grmhd::AnalyticData::SphericalTorus Class Reference

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

#include <SphericalTorus.hpp>

Classes
struct	CompressionLevel
struct	FractionOfTorus
struct	MinPolarAngle
struct	RadialRange

Public Types
using	options = implementation defined

Public Member Functions
	SphericalTorus (const std::array< double, 2 > &radial_range, double min_polar_angle, double fraction_of_torus, double compression_level, const Options::Context &context={})
	SphericalTorus (double r_min, double r_max, double min_polar_angle, double fraction_of_torus=1.0, double compression_level=0.0, const Options::Context &context={})
template<typename T >
tnsr::I< T, 3 >	operator() (const tnsr::I< T, 3 > &source_coords) const
tnsr::I< double, 3 >	inverse (const tnsr::I< double, 3 > &target_coords) const
template<typename T >
Jacobian< T, 3, Frame::BlockLogical, Frame::Inertial >	jacobian (const tnsr::I< T, 3 > &source_coords) const
template<typename T >
InverseJacobian< T, 3, Frame::BlockLogical, Frame::Inertial >	inv_jacobian (const tnsr::I< T, 3 > &source_coords) const
template<typename T >
tnsr::Ijj< T, 3, Frame::NoFrame >	hessian (const tnsr::I< T, 3 > &source_coords) const
template<typename T >
tnsr::Ijk< T, 3, Frame::NoFrame >	derivative_of_inv_jacobian (const tnsr::I< 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

$$\begin{array}{}\text{(1)}& \overrightarrow{x}(\xi ,\eta ,\zeta )=\left[\begin{array}{c}r\sin \theta \cos \varphi \\ r\sin \theta \sin \varphi \\ r\cos \theta \end{array}\right]\end{array}$$

where

$$\begin{array}{}\text{(2)}& r& =r_{\mathrm{m}\mathrm{i}\mathrm{n}}\frac{1-\xi }{2}+r_{\mathrm{m}\mathrm{a}\mathrm{x}}\frac{1+\xi }{2},\text{(3)}& {\eta }_{\mathrm{n}\mathrm{e}\mathrm{w}}& =a_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}{\eta }^3+(1-a_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}})\eta ,\text{(4)}& \theta & =\pi /2-(\pi /2-{\theta }_{\mathrm{m}\mathrm{i}\mathrm{n}}){\eta }_{\mathrm{n}\mathrm{e}\mathrm{w}},\text{(5)}& \varphi & =f_{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{u}\mathrm{s}}\pi \zeta .\end{array}$$

• $r_{\mathrm{m}\mathrm{i}\mathrm{n}}$ and $r_{\mathrm{m}\mathrm{a}\mathrm{x}}$ are inner and outer radius of torus.
• ${\theta }_{\mathrm{m}\mathrm{i}\mathrm{n}}\in (0,\pi /2)$ 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.
• $f_{\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{u}\mathrm{s}}\in (0,1)$ is azimuthal fraction that the torus covers.
• $a_{\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}}\in [0,1)$ sets the level of equatorial compression for theta, with zero being none.

Member Data Documentation

help

constexpr Options::String grmhd::AnalyticData::SphericalTorus::help

staticconstexpr

Initial value:

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

---

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

• src/PointwiseFunctions/AnalyticData/GrMhd/SphericalTorus.hpp