Magnetized fluid disk orbiting a Kerr black hole. More...

#include <MagnetizedFmDisk.hpp>

Classes
struct	BFieldNormGridRes
	Grid resolution used in magnetic field normalization. More...

struct	InversePlasmaBeta
	The maximum-magnetic-pressure-to-maximum-fluid-pressure ratio. More...

struct	ThresholdDensity
	The rest mass density (in units of the maximum rest mass density in the disk) below which the matter in the disk is initially unmagetized. More...

Public Types
template<typename DataType >
using	tags = tmpl::push_back< typename gr::AnalyticSolution< 3 >::template tags< DataType >, hydro::Tags::RestMassDensity< DataType >, hydro::Tags::SpecificInternalEnergy< DataType >, hydro::Tags::Pressure< DataType >, hydro::Tags::SpatialVelocity< DataType, 3 >, hydro::Tags::MagneticField< DataType, 3 >, hydro::Tags::DivergenceCleaningField< DataType >, hydro::Tags::LorentzFactor< DataType >, hydro::Tags::SpecificEnthalpy< DataType > >

using	options = tmpl::push_back< fm_disk::options, ThresholdDensity, InversePlasmaBeta, BFieldNormGridRes >

using	equation_of_state_type = EquationsOfState::PolytropicFluid< true >

Public Member Functions
	MagnetizedFmDisk (const MagnetizedFmDisk &)=delete

MagnetizedFmDisk &	operator= (const MagnetizedFmDisk &)=delete

	MagnetizedFmDisk (MagnetizedFmDisk &&) noexcept=default

MagnetizedFmDisk &	operator= (MagnetizedFmDisk &&) noexcept=default

	MagnetizedFmDisk (double bh_mass, double bh_dimless_spin, double inner_edge_radius, double max_pressure_radius, double polytropic_constant, double polytropic_exponent, double threshold_density, double inverse_plasma_beta, size_t normalization_grid_res=BFieldNormGridRes::suggested_value()) noexcept

void	pup (PUP::er &) noexcept

const EquationsOfState::PolytropicFluid< true > &	equation_of_state () const noexcept

template<typename DataType , typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, 3 > &x, const double t, tmpl::list< Tags... >) const noexcept
	The fluid variables in Cartesian Kerr-Schild coordinates at `(x, t)` More...

template<typename DataType , typename Tag >
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataType, 3 > &x, const double t, tmpl::list< Tag >) const noexcept

template<typename DataType , bool NeedSpacetime>
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::RestMassDensity< DataType > >, const IntermediateVariables< DataType, NeedSpacetime > &vars, size_t index) const noexcept -> tuples::TaggedTuple< hydro::Tags::RestMassDensity< DataType > >

template<typename DataType , bool NeedSpacetime>
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpecificEnthalpy< DataType > >, const IntermediateVariables< DataType, NeedSpacetime > &vars, size_t index) const noexcept -> tuples::TaggedTuple< hydro::Tags::SpecificEnthalpy< DataType > >

template<typename DataType , bool NeedSpacetime>
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::Pressure< DataType > >, const IntermediateVariables< DataType, NeedSpacetime > &vars, size_t index) const noexcept -> tuples::TaggedTuple< hydro::Tags::Pressure< DataType > >

template<typename DataType , bool NeedSpacetime>
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpecificInternalEnergy< DataType > >, const IntermediateVariables< DataType, NeedSpacetime > &vars, size_t index) const noexcept -> tuples::TaggedTuple< hydro::Tags::SpecificInternalEnergy< DataType > >

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpatialVelocity< DataType, 3 > >, const IntermediateVariables< DataType, true > &vars, size_t index) const noexcept -> tuples::TaggedTuple< hydro::Tags::SpatialVelocity< DataType, 3 > >

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::LorentzFactor< DataType > >, const IntermediateVariables< DataType, true > &vars, size_t index) const noexcept -> tuples::TaggedTuple< hydro::Tags::LorentzFactor< DataType > >

template<typename DataType , bool NeedSpacetime>
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::MagneticField< DataType, 3 > >, const IntermediateVariables< DataType, NeedSpacetime > &vars, size_t index) const noexcept -> tuples::TaggedTuple< hydro::Tags::MagneticField< DataType, 3 > >

template<typename DataType , bool NeedSpacetime>
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::DivergenceCleaningField< DataType > >, const IntermediateVariables< DataType, NeedSpacetime > &vars, size_t index) const noexcept -> tuples::TaggedTuple< hydro::Tags::DivergenceCleaningField< DataType > >

template<typename DataType , typename Tag , Requires< not tmpl::list_contains_v< hydro::grmhd_tags< DataType >, Tag > > = nullptr>
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataType, 3 > &, tmpl::list< Tag >, IntermediateVariables< DataType, true > &vars, const size_t index) const noexcept


template<typename DataType , typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tags... >) const noexcept
	The grmhd variables in Cartesian Kerr-Schild coordinates at `(x, t)` More...

template<typename DataType , typename Tag >
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tag >) const noexcept
	The grmhd variables in Cartesian Kerr-Schild coordinates at `(x, t)` More...

Static Public Attributes
static constexpr size_t	volume_dim = 3_st

static constexpr Options::String	help

Friends
bool	operator== (const MagnetizedFmDisk &lhs, const MagnetizedFmDisk &rhs) noexcept

Detailed Description

Magnetized fluid disk orbiting a Kerr black hole.

In the context of simulating accretion disks, this class implements a widely used (e.g. [47], [89], [111]) initial setup for the GRMHD variables, consisting of a Fishbone-Moncrief disk [42] (see also RelativisticEuler::Solutions::FishboneMoncriefDisk), threaded by a weak poloidal magnetic field. The magnetic field is constructed from an axially symmetric toroidal magnetic potential which, in Kerr ("spherical Kerr-Schild") coordinates, has the form

\begin{align*} A_\phi(r,\theta) \propto \text{max}(\rho(r,\theta) - \rho_\text{thresh}, 0), \end{align*}

where \(\rho_\text{thresh}\) is a user-specified threshold density that confines the magnetic flux to exist inside of the fluid disk only. A commonly used value for this parameter is \(\rho_\text{thresh} = 0.2\rho_\text{max}\), where \(\rho_\text{max}\) is the maximum value of the rest mass density in the disk. Using this potential, the Eulerian magnetic field takes the form

\begin{align*} B^r = \frac{F_{\theta\phi}}{\sqrt{\gamma}},\quad B^\theta = \frac{F_{\phi r}}{\sqrt{\gamma}},\quad B^\phi = 0, \end{align*}

where \(F_{ij} = \partial_i A_j - \partial_j A_i\) are the spatial components of the Faraday tensor, and \(\gamma\) is the determinant of the spatial metric. The magnetic field is then normalized so that the plasma- \(\beta\) parameter, \(\beta = 2p/b^2\), equals some value specified by the user. Here, \(p\) is the fluid pressure, and

\begin{align*} b^2 = b^\mu b_\mu = \frac{B_iB^i}{W^2} + (B^iv_i)^2 \end{align*}

is the norm of the magnetic field in the fluid frame, with \(v_i\) being the spatial velocity, and \(W\) the Lorentz factor.

Member Function Documentation

◆ variables() [1/3]

template<typename DataType , typename... Tags>

tuples::TaggedTuple< Tags... > RelativisticEuler::Solutions::FishboneMoncriefDisk::variables	(	const tnsr::I< DataType, 3 > &	x,
		const double	t,
		tmpl::list< Tags... >
	)		const

inlinenoexcept

The fluid variables in Cartesian Kerr-Schild coordinates at (x, t)

Note: The functions are optimized for retrieving the hydro variables before the metric variables.

◆ variables() [2/3]

template<typename DataType , typename Tag >

tuples::TaggedTuple< Tag > grmhd::AnalyticData::MagnetizedFmDisk::variables	(	const tnsr::I< DataType, 3 > &	x,
		tmpl::list< Tag >
	)		const

inlinenoexcept

The grmhd variables in Cartesian Kerr-Schild coordinates at (x, t)

Note: The functions are optimized for retrieving the hydro variables before the metric variables.

◆ variables() [3/3]

template<typename DataType , typename... Tags>

tuples::TaggedTuple< Tags... > grmhd::AnalyticData::MagnetizedFmDisk::variables	(	const tnsr::I< DataType, 3 > &	x,
		tmpl::list< Tags... >
	)		const

inlinenoexcept

The grmhd variables in Cartesian Kerr-Schild coordinates at (x, t)

Note: The functions are optimized for retrieving the hydro variables before the metric variables.

Member Data Documentation

◆ help

constexpr Options::String grmhd::AnalyticData::MagnetizedFmDisk::help

staticconstexpr

Initial value:

= {

"Magnetized Fishbone-Moncrief disk."}

Classes

Public Types

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Function Documentation

◆ variables() [1/3]

◆ variables() [2/3]

◆ variables() [3/3]

Member Data Documentation

◆ help