Analytic initial data for a Kelvin-Helmholtz instability simulation. More...

#include <KhInstability.hpp>

Classes
struct	AdiabaticIndex
	The adiabatic index of the fluid. More...

struct	BackgroundDensity
	The mass density outside of the strip. More...

struct	BackgroundVelocity
	The velocity along $x$ outside of the strip. More...

struct	MagneticField
	The uniform magnetic field. More...

struct	PerturbAmplitude
	The amplitude of the perturbation. More...

struct	PerturbWidth
	The characteristic length for the width of the perturbation. More...

struct	Pressure
	The initial (constant) pressure of the fluid. More...

struct	StripBimedianHeight
	The vertical coordinate of the horizontal bimedian of the strip. More...

struct	StripDensity
	The mass density in the strip. More...

struct	StripThickness
	The thickness of the strip. More...

struct	StripVelocity
	The velocity along $x$ in the strip. More...

Public Types
using	equation_of_state_type = EquationsOfState::IdealFluid< true >

using	options = implementation defined

Public Types inherited from grmhd::AnalyticDataBase
template<typename DataType >
using	tags = implementation defined

Public Member Functions
	KhInstability (const KhInstability &)=default

KhInstability &	operator= (const KhInstability &)=default

	KhInstability (KhInstability &&)=default

KhInstability &	operator= (KhInstability &&)=default

	KhInstability (double adiabatic_index, double strip_bimedian_height, double strip_thickness, double strip_density, double strip_velocity, double background_density, double background_velocity, double pressure, double perturbation_amplitude, double perturbation_width, const std::array< double, 3 > &magnetic_field)

auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override

template<typename DataType , typename Tag1 , typename Tag2 , typename... Tags>
tuples::TaggedTuple< Tag1, Tag2, Tags... >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tag1, Tag2, Tags... >) const
	Retrieve a collection of hydrodynamic variables at position x.

template<typename DataType , typename Tag , Requires< tmpl::list_contains_v< gr::analytic_solution_tags< 3, DataType >, Tag > > = nullptr>
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< Tag >) const
	Retrieve the metric variables.

const EquationsOfState::IdealFluid< true > &	equation_of_state () const

void	pup (PUP::er &) override


template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::RestMassDensity< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::RestMassDensity< DataType > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::ElectronFraction< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::ElectronFraction< DataType > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpecificInternalEnergy< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::SpecificInternalEnergy< DataType > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::Pressure< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Pressure< DataType > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpatialVelocity< DataType, 3 > >) const -> tuples::TaggedTuple< hydro::Tags::SpatialVelocity< DataType, 3 > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::MagneticField< DataType, 3 > >) const -> tuples::TaggedTuple< hydro::Tags::MagneticField< DataType, 3 > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::DivergenceCleaningField< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::DivergenceCleaningField< DataType > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::LorentzFactor< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::LorentzFactor< DataType > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::SpecificEnthalpy< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::SpecificEnthalpy< DataType > >
	Retrieve the GRMHD variables at a given position.

template<typename DataType >
auto	variables (const tnsr::I< DataType, 3 > &x, tmpl::list< hydro::Tags::Temperature< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Temperature< DataType > >
	Retrieve the GRMHD variables at a given position.

virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

Public Member Functions inherited from hydro::TemperatureInitialization< KhInstability >
auto	variables (const tnsr::I< DataType, Dim > &x, tmpl::list< hydro::Tags::Temperature< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Temperature< DataType > >

auto	variables (const tnsr::I< DataType, Dim > &x, const double t, tmpl::list< hydro::Tags::Temperature< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Temperature< DataType > >

auto	variables (ExtraVars &extra_variables, const tnsr::I< DataType, Dim > &x, Args &... extra_args, tmpl::list< hydro::Tags::Temperature< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Temperature< DataType > >

Static Public Attributes
static constexpr Options::String	help

Static Public Attributes inherited from grmhd::AnalyticDataBase
static constexpr size_t	volume_dim = 3_st

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

bool	operator!= (const KhInstability &lhs, const KhInstability &rhs)

Detailed Description

Analytic initial data for a Kelvin-Helmholtz instability simulation.

This is similar to the data from Section 4.7 of [18]. The initial state consists of a horizontal strip of mass density $ρ_{in}$ moving with horizontal speed $v_{in}$ . The rest of the fluid possesses mass density $ρ_{out}$ , and its horizontal velocity is $v_{out}$ , both constant. Mathematically,

$\begin{aligned} ρ (x, y) = {\begin{cases} ρ_{in}, & | y - y_{mid} | < b / 2 \\ ρ_{out}, & otherwise, \end{cases} \end{aligned}$

and

$\begin{aligned} v_{x} (x, y) = {\begin{cases} v_{in}, & | y - y_{mid} | < b / 2 \\ v_{out}, & otherwise, \end{cases} \end{aligned}$

where $b > 0$ is the thickness of the strip, and $y = y_{mid}$ is its horizontal bimedian. The initial pressure is set equal to a constant, and the system is evolved assuming an ideal fluid of known adiabatic index. Finally, in order to excite the instability, the vertical velocity is initialized to

$\begin{aligned} v_{y} (x, y) = A \sin (4 π x) [\exp (- \frac{(y - y_{top})^{2}}{2 σ^{2}}) + \exp (- \frac{(y - y_{bot})^{2}}{2 σ^{2}})], \end{aligned}$

whose net effect is to perturb the horizontal boundaries of the strip periodically along the $x -$ axis. Here $A$ is the amplitude, $σ$ is a characteristic length for the perturbation width, and $y_{top} = y_{mid} + b / 2$ and $y_{bot} = y_{mid} - b / 2$ are the vertical coordinates of the top and bottom boundaries of the strip, respectively.

A uniform magnetic field can be added.

Member Function Documentation

◆ get_clone()

auto grmhd::AnalyticData::KhInstability::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

Member Data Documentation

◆ help

constexpr Options::String grmhd::AnalyticData::KhInstability::help

staticconstexpr

Initial value:

= {

"Initial data to simulate the magnetized KH instability."}

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

src/PointwiseFunctions/AnalyticData/GrMhd/KhInstability.hpp

Classes

Public Types

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Function Documentation

◆ get_clone()

Member Data Documentation

◆ help