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

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

#include <StandingWave.hpp>

Classes
struct	Amplitude
struct	Center
struct	WaveVector

Public Types
using	options = tmpl::list<WaveVector, Center, Amplitude>
using	tags

Public Member Functions
	StandingWave (std::array< double, Dim > wave_vector, std::array< double, Dim > center, double amplitude)
	StandingWave (const StandingWave &)=default
StandingWave &	operator= (const StandingWave &)=default
	StandingWave (StandingWave &&)=default
StandingWave &	operator= (StandingWave &&)=default
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
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 derivatives of the evolution variables.
void	pup (PUP::er &p) override

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

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

Detailed Description

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

A standing wave solution to the Euclidean wave equation.

The solution is given by \(\Psi(\vec{x},t) = A \sin(\vec{k} \cdot (\vec{x} - \vec{x_0})) \cos(\omega t)\) with the wave vector \(\vec{k}\), frequency \(\omega = ||\vec{k}||\), amplitude \(A\), and center \(\vec{x_0}\). The first-order variables follow the ScalarWave conventions \(\Pi = -\partial_t \Psi\) and \(\Phi_i = \partial_i \Psi\).

At \(t = 0\) this gives \(\Pi = 0\), meaning the initial data decomposes into equal left-moving and right-moving components.

Template Parameters

Dim	the spatial dimension of the solution

Member Typedef Documentation

tags

template<size_t Dim>

using ScalarWave::Solutions::StandingWave< Dim >::tags

Initial value:

 
      tmpl::list<Tags::Psi, Tags::Pi, Tags::Phi<Dim>, ::Tags::dt<Tags::Psi>,
                 ::Tags::dt<Tags::Pi>, ::Tags::dt<Tags::Phi<Dim>>>

Member Function Documentation

get_clone()

template<size_t Dim>

auto ScalarWave::Solutions::StandingWave< 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>

Options::String ScalarWave::Solutions::StandingWave< Dim >::help

staticconstexpr

Initial value:

= {
      "A standing wave solution of the Euclidean wave equation. "
      "Psi = A sin(k.(x-x0)) cos(omega t), with omega = |k|. "
      "At t=0, Pi=0 so the wave has equal left- and right-moving components."}

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

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