Class WallSmooth

• Defined in File RegularizedWall.hxx

Inheritance Relationships

Base Type

• public Mechatronix::RegularizedBase (Class RegularizedBase)

Class Documentation

class Mechatronix::WallSmooth : public Mechatronix::RegularizedBase

Wall function smoothed

\[ w(x)=\frac{1}{4} {\frac {A \left( \sqrt {\pi }+\sqrt {\pi } {\textrm{erf}\left(Bx\right)}+2\,\sqrt {\pi }{B}^{2} {\textrm{erf}\left(Bx\right)}{x}^{2}+2\,{\mathrm{e}^{-{x}^{2}{B}^{2}}}xB+2\, {x}^{2}{B}^{2}\sqrt {\pi } \right) }{{B}^{2}\sqrt {\pi }}} \]

where \( A \) and \( B \) are such that

\[ w(0) = \epsilon, \qquad w(h)=1 \]

Inizialization

inline explicit WallSmooth()

virtual void setup(GenericContainer const &gc) override

void setup(real_type h, real_type epsilon)

Initialize regularized.

setup parameters A and B given h and epsilon.

parameterd are evaluated such that \( w(h)=1 \) and \( w(0)=\epsilon \).

inline void update_h(real_type h)

inline void update_epsilon(real_type epsilon)

Evaluate

virtual real_type operator()(real_type x) const override

Evaluate

\[ w(x)=\frac{1}{4} {\frac {A \left( \sqrt {\pi }+\sqrt {\pi } {\textrm{erf}\left(Bx\right)}+2\,\sqrt {\pi }{B}^{2} {\textrm{erf}\left(Bx\right)}{x}^{2}+2\,{\mathrm{e}^{-{x}^{2}{B}^{2}}}xB+2\, {x}^{2}{B}^{2}\sqrt {\pi } \right) }{{B}^{2}\sqrt {\pi }}} \]

where \( A \) and \( B \) are such that

\[ w(0) = \epsilon, \qquad w(h)=1 \]

virtual real_type D(real_type x) const override

Evaluate

\[ w'(x)= {\frac {A \left( xB\sqrt {\pi }+{\mathrm{erf}\left(Bx\right)}Bx \sqrt {\pi }+{\mathrm{e}^{-{x}^{2}{B}^{2}}} \right) }{B\sqrt {\pi }}} \]

where \( A \) and \( B \) are such that

\[ w(0) = \epsilon, \qquad w(h)=1 \]

virtual real_type DD(real_type x) const override

Evaluate

\[ w''(x) = A (1+\textrm{erf}(Bx)) \]

where \( A \) and \( B \) are such that

\[ w(0) = \epsilon, \qquad w(h)=1 \]

Info

virtual string info() const override