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Reference documentation for deal.II version 9.1.1
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#include <deal.II/base/flow_function.h>
Public Member Functions | |
StokesLSingularity () | |
Constructor setting up some data. | |
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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_laplacian_list (const std::vector< Point< dim >> &points, std::vector< Vector< double >> &values) const override |
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Function (const unsigned int n_components=1, const time_type initial_time=0.0) | |
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 |
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FunctionTime (const Number initial_time=Number(0.0)) | |
virtual | ~FunctionTime ()=default |
Number | get_time () const |
virtual void | set_time (const Number new_time) |
virtual void | advance_time (const Number delta_t) |
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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. | |
double | Psi_1 (double phi) const |
The derivative of Psi() | |
double | Psi_2 (double phi) const |
The 2nd derivative of Psi() | |
double | Psi_3 (double phi) const |
The 3rd derivative of Psi() | |
double | Psi_4 (double phi) const |
The 4th derivative of Psi() | |
Private Attributes | |
const double | omega |
The angle of the reentrant corner, set to 3*pi/2. | |
const double | coslo |
Cosine of lambda times omega. | |
const double | lp |
Auxiliary variable 1+lambda. | |
const double | lm |
Auxiliary variable 1-lambda. | |
Static Private Attributes | |
static const double | lambda = 0.54448373678246 |
Additional Inherited Members | |
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using | time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type |
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using | time_type = Number |
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static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
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const unsigned int | n_components |
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static const unsigned int | dimension |
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double | mean_pressure |
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.
Definition at line 247 of file flow_function.h.
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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.