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grmhd::AnalyticData::KhInstability Class Reference
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 = tmpl::list< AdiabaticIndex, StripBimedianHeight, StripThickness, StripDensity, StripVelocity, BackgroundDensity, BackgroundVelocity, Pressure, PerturbAmplitude, PerturbWidth, MagneticField > |
 Public Types inherited from grmhd::AnalyticDataBase | |
| template<typename DataType > | |
| using | tags = tmpl::push_back< typename gr::AnalyticSolution< 3 >::template tags< DataType >, hydro::Tags::RestMassDensity< DataType >, hydro::Tags::ElectronFraction< DataType >, hydro::Tags::SpecificInternalEnergy< DataType >, hydro::Tags::Temperature< 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 > > |
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 [17]. The initial state consists of a horizontal strip of mass density \(\rho_\text{in}\) moving with horizontal speed \(v_{\text{in}}\). The rest of the fluid possesses mass density \(\rho_\text{out}\), and its horizontal velocity is \(v_{\text{out}}\), both constant. Mathematically,
\begin{align*} \rho(x, y) = \begin{cases} \rho_\text{in}, & \left|y - y_\text{mid}\right| < b/2\\ \rho_\text{out}, & \text{otherwise}, \end{cases} \end{align*}
and
\begin{align*} v_x(x, y) = \begin{cases} v_{\text{in}}, & \left|y - y_\text{mid}\right| < b/2\\ v_{\text{out}}, & \text{otherwise}, \end{cases} \end{align*}
where \(b > 0\) is the thickness of the strip, and \(y = y_\text{mid}\) 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{align*} v_y(x, y) = A\sin(4\pi x) \left[\exp\left(-\dfrac{(y - y_\text{top})^2}{2\sigma^2}\right) + \exp\left(-\dfrac{(y - y_\text{bot})^2}{2\sigma^2}\right)\right], \end{align*}
whose net effect is to perturb the horizontal boundaries of the strip periodically along the \(x-\)axis. Here \(A\) is the amplitude, \(\sigma\) is a characteristic length for the perturbation width, and \(y_\text{top} = y_\text{mid} + b/2\) and \(y_\text{bot} = y_\text{mid} - b/2\) 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()
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overridevirtual |
Implements evolution::initial_data::InitialData.
Member Data Documentation
◆ help
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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