Smooth wave propagating in Minkowski spacetime. More...

#include <SmoothFlow.hpp>

Public Types
using	options = typename smooth_flow::options
Public Types inherited from RelativisticEuler::AnalyticSolution< Dim >
template<typename DataType>
using	tags

Public Member Functions
	SmoothFlow (const SmoothFlow &)=default
SmoothFlow &	operator= (const SmoothFlow &)=default
	SmoothFlow (SmoothFlow &&)=default
SmoothFlow &	operator= (SmoothFlow &&)=default
	SmoothFlow (const std::array< double, Dim > &mean_velocity, const std::array< double, Dim > &wavevector, double pressure, double adiabatic_index, double perturbation_size)
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
template<typename DataType>
auto	variables (const tnsr::I< DataType, Dim > &x, double t, tmpl::list< hydro::Tags::Temperature< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Temperature< DataType > >
template<typename DataType>
auto	variables (const tnsr::I< DataType, Dim > &x, double, tmpl::list< hydro::Tags::ElectronFraction< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::ElectronFraction< DataType > >
template<typename DataType, typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, Dim > &x, const double t, tmpl::list< Tags... >) const
	Retrieve a collection of hydro variables at (x, t)
template<typename DataType, typename Tag>
tuples::TaggedTuple< Tag >	variables (const tnsr::I< DataType, Dim > &x, double t, tmpl::list< Tag >) const
	Retrieve the metric variables.
template<typename DataType>
tuples::TaggedTuple< hydro::Tags::MagneticField< DataType, Dim > >	variables (const tnsr::I< DataType, Dim > &x, double t, tmpl::list< hydro::Tags::MagneticField< DataType, Dim > >) const
template<typename DataType>
tuples::TaggedTuple< hydro::Tags::DivergenceCleaningField< DataType > >	variables (const tnsr::I< DataType, Dim > &x, double t, tmpl::list< hydro::Tags::DivergenceCleaningField< DataType > >) const
void	pup (PUP::er &) override
const EquationsOfState::IdealFluid< IsRelativistic > &	equation_of_state () const
auto	variables (const tnsr::I< DataType, Dim > &x, double t, tmpl::list< hydro::Tags::RestMassDensity< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::RestMassDensity< DataType > >
	Retrieve hydro variable at (x, t)
auto	variables (const tnsr::I< DataType, Dim > &x, double t, tmpl::list< hydro::Tags::SpecificInternalEnergy< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::SpecificInternalEnergy< DataType > >
auto	variables (const tnsr::I< DataType, Dim > &x, double, tmpl::list< hydro::Tags::Pressure< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Pressure< DataType > >
auto	variables (const tnsr::I< DataType, Dim > &x, double, tmpl::list< hydro::Tags::SpatialVelocity< DataType, Dim > >) const -> tuples::TaggedTuple< hydro::Tags::SpatialVelocity< DataType, Dim > >
auto	variables (const tnsr::I< DataType, Dim > &x, double, tmpl::list< hydro::Tags::LorentzFactor< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::LorentzFactor< DataType > >
auto	variables (const tnsr::I< DataType, Dim > &x, double t, tmpl::list< hydro::Tags::SpecificEnthalpy< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::SpecificEnthalpy< DataType > >
Public Member Functions inherited from hydro::TemperatureInitialization< SmoothFlow< Dim > >
auto	variables (const tnsr::I< DataType, Dim > &x, 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 RelativisticEuler::AnalyticSolution< Dim >
static constexpr size_t	volume_dim = Dim

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

Detailed Description

template<size_t Dim>
class RelativisticEuler::Solutions::SmoothFlow< Dim >

Smooth wave propagating in Minkowski spacetime.

The relativistic Euler equations in Minkowski spacetime accept a solution with constant pressure and uniform spatial velocity provided that the rest mass density satisfies the advection equation

\begin{align*}\partial_t\rho + v^i\partial_i\rho = 0, \end{align*}

and the specific internal energy is a function of the rest mass density only, \(\epsilon = \epsilon(\rho)\). For testing purposes, this class implements this solution for the case where \(\rho\) is a sine wave. The user specifies the mean flow velocity of the fluid, the wavevector of the density profile, and the amplitude \(A\) of the density profile. In Cartesian coordinates \((x, y, z)\), and using dimensionless units, the primitive variables at a given time \(t\) are then

\begin{align*}\rho(\vec{x},t) &= 1 + A \sin(\vec{k}\cdot(\vec{x} - \vec{v}t)) \\ \vec{v}(\vec{x},t) &= [v_x, v_y, v_z]^{T},\\ P(\vec{x},t) &= P, \\ \epsilon(\vec{x}, t) &= \frac{P}{(\gamma - 1)\rho}\\ \end{align*}

where we have assumed \(\epsilon\) and \(\rho\) to be related through an equation mathematically equivalent to the equation of state of an ideal gas, where the pressure is held constant.

Member Function Documentation

◆ get_clone()

template<size_t Dim>

auto RelativisticEuler::Solutions::SmoothFlow< 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 RelativisticEuler::Solutions::SmoothFlow< Dim >::help

staticconstexpr

Initial value:

= {

"Smooth flow in Minkowski spacetime."}

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

src/PointwiseFunctions/AnalyticSolutions/RelativisticEuler/SmoothFlow.hpp

Public Types

Public Member Functions

Static Public Attributes

Friends

Detailed Description

Member Function Documentation

◆ get_clone()

Member Data Documentation

◆ help