#include <deal.II/base/flow_function.h>

Inheritance diagram for Functions::StokesLSingularity:

Public Member Functions
	StokesLSingularity ()
	Constructor setting up some data. More...

virtual void	vector_values (const std::vector< Point< 2 >> &points, std::vector< std::vector< double >> &values) const override

virtual void	vector_gradients (const std::vector< Point< 2 >> &points, std::vector< std::vector< Tensor< 1, 2 >>> &gradients) const override

virtual void	vector_laplacians (const std::vector< Point< 2 >> &points, std::vector< std::vector< double >> &values) const override

Public Member Functions inherited from Functions::FlowFunction< 2 >
	FlowFunction ()

virtual	~FlowFunction () override=default

void	pressure_adjustment (double p)

virtual void	vector_values (const std::vector< Point< dim >> &points, std::vector< std::vector< double >> &values) const override=0

virtual void	vector_gradients (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim >>> &gradients) const override=0

virtual void	vector_laplacians (const std::vector< Point< dim >> &points, std::vector< std::vector< double >> &values) const=0

virtual void	vector_value (const Point< dim > &points, Vector< double > &value) const override

virtual double	value (const Point< dim > &points, const unsigned int component) const override

virtual void	vector_value_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const override

virtual void	vector_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim >>> &gradients) const override

virtual void	vector_laplacian_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const override

std::size_t	memory_consumption () const

Public Member Functions inherited from Function< dim >
	Function (const unsigned int n_components=1, const time_type initial_time=0.0)

	Function (const Function &f)=default

virtual	~Function () override=0

Function &	operator= (const Function &f)

virtual void	value_list (const std::vector< Point< dim >> &points, std::vector< double > &values, const unsigned int component=0) const

virtual Tensor< 1, dim, double >	gradient (const Point< dim > &p, const unsigned int component=0) const

virtual void	vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, double >> &gradients) const

virtual void	gradient_list (const std::vector< Point< dim >> &points, std::vector< Tensor< 1, dim, double >> &gradients, const unsigned int component=0) const

virtual void	vector_gradients (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, double >>> &gradients) const

virtual void	vector_gradient_list (const std::vector< Point< dim >> &points, std::vector< std::vector< Tensor< 1, dim, double >>> &gradients) const

virtual double	laplacian (const Point< dim > &p, const unsigned int component=0) const

virtual void	vector_laplacian (const Point< dim > &p, Vector< double > &values) const

virtual void	laplacian_list (const std::vector< Point< dim >> &points, std::vector< double > &values, const unsigned int component=0) const

virtual SymmetricTensor< 2, dim, double >	hessian (const Point< dim > &p, const unsigned int component=0) const

virtual void	vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, double >> &values) const

virtual void	hessian_list (const std::vector< Point< dim >> &points, std::vector< SymmetricTensor< 2, dim, double >> &values, const unsigned int component=0) const

virtual void	vector_hessian_list (const std::vector< Point< dim >> &points, std::vector< std::vector< SymmetricTensor< 2, dim, double >>> &values) const

std::size_t	memory_consumption () const

Public Member Functions inherited from FunctionTime< numbers::NumberTraits< double >::real_type >
	FunctionTime (const numbers::NumberTraits< double >::real_type initial_time=numbers::NumberTraits< double >::real_type(0.0))

virtual	~FunctionTime ()=default

numbers::NumberTraits< double >::real_type	get_time () const

virtual void	set_time (const numbers::NumberTraits< double >::real_type new_time)

virtual void	advance_time (const numbers::NumberTraits< double >::real_type delta_t)

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Private Member Functions
double	Psi (double phi) const
	The auxiliary function Psi. More...

double	Psi_1 (double phi) const
	The derivative of Psi() More...

double	Psi_2 (double phi) const
	The 2nd derivative of Psi() More...

double	Psi_3 (double phi) const
	The 3rd derivative of Psi() More...

double	Psi_4 (double phi) const
	The 4th derivative of Psi() More...

Private Attributes
const double	omega
	The angle of the reentrant corner, set to 3*pi/2. More...

const double	coslo
	Cosine of lambda times omega. More...

const double	lp
	Auxiliary variable 1+lambda. More...

const double	lm
	Auxiliary variable 1-lambda. More...

Static Private Attributes
static const double	lambda = 0.54448373678246

Additional Inherited Members
Public Types inherited from Function< dim >
using	time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type

Public Types inherited from FunctionTime< numbers::NumberTraits< double >::real_type >
using	time_type = numbers::NumberTraits< double >::real_type

Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Public Attributes inherited from Function< dim >
const unsigned int	n_components

Static Public Attributes inherited from Function< dim >
static const unsigned int	dimension

Protected Attributes inherited from Functions::FlowFunction< 2 >
double	mean_pressure

Detailed Description

A singular solution to Stokes' equations on a 2d L-shaped domain.

This function satisfies \(-\triangle \mathbf{u} + \nabla p = 0\) and represents a typical singular solution around a reentrant corner of an L-shaped domain that can be created using GridGenerator::hyper_L(). The velocity vanishes on the two faces of the re-entrant corner and \(\nabla\mathbf{u}\) and \(p\) are singular at the origin while they are smooth in the rest of the domain because they can be written as a product of a smooth function and the term \(r^{\lambda-1}\) where \(r\) is the radius and \(\lambda \approx 0.54448\) is a fixed parameter.

Taken from Houston, Schötzau, Wihler, proceeding ENUMATH 2003.

Author: Guido Kanschat, 2007

Definition at line 247 of file flow_function.h.

Constructor & Destructor Documentation

◆ StokesLSingularity()

Functions::StokesLSingularity::StokesLSingularity ( )

Constructor setting up some data.

Definition at line 496 of file flow_function.cc.

Member Function Documentation

◆ vector_values()

void Functions::StokesLSingularity::vector_values	(	const std::vector< Point< 2 >> &	points,
		std::vector< std::vector< double >> &	values
	)		const

overridevirtual

Definition at line 549 of file flow_function.cc.

◆ vector_gradients()

void Functions::StokesLSingularity::vector_gradients	(	const std::vector< Point< 2 >> &	points,
		std::vector< std::vector< Tensor< 1, 2 >>> &	gradients
	)		const

overridevirtual

Definition at line 589 of file flow_function.cc.

◆ vector_laplacians()

void Functions::StokesLSingularity::vector_laplacians	(	const std::vector< Point< 2 >> &	points,
		std::vector< std::vector< double >> &	values
	)		const

overridevirtual

Definition at line 649 of file flow_function.cc.

◆ Psi()

double Functions::StokesLSingularity::Psi ( double phi ) const

inlineprivate

The auxiliary function Psi.

Definition at line 505 of file flow_function.cc.

◆ Psi_1()

double Functions::StokesLSingularity::Psi_1 ( double phi ) const

inlineprivate

The derivative of Psi()

Definition at line 513 of file flow_function.cc.

◆ Psi_2()

double Functions::StokesLSingularity::Psi_2 ( double phi ) const

inlineprivate

The 2nd derivative of Psi()

Definition at line 521 of file flow_function.cc.

◆ Psi_3()

double Functions::StokesLSingularity::Psi_3 ( double phi ) const

inlineprivate

The 3rd derivative of Psi()

Definition at line 529 of file flow_function.cc.

◆ Psi_4()

double Functions::StokesLSingularity::Psi_4 ( double phi ) const

inlineprivate

The 4th derivative of Psi()

Definition at line 539 of file flow_function.cc.

Member Data Documentation

◆ omega

const double Functions::StokesLSingularity::omega

private

The angle of the reentrant corner, set to 3*pi/2.

Definition at line 281 of file flow_function.h.

◆ lambda

const double Functions::StokesLSingularity::lambda = 0.54448373678246

staticprivate

The exponent of the radius, computed as the solution to \(\sin(\lambda\omega)+\lambda \sin(\omega)=0\)

Definition at line 284 of file flow_function.h.

◆ coslo

const double Functions::StokesLSingularity::coslo

private

Cosine of lambda times omega.

Definition at line 286 of file flow_function.h.

◆ lp

const double Functions::StokesLSingularity::lp

private

Auxiliary variable 1+lambda.

Definition at line 288 of file flow_function.h.

◆ lm

const double Functions::StokesLSingularity::lm

private

Auxiliary variable 1-lambda.

Definition at line 290 of file flow_function.h.

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

include/deal.II/base/flow_function.h
source/base/flow_function.cc

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ StokesLSingularity()

Member Function Documentation

◆ vector_values()

◆ vector_gradients()

◆ vector_laplacians()

◆ Psi()

◆ Psi_1()

◆ Psi_2()

◆ Psi_3()

◆ Psi_4()

Member Data Documentation

◆ omega

◆ lambda

◆ coslo

◆ lp

◆ lm