ScalarWave::Solutions::PlaneWave< Dim > Class Template Reference

A plane wave solution to the Euclidean wave equation. More...

#include <PlaneWave.hpp>

Classes
struct	Center
struct	Profile
struct	WaveVector

Public Types
using	options = tmpl::list< WaveVector, Center, Profile >
using	tags = tmpl::list< Tags::Psi, Tags::Pi, Tags::Phi< 3 >, ::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim > > >

Public Member Functions
	PlaneWave (std::array< double, Dim > wave_vector, std::array< double, Dim > center, std::unique_ptr< MathFunction< 1, Frame::Inertial > > profile)
	PlaneWave (const PlaneWave &)
PlaneWave &	operator= (const PlaneWave &)
	PlaneWave (PlaneWave &&)=default
PlaneWave &	operator= (PlaneWave &&)=default
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
template<typename T >
Scalar< T >	psi (const tnsr::I< T, Dim > &x, double t) const
	The value of the scalar field.
template<typename T >
Scalar< T >	dpsi_dt (const tnsr::I< T, Dim > &x, double t) const
	The time derivative of the scalar field.
template<typename T >
tnsr::i< T, Dim >	dpsi_dx (const tnsr::I< T, Dim > &x, double t) const
	The spatial derivatives of the scalar field.
template<typename T >
Scalar< T >	d2psi_dt2 (const tnsr::I< T, Dim > &x, double t) const
	The second time derivative of the scalar field.
template<typename T >
tnsr::i< T, Dim >	d2psi_dtdx (const tnsr::I< T, Dim > &x, double t) const
	The second mixed derivatives of the scalar field.
template<typename T >
tnsr::ii< T, Dim >	d2psi_dxdx (const tnsr::I< T, Dim > &x, double t) const
	The second spatial derivatives of the scalar field.
tuples::TaggedTuple< Tags::Psi, Tags::Pi, Tags::Phi< Dim > >	variables (const tnsr::I< DataVector, Dim > &x, double t, tmpl::list< Tags::Psi, Tags::Pi, Tags::Phi< Dim > >) const
	Retrieve the evolution variables at time t and spatial coordinates x
tuples::TaggedTuple<::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim > > >	variables (const tnsr::I< DataVector, Dim > &x, double t, tmpl::list<::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim > > >) const
	Retrieve the time derivative of the evolution variables at time t and spatial coordinates x More...
void	pup (PUP::er &p) override
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

Static Public Attributes
static constexpr size_t	volume_dim = Dim
static constexpr Options::String	help

Friends
template<size_t LocalDim>
bool	operator== (const PlaneWave< LocalDim > &lhs, const PlaneWave< LocalDim > &rhs)
template<size_t LocalDim>
bool	operator!= (const PlaneWave< LocalDim > &lhs, const PlaneWave< LocalDim > &rhs)

Detailed Description

template<size_t Dim>
class ScalarWave::Solutions::PlaneWave< Dim >

A plane wave solution to the Euclidean wave equation.

The solution is given by \(\Psi(\vec{x},t) = F(u(\vec{x},t))\) where the profile \(F\) of the plane wave is an arbitrary one-dimensional function of \(u = \vec{k} \cdot (\vec{x} - \vec{x_o}) - \omega t\) with the wave vector \(\vec{k}\), the frequency \(\omega = ||\vec{k}||\) and initial center of the profile \(\vec{x_o}\).

Template Parameters

Dim	the spatial dimension of the solution

Member Function Documentation

get_clone()

template<size_t Dim>

auto ScalarWave::Solutions::PlaneWave< Dim >::get_clone ( ) const -> std::unique_ptr< evolution::initial_data::InitialData >

overridevirtual

Implements evolution::initial_data::InitialData.

variables()

template<size_t Dim>

tuples::TaggedTuple<::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim > > > ScalarWave::Solutions::PlaneWave< Dim >::variables	(	const tnsr::I< DataVector, Dim > &	x,
		double	t,
		tmpl::list<::Tags::dt< Tags::Psi >, ::Tags::dt< Tags::Pi >, ::Tags::dt< Tags::Phi< Dim > > >
	)		const

Retrieve the time derivative of the evolution variables at time t and spatial coordinates x

Note

This function's expected use case is setting the past time derivative values for Adams-Bashforth-like steppers.

Member Data Documentation

help

template<size_t Dim>

constexpr Options::String ScalarWave::Solutions::PlaneWave< Dim >::help

staticconstexpr

Initial value:

= {
      "A plane wave solution of the Euclidean wave equation"}

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

• src/PointwiseFunctions/AnalyticSolutions/WaveEquation/PlaneWave.hpp