ForceFree::Solutions::AlfvenWave Class Reference

Alfven wave propagating along \(x\) direction in flat spacetime with the wave speed \(\mu\). More...

#include <AlfvenWave.hpp>

Classes
struct	WaveSpeed
	The wave speed. More...

Public Types
using	options = tmpl::list<WaveSpeed>

Public Member Functions
	AlfvenWave (const AlfvenWave &)=default
AlfvenWave &	operator= (const AlfvenWave &)=default
	AlfvenWave (AlfvenWave &&)=default
AlfvenWave &	operator= (AlfvenWave &&)=default
	AlfvenWave (double wave_speed, const Options::Context &context={})
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
void	pup (PUP::er &p) override
template<typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataVector, 3 > &x, const double t, tmpl::list< Tags... >) const
	Retrieve a collection of EM variables at (x, t)
template<typename Tag>
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataVector, 3 > &x, double t, tmpl::list< Tag >) const
	Retrieve the metric variables.
Public Member Functions inherited from evolution::initial_data::InitialData
virtual const InitialData &	unwrap () const
	Unwrap wrapper types (e.g. WithNoise, which wraps analytic initial data and adds random noise) to reach the underlying analytic solution or data.

Static Public Attributes
static constexpr Options::String	help

Friends
bool	operator== (const AlfvenWave &lhs, const AlfvenWave &rhs)
auto	variables (const tnsr::I< DataVector, 3 > &x, double t, tmpl::list< Tags::TildeE >) const -> tuples::TaggedTuple< Tags::TildeE >
	Retrieve the EM variables at (x,t).
auto	variables (const tnsr::I< DataVector, 3 > &x, double t, tmpl::list< Tags::TildeB >) const -> tuples::TaggedTuple< Tags::TildeB >
	Retrieve the EM variables at (x,t).
auto	variables (const tnsr::I< DataVector, 3 > &x, double t, tmpl::list< Tags::TildeQ >) const -> tuples::TaggedTuple< Tags::TildeQ >
	Retrieve the EM variables at (x,t).
static auto	variables (const tnsr::I< DataVector, 3 > &x, double t, tmpl::list< Tags::TildePsi >) -> tuples::TaggedTuple< Tags::TildePsi >
	Retrieve the EM variables at (x,t).
static auto	variables (const tnsr::I< DataVector, 3 > &x, double t, tmpl::list< Tags::TildePhi >) -> tuples::TaggedTuple< Tags::TildePhi >
	Retrieve the EM variables at (x,t).

Detailed Description

Alfven wave propagating along \(x\) direction in flat spacetime with the wave speed \(\mu\).

This test problem was introduced in [123] with \(\mu=0\).

In the wave frame (with prime superscript), the stationary solution is given by

\begin{align*} B'_x & = B'_y = 1.0 ,\\ B'_z(x') & = \left\{\begin{array}{ll} 1.0 & \text{if } x' < -0.1 \\ 1.15 + 0.15 \sin (5\pi x') & \text{if } -0.1 < x' < 0.1 \\ 1.3 & \text{if } x' > 0.1 \end{array}\right\} ,\\ E'_x & = -B'_z ,\\ E'_y & = 0 \\ E'_z & = 1.0 \end{align*}

and

\begin{align*} q' & = \left\{\begin{array}{ll} - 0.75 \pi \cos (5 \pi x') & \text{if } -0.1 < x' < 0.1 \\ 0 & \text{otherwise} \end{array}\right\} , \\ J_x' & = 0 , \\ J_y' & = \left\{\begin{array}{ll} - 0.75 \pi \cos (5 \pi x') & \text{if } -0.1 < x' < 0.1 \\ 0 & \text{otherwise} \end{array}\right\} , \\ J_z' & = 0 . \end{align*}

Applying the Lorentz transformation, electromagnetic fields and 4-current in the grid frame at \(t=0\) are given by

\begin{align*} E_x(x) & = E'_x(\gamma x) , \\ E_y(x) & = \gamma[E'_y(\gamma x) + \mu B'_z(\gamma x)] , \\ E_z(x) & = \gamma[E'_z(\gamma x) - \mu B'_y(\gamma x)] , \\ B_x(x) & = B'_x(\gamma x), \\ B_y(x) & = \gamma[ B'_y(\gamma x) - \mu E'_z(\gamma x) ] , \\ B_z(x) & = \gamma[ B'_z(\gamma x) + \mu E'_y(\gamma x) ] . \end{align*}

and

\begin{align*} q(x) & = \gamma q'(\gamma x) , \\ J_x(x) & = \gamma \mu q'(\gamma x) , \\ J_y(x) & = J_y'(\gamma x) , \\ J_z(x) & = 0 . \end{align*}

The wave speed can be chosen any value \(-1 < \mu < 1\), and the solution at time \(t\) is \(f(x,t) = f(x-\mu t, 0)\) for any physical quantities.

Member Function Documentation

get_clone()

auto ForceFree::Solutions::AlfvenWave::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

Member Data Documentation

help

Options::String ForceFree::Solutions::AlfvenWave::help

staticconstexpr

Initial value:

{
      "Alfven wave propagating along x direction in flat spacetime with the "
      "wave speed mu"}

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

• src/PointwiseFunctions/AnalyticSolutions/ForceFree/AlfvenWave.hpp