NewtonianEuler::AnalyticData::KhInstability< Dim > Class Template Reference

Initial data to simulate the Kelvin-Helmholtz instability. 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	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< false >
using	options = tmpl::list< AdiabaticIndex, StripBimedianHeight, StripThickness, StripDensity, StripVelocity, BackgroundDensity, BackgroundVelocity, Pressure, PerturbAmplitude, PerturbWidth >

Public Member Functions
	KhInstability (const KhInstability &)=default
KhInstability &	operator= (const KhInstability &)=default
	KhInstability (KhInstability &&)=default
KhInstability &	operator= (KhInstability &&)=default
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
	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)
template<typename DataType , typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, Dim, Frame::Inertial > &x, tmpl::list< Tags... >) const
	Retrieve a collection of hydrodynamic variables at position x.
const EquationsOfState::IdealFluid< false > &	equation_of_state () const
void	pup (PUP::er &) override
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

Static Public Attributes
static constexpr Options::String	help

Friends
template<size_t SpatialDim>
bool	operator== (const KhInstability< SpatialDim > &lhs, const KhInstability< SpatialDim > &rhs)

Detailed Description

template<size_t Dim>
class NewtonianEuler::AnalyticData::KhInstability< Dim >

Initial data to simulate the Kelvin-Helmholtz instability.

For comparison purposes, this class implements the planar shear of [159], which is evolved using periodic boundary conditions. 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.

Note

The periodic form of the perturbation enforces the horizontal extent of the domain to be a multiple of 0.5. The domain chosen in [159] is the square \([0, 1]^2\), which covers two wavelengths of the perturbation. In addition, the authors ran their simulations using

AdiabaticIndex: 1.4
StripBimedianHeight: 0.5
StripThickness: 0.5
StripDensity: 2.0
StripVelocity: 0.5
BackgroundDensity: 1.0
BackgroundVelocity: -0.5
Pressure: 2.5
PerturbAmplitude: 0.1
PerturbWidth: 0.035355339059327376 # 0.05/sqrt(2)

Note

This class can be used to initialize 2D and 3D data. In 3D, the strip is aligned to the \(xy-\)plane, and the vertical direction is taken to be the \(z-\)axis.

Member Function Documentation

get_clone()

template<size_t Dim>

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

overridevirtual

Implements evolution::initial_data::InitialData.

Member Data Documentation

help

template<size_t Dim>

constexpr Options::String NewtonianEuler::AnalyticData::KhInstability< Dim >::help

staticconstexpr

Initial value:

= {
      "Initial data to simulate the KH instability."}

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

• src/PointwiseFunctions/AnalyticData/NewtonianEuler/KhInstability.hpp