RelativisticEuler::Solutions::SmoothFlow< Dim > Class Template Reference

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 = implementation defined

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
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0
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 > >
auto	variables (const tnsr::I< DataType, Dim > &x, const double t, tmpl::list< hydro::Tags::Temperature< DataType > >) const -> tuples::TaggedTuple< hydro::Tags::Temperature< DataType > >
auto	variables (ExtraVars &extra_variables, const tnsr::I< DataType, Dim > &x, Args &... extra_args, 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

$$\begin{array}{r}{\partial }_t\rho +v^i{\partial }_i\rho =0,\end{array}$$

and the specific internal energy is a function of the rest mass density only, $ϵ=ϵ(\rho )$. 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

$$\begin{array}{rl}\rho (\overrightarrow{x},t)& =1+A\sin (\overrightarrow{k}\cdot (\overrightarrow{x}-\overrightarrow{v}t))\\ \overrightarrow{v}(\overrightarrow{x},t)& =[v_x,v_y,v_z{]}^T,\\ P(\overrightarrow{x},t)& =P,\\ ϵ(\overrightarrow{x},t)& =\frac{P}{(\gamma -1)\rho }\end{array}$$

where we have assumed $ϵ$ 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>

constexpr Options::String RelativisticEuler::Solutions::SmoothFlow< Dim >::help

staticconstexpr

Initial value:

= {
      "Smooth flow in Minkowski spacetime."}

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

• src/PointwiseFunctions/AnalyticSolutions/RelativisticEuler/SmoothFlow.hpp