domain::CoordinateMaps::SphericalTorus Class Reference

Torus made by removing two polar cones from a spherical shell. More...

#include <SphericalTorus.hpp>

Classes
struct	FractionOfTorus
struct	MinPolarAngle
struct	RadialRange

Public Types
using	options = tmpl::list< RadialRange, MinPolarAngle, FractionOfTorus >

Public Member Functions
	SphericalTorus (const std::array< double, 2 > &radial_range, const double min_polar_angle, const double fraction_of_torus, const Options::Context &context={})
	SphericalTorus (double r_min, double r_max, double min_polar_angle, double fraction_of_torus=1.0, const Options::Context &context={})
template<typename T >
std::array< tt::remove_cvref_wrap_t< T >, 3 >	operator() (const std::array< T, 3 > &source_coords) const
std::optional< std::array< double, 3 > >	inverse (const std::array< double, 3 > &target_coords) const
template<typename T >
tnsr::Ij< tt::remove_cvref_wrap_t< T >, 3, Frame::NoFrame >	jacobian (const std::array< T, 3 > &source_coords) const
template<typename T >
tnsr::Ij< tt::remove_cvref_wrap_t< T >, 3, Frame::NoFrame >	inv_jacobian (const std::array< T, 3 > &source_coords) const
template<typename T >
tnsr::Ijj< tt::remove_cvref_wrap_t< T >, 3, Frame::NoFrame >	hessian (const std::array< T, 3 > &source_coords) const
template<typename T >
tnsr::Ijk< tt::remove_cvref_wrap_t< T >, 3, Frame::NoFrame >	derivative_of_inv_jacobian (const std::array< T, 3 > &source_coords) const
void	pup (PUP::er &p)
bool	is_identity () const

Static Public Attributes
static constexpr size_t	dim = 3
static constexpr Options::String	help

Friends
bool	operator== (const SphericalTorus &lhs, const SphericalTorus &rhs)

Detailed Description

Torus made by removing two polar cones from a spherical shell.

Maps source coordinates \((\xi, \eta, \zeta)\) to

\begin{align} \vec{x}(\xi, \eta, \zeta) = \begin{bmatrix} r \sin\theta\cos\phi \\ r \sin\theta\sin\phi \\ r \cos\theta \end{bmatrix} \end{align}

where

\begin{align} r & = r_\mathrm{min}\frac{1-\xi}{2} + r_\mathrm{max}\frac{1+\xi}{2}, \\ \theta & = \pi/2 - (\pi/2 - \theta_\mathrm{min}) \eta, \\ \phi & = f_\mathrm{torus} \pi \zeta. \end{align}

• \(r_\mathrm{min}\) and \(r_\mathrm{max}\) are inner and outer radius of torus.
• \(\theta_\mathrm{min}\in(0,\pi/2)\) is the minimum polar angle (measured from +z axis) of torus, which is equal to the half of the apex angle of the removed polar cones.
• \(f_\mathrm{torus}\in(0, 1)\) is azimuthal fraction that the torus covers.

Warning

Internal namings of code variables in SphericalTorus.cpp uses a different convention of angular variables for spherical coordinates. Therein theta denotes the azimuthal angle, and phi denotes the elevation angle measured from equator, which is equal to ( \(\pi/2\) - polar angle) with the polar angle being measured from +z axis.

Member Data Documentation

help

constexpr Options::String domain::CoordinateMaps::SphericalTorus::help

staticconstexpr

Initial value:

=
      "Torus made by removing polar cones from a spherical shell"

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

• src/Domain/CoordinateMaps/SphericalTorus.hpp