation_increment

Vector< Vector< unsigned > >	Sparse_assemble_with_arrays_previous_allocation

double	Numerical_zero_for_sparse_assembly

double	FD_step_used_in_get_hessian_vector_products

bool	Mass_matrix_reuse_is_enabled

bool	Mass_matrix_has_been_computed

bool	Discontinuous_element_formulation

double	Minimum_dt
	Minimum desired dt: if dt falls below this value, exit. More...

double	Maximum_dt
	Maximum desired dt. More...

double	DTSF_max_increase

double	DTSF_min_decrease

double	Minimum_dt_but_still_proceed

bool	Scale_arc_length
	Boolean to control whether arc-length should be scaled. More...

double	Desired_proportion_of_arc_length
	Proportion of the arc-length to taken by the parameter. More...

double	Theta_squared

int	Sign_of_jacobian
	Storage for the sign of the global Jacobian. More...

double	Continuation_direction

double	Parameter_derivative
	Storage for the derivative of the global parameter wrt arc-length. More...

double	Parameter_current
	Storage for the present value of the global parameter. More...

bool	Use_continuation_timestepper
	Boolean to control original or new storage of dof stuff. More...

unsigned	Dof_derivative_offset

unsigned	Dof_current_offset

Vector< double >	Dof_derivative
	Storage for the derivative of the problem variables wrt arc-length. More...

Vector< double >	Dof_current
	Storage for the present values of the variables. More...

double	Ds_current
	Storage for the current step value. More...

unsigned	Desired_newton_iterations_ds

double	Minimum_ds
	Minimum desired value of arc-length. More...

bool	Bifurcation_detection
	Boolean to control bifurcation detection via determinant of Jacobian. More...

bool	Bisect_to_find_bifurcation
	Boolean to control wheter bisection is used to located bifurcation. More...

bool	First_jacobian_sign_change
	Boolean to indicate whether a sign change has occured in the Jacobian. More...

bool	Arc_length_step_taken
	Boolean to indicate whether an arc-length step has been taken. More...

bool	Use_finite_differences_for_continuation_derivatives

OomphCommunicator *	Communicator_pt
	The communicator for this problem. More...

bool	Always_take_one_newton_step

double	Timestep_reduction_factor_after_nonconvergence

bool	Keep_temporal_error_below_tolerance

Static Protected Attributes inherited from oomph::Problem
static ContinuationStorageScheme	Continuation_time_stepper
	Storage for the single static continuation timestorage object. More...

Detailed Description

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

Biharmonic Fluid Problem Class - describes stokes flow in 2D. Developed for the topologically rectangular Hermite Element Mesh. Contains functions allowing the following boundary conditions to be applied (on a given edge):

wall : v_n = 0 and v_t = 0 (psi must also be prescribed)
traction free : v_t = 0
flow : v_n and v_t are prescribed NOTE 1 : psi is the stream function
- fluid velocity normal to boundary v_n = +/- dpsi/dt
- fluid velocity tangential to boundary v_t = -/+ dpsi/dn NOTE 2 : when a solid wall boundary condition is applied to ensure that v_n = 0 the the streamfunction psi must also be prescribed (and constant)

Member Typedef Documentation

◆ FluidBCFctPt

template<unsigned DIM>

typedef void(* oomph::BiharmonicFluidProblem< DIM >::FluidBCFctPt) (const double &s, Vector< double > &u)

Definition of a dirichlet boundary condition function pointer. Takes the position along a boundary (s) in the macro element coordinate scheme and returns the fluid velocity normal (dpsi/dt) to the boundary (u[0]) and the fluid velocity tangential (dpsidn) to the boundary (u[1]).

Constructor & Destructor Documentation

◆ BiharmonicFluidProblem()

template<unsigned DIM>

oomph::BiharmonicFluidProblem< DIM >::BiharmonicFluidProblem ( )

inline

constructor

     {
       // initialise the number of non bulk elements
       Npoint_element = 0;
     }

References oomph::BiharmonicFluidProblem< DIM >::Npoint_element.

Member Function Documentation

◆ actions_after_newton_solve()

template<unsigned DIM>

void oomph::BiharmonicFluidProblem< DIM >::actions_after_newton_solve ( )

inlinevirtual

action after solve

Reimplemented from oomph::Problem.

260 {}

◆ actions_before_newton_solve()

template<unsigned DIM>

void oomph::BiharmonicFluidProblem< DIM >::actions_before_newton_solve ( )

inlinevirtual

actions before solve, performs self test

Reimplemented from oomph::Problem.

     {
 #ifdef PARANOID
       if (0 == self_test())
       {
         oomph_info << "self test passed" << std::endl;
       }
       else
       {
         oomph_info << "self test failed" << std::endl;
       }
 #endif
     }

References oomph::oomph_info, and oomph::Problem::self_test().

◆ doc_solution()

template<unsigned DIM>

void oomph::BiharmonicFluidProblem< DIM >::doc_solution	(	DocInfo &	doc_info,
		FiniteElement::SteadyExactSolutionFctPt	exact_soln_pt = `0`
	)

documents the solution, and if an exact solution is provided, then the error between the numerical and exact solution is presented

   {
     // create an output stream
     std::ofstream some_file;
     std::ostringstream filename;
  
     // Number of plot points: npts x npts
     unsigned npts = 5;
  
     // Output solution
     filename << doc_info.directory() << "/soln_" << doc_info.label() << ".dat";
     some_file.open(filename.str().c_str());
     mesh_pt()->output(some_file, npts);
     some_file.close();
  
     // Output fluid velocity solution
     filename.str("");
     filename << doc_info.directory() << "/soln_velocity_" << doc_info.label()
              << ".dat";
     some_file.open(filename.str().c_str());
     unsigned n_element = mesh_pt()->nelement();
     for (unsigned i = 0; i < n_element - Npoint_element; i++)
     {
       BiharmonicElement<2>* biharmonic_element_pt =
         dynamic_cast<BiharmonicElement<2>*>(mesh_pt()->element_pt(i));
       biharmonic_element_pt->output_fluid_velocity(some_file, npts);
     }
     some_file.close();
  
     // if the exact solution is not provided
     if (exact_soln_pt != 0)
     {
       // Output exact solution
       filename.str("");
       filename << doc_info.directory() << "/exact_soln_" << doc_info.label()
                << ".dat";
       some_file.open(filename.str().c_str());
       mesh_pt()->output_fct(some_file, npts, exact_soln_pt);
       some_file.close();
  
       // Doc error and return of the square of the L2 error
       double error, norm;
       filename.str("");
       filename << doc_info.directory() << "/error_" << doc_info.label()
                << ".dat";
       some_file.open(filename.str().c_str());
       mesh_pt()->compute_error(some_file, exact_soln_pt, error, norm);
       some_file.close();
  
       // Doc L2 error and norm of solution
       oomph_info << "\nNorm of error   : " << sqrt(error) << std::endl;
       oomph_info << "Norm of solution: " << sqrt(norm) << std::endl
                  << std::endl;
     }
   }

References oomph::DocInfo::directory(), calibrate::error, MergeRestartFiles::filename, i, oomph::DocInfo::label(), oomph::oomph_info, oomph::BiharmonicEquations< DIM >::output_fluid_velocity(), and sqrt().

◆ impose_fluid_flow_on_edge()

template<unsigned DIM>

void oomph::BiharmonicFluidProblem< DIM >::impose_fluid_flow_on_edge	(	const unsigned &	b,
		FluidBCFctPt	u_imposed_fn
	)

protected

Impose a prescribed fluid flow comprising the velocity normal to the boundary (u_imposed_fn[0]) and the velocity tangential to the boundary (u_imposed_fn[1])

   {
     // number of nodes on boundary b
     unsigned n_node = mesh_pt()->nboundary_node(b);
  
     // fixed faced index for boundary
     int face_index = mesh_pt()->face_index_at_boundary(b, 0);
  
     // Need to get the s_fixed_index
     unsigned s_fixed_index = 0;
     // Also set the edge sign
     int edge_sign = 0;
  
     switch (face_index)
     {
       case -1:
         s_fixed_index = 0;
         edge_sign = -1;
         break;
  
       case 1:
         s_fixed_index = 0;
         edge_sign = 1;
         break;
  
       case -2:
         s_fixed_index = 1;
         edge_sign = 1;
         break;
  
       case 2:
         s_fixed_index = 1;
         edge_sign = -1;
         break;
  
       default:
         throw OomphLibError("Face Index not +/-1 or +/-2: Need 2D QElements",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
     }
  
  
     // node position along edge b in macro element boundary representation
     // [-1,1]
     Vector<double> s(1);
  
     // finite difference step
     const double h = 10e-8;
  
     // loop over nodes on boundary b
     for (unsigned n = 0; n < n_node; n++)
     {
       // get m_t and dm_t/ds_t for this node
       Vector<double> m_N(2);
       mesh_pt()->boundary_node_pt(b, n)->get_coordinates_on_boundary(b, m_N);
  
       // vectors for dx_i/ds_n and dx_i/ds_t
       Vector<double> dxds_n(2);
       Vector<double> dxds_t(2);
       dxds_n[0] =
         mesh_pt()->boundary_node_pt(b, n)->x_gen(1 + s_fixed_index, 0);
       dxds_n[1] =
         mesh_pt()->boundary_node_pt(b, n)->x_gen(1 + s_fixed_index, 1);
       dxds_t[0] =
         mesh_pt()->boundary_node_pt(b, n)->x_gen(2 - s_fixed_index, 0);
       dxds_t[1] =
         mesh_pt()->boundary_node_pt(b, n)->x_gen(2 - s_fixed_index, 1);
  
       // vector for d2xi/ds_n ds_t
       Vector<double> d2xds_nds_t(2);
       d2xds_nds_t[0] = mesh_pt()->boundary_node_pt(b, n)->x_gen(3, 0);
       d2xds_nds_t[1] = mesh_pt()->boundary_node_pt(b, n)->x_gen(3, 1);
  
       // compute dn/ds_n
       double dnds_n =
         ((dxds_n[0] * dxds_t[1]) - (dxds_n[1] * dxds_t[0])) /
         (sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]) * edge_sign);
  
       // compute dt/ds_n
       double dtds_n = ((dxds_n[0] * dxds_t[0]) + (dxds_n[1] * dxds_t[1])) /
                       sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]);
  
       // compute dt/ds_t
       double dtds_t = sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]);
  
       // compute d2t/ds_nds_t
       double d2tds_nds_t =
         (dxds_t[0] * d2xds_nds_t[0] + dxds_t[1] * d2xds_nds_t[1]) /
         sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]);
  
       // get imposed velocities
       Vector<double> u(2);
       (*u_imposed_fn)(m_N[0], u);
       u[0] *= edge_sign;
       u[1] *= -edge_sign;
  
       // compute  d/dm_t(dpsidn) by finite difference
       double ddm_tdudn = 0;
       double ddm_tdudt = 0;
       Vector<double> u_L(2);
       Vector<double> u_R(2);
       // evaluate dudn_fn about current node
       if (n == 0)
       {
         (*u_imposed_fn)(m_N[0], u_L);
         (*u_imposed_fn)(m_N[0] + h, u_R);
       }
       else if (n == n_node - 1)
       {
         (*u_imposed_fn)(m_N[0] - h, u_L);
         (*u_imposed_fn)(m_N[0], u_R);
       }
       else
       {
         (*u_imposed_fn)(m_N[0] - 0.5 * h, u_L);
         (*u_imposed_fn)(m_N[0] + 0.5 * h, u_R);
       }
       // compute
       ddm_tdudn = (u_R[1] - u_L[1]) / h;
       ddm_tdudt = (u_R[0] - u_L[0]) / h;
  
       // compute du/ds_t
       double duds_t = dtds_t * u[0];
  
       // compute du/ds_n
       double duds_n = dnds_n * u[1] + dtds_n * u[0];
  
       // compute d2u/ds_n ds_t
       double d2uds_nds_t = dnds_n * m_N[1] * ddm_tdudn + d2tds_nds_t * u[0] +
                            dtds_n * m_N[1] * ddm_tdudt;
  
       // pin du/ds_n dof and set value
       mesh_pt()->boundary_node_pt(b, n)->pin(1 + s_fixed_index);
       mesh_pt()->boundary_node_pt(b, n)->set_value(1 + s_fixed_index, duds_n);
  
       // pin du/ds_t dof and set value
       mesh_pt()->boundary_node_pt(b, n)->pin(2 - s_fixed_index);
       mesh_pt()->boundary_node_pt(b, n)->set_value(2 - s_fixed_index, duds_t);
  
       // pin du/ds_t dof and set value
       mesh_pt()->boundary_node_pt(b, n)->pin(3);
       mesh_pt()->boundary_node_pt(b, n)->set_value(3, d2uds_nds_t);
     }
   }

References b, e(), n, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, s, and sqrt().

◆ impose_solid_boundary_on_edge()

template<unsigned DIM>

void oomph::BiharmonicFluidProblem< DIM >::impose_solid_boundary_on_edge	(	const unsigned &	b,
		const double &	psi = `0`
	)

protected

Imposes a solid boundary on boundary b - no flow into boundary or along boundary v_n = 0 and v_t = 0. User must presribe the streamfunction psi to ensure dpsi/dt = 0 is imposed at all points on the boundary and not just at the nodes

Imposes a solid boundary - no flow into boundary or along boundary v_n = 0 and v_t = 0. User must presribe the streamfunction psi to ensure dpsi/dt = 0 is imposed at all points on the boundary and not just at the nodes

   {
     // number of nodes on boundary b
     unsigned n_node = mesh_pt()->nboundary_node(b);
  
     // loop over nodes on boundary b
     for (unsigned n = 0; n < n_node; n++)
     {
       // loop over DOFs to be pinned du/ds_n, du/ds_t and d2u/ds_nds_t
       for (unsigned k = 1; k < 4; k++)
       {
         // pin and zero DOF k
         mesh_pt()->boundary_node_pt(b, n)->pin(k);
         mesh_pt()->boundary_node_pt(b, n)->set_value(k, 0.0);
       }
       mesh_pt()->boundary_node_pt(b, n)->pin(0);
       mesh_pt()->boundary_node_pt(b, n)->set_value(0, psi);
     }
   }

References b, k, and n.

◆ impose_traction_free_edge()

template<unsigned DIM>

void oomph::BiharmonicFluidProblem< DIM >::impose_traction_free_edge ( const unsigned & b )

protected

Impose a traction free edge - i.e. v_t = 0 or dpsi/dn = 0. In general dpsi/dn = 0 can only be imposed using equation elements to set the DOFs dpsi/ds_n, however in the special case of dt/ds_n = 0, then dpsi/ds_n = 0 and can be imposed using pinning - this is handled automatically in this function. For a more detailed description of the equations see the description of the class BiharmonicFluidBoundaryElement

Impose a traction free edge - i.e. v_t = 0 or dpsi/dn = 0. In general dpsi/dn = 0 can only be imposed using equation elements to set the DOFs dpsi/ds_n, however in the special case of dt/ds_n = 0, then dpsi/ds_n = 0 and can be imposed using pinning - this is handled automatically in this function. For a more detailed description of the equations see the description of the class : BiharmonicFluidBoundaryElement

   {
     // fixed faced index for boundary
     int face_index = mesh_pt()->face_index_at_boundary(b, 0);
  
     // Need to get the s_fixed_index
     unsigned s_fixed_index = 0;
     switch (face_index)
     {
       case -1:
       case 1:
         s_fixed_index = 0;
         break;
  
       case -2:
       case 2:
         s_fixed_index = 1;
         break;
  
       default:
         throw OomphLibError("Face Index not +/-1 or +/-2: Need 2D QElements",
                             OOMPH_CURRENT_FUNCTION,
                             OOMPH_EXCEPTION_LOCATION);
     }
  
     // create a point to a hijacked biharmonic element
     Hijacked<BiharmonicElement<2>>* hijacked_element_pt;
  
     // vectors for dx_i/ds_n and dx_i/ds_t
     Vector<double> dxds_n(2);
     Vector<double> dxds_t(2);
  
     // number of nodes along edge
     unsigned n_node = mesh_pt()->nboundary_node(b);
  
     // loop over boudnary nodes
     for (unsigned n = 0; n < n_node; n++)
     {
       // get dx_i/ds_t and dx_i/ds_n at node n
       dxds_n[0] =
         mesh_pt()->boundary_node_pt(b, n)->x_gen(1 + s_fixed_index, 0);
       dxds_n[1] =
         mesh_pt()->boundary_node_pt(b, n)->x_gen(1 + s_fixed_index, 1);
       dxds_t[0] =
         mesh_pt()->boundary_node_pt(b, n)->x_gen(2 - s_fixed_index, 0);
       dxds_t[1] =
         mesh_pt()->boundary_node_pt(b, n)->x_gen(2 - s_fixed_index, 1);
  
       // compute dt/ds_n
       double dtds_n = ((dxds_n[0] * dxds_t[0]) + (dxds_n[1] * dxds_t[1])) /
                       sqrt(dxds_t[0] * dxds_t[0] + dxds_t[1] * dxds_t[1]);
  
       // if dt/ds_n = 0 we can impose the traction free edge at this node by
       // pinning dpsi/ds_n = 0, otherwise the equation elements
       // BiharmonicFluidBoundaryElement are used
       if (dtds_n == 0.0)
       {
         // pin dpsi/dn
         mesh_pt()->boundary_node_pt(b, n)->pin(1 + s_fixed_index);
         mesh_pt()->boundary_node_pt(b, n)->set_value(1 + s_fixed_index, 0.0);
       }
  
       // otherwise impose equation elements
       else
       {
         // hijack DOFs in element either side of node
         // boundary 0
         if (b == 0)
         {
           // hijack DOFs in left element
           if (n > 0)
           {
             hijacked_element_pt = dynamic_cast<Hijacked<BiharmonicElement<2>>*>(
               mesh_pt()->boundary_element_pt(b, n - 1));
             delete hijacked_element_pt->hijack_nodal_value(1,
                                                            1 + s_fixed_index);
           }
           // hijack DOFs in right element
           if (n < (n_node - 1))
           {
             hijacked_element_pt = dynamic_cast<Hijacked<BiharmonicElement<2>>*>(
               mesh_pt()->boundary_element_pt(b, n));
             delete hijacked_element_pt->hijack_nodal_value(0,
                                                            1 + s_fixed_index);
           }
         }
         // boundary 1
         else if (b == 1)
         {
           // hijack DOFs in left element
           if (n > 0)
           {
             hijacked_element_pt = dynamic_cast<Hijacked<BiharmonicElement<2>>*>(
               mesh_pt()->boundary_element_pt(b, n - 1));
             delete hijacked_element_pt->hijack_nodal_value(3,
                                                            1 + s_fixed_index);
           }
           // hijack DOFs in right element
           if (n < n_node - 1)
           {
             hijacked_element_pt = dynamic_cast<Hijacked<BiharmonicElement<2>>*>(
               mesh_pt()->boundary_element_pt(b, n));
             delete hijacked_element_pt->hijack_nodal_value(1,
                                                            1 + s_fixed_index);
           }
         }
  
         // boundary 2
         else if (b == 2)
         {
           // hijack DOFs in left element
           if (n > 0)
           {
             hijacked_element_pt = dynamic_cast<Hijacked<BiharmonicElement<2>>*>(
               mesh_pt()->boundary_element_pt(b, n - 1));
             delete hijacked_element_pt->hijack_nodal_value(3,
                                                            1 + s_fixed_index);
           }
           if (n < n_node - 1)
           {
             // hijack DOFs in right element
             hijacked_element_pt = dynamic_cast<Hijacked<BiharmonicElement<2>>*>(
               mesh_pt()->boundary_element_pt(b, n));
             delete hijacked_element_pt->hijack_nodal_value(2,
                                                            1 + s_fixed_index);
           }
         }
         // boundary 3
         else if (b == 3)
         {
           // hijack DOFs in left element
           if (n > 0)
           {
             hijacked_element_pt = dynamic_cast<Hijacked<BiharmonicElement<2>>*>(
               mesh_pt()->boundary_element_pt(b, n - 1));
             delete hijacked_element_pt->hijack_nodal_value(2,
                                                            1 + s_fixed_index);
           }
           if (n < n_node - 1)
           {
             // hijack DOFs in right element
             hijacked_element_pt = dynamic_cast<Hijacked<BiharmonicElement<2>>*>(
               mesh_pt()->boundary_element_pt(b, n));
             delete hijacked_element_pt->hijack_nodal_value(0,
                                                            1 + s_fixed_index);
           }
         }
  
         // create the boundary point element
         BiharmonicFluidBoundaryElement* boundary_point_element_pt =
           new BiharmonicFluidBoundaryElement(mesh_pt()->boundary_node_pt(b, n),
                                              s_fixed_index);
  
         // add element to mesh
         mesh_pt()->add_element_pt(boundary_point_element_pt);
  
         // increment number of non bulk elements
         Npoint_element++;
       }
     }
   }

References b, oomph::Hijacked< ELEMENT >::hijack_nodal_value(), n, OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION, and sqrt().

Member Data Documentation

◆ Npoint_element

template<unsigned DIM>

unsigned oomph::BiharmonicFluidProblem< DIM >::Npoint_element

private

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

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

Public Types

Public Member Functions

Protected Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

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

Member Typedef Documentation

◆ FluidBCFctPt

Constructor & Destructor Documentation

◆ BiharmonicFluidProblem()

Member Function Documentation

◆ actions_after_newton_solve()

◆ actions_before_newton_solve()

◆ doc_solution()

◆ impose_fluid_flow_on_edge()

◆ impose_solid_boundary_on_edge()

◆ impose_traction_free_edge()

Member Data Documentation

◆ Npoint_element

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