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

Smooth density wave advecting across the domain. More...

#include <SmoothFlow.hpp>

Public Types
using	options = typename smooth_flow::options

Public Member Functions
	SmoothFlow (const SmoothFlow &)=default
SmoothFlow &	operator= (const SmoothFlow &)=default
	SmoothFlow (SmoothFlow &&)=default
SmoothFlow &	operator= (SmoothFlow &&)=default
auto	get_clone () const -> std::unique_ptr< evolution::initial_data::InitialData > override
	SmoothFlow (const std::array< double, Dim > &mean_velocity, const std::array< double, Dim > &wavevector, double pressure, double adiabatic_index, double perturbation_size)
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)
void	pup (PUP::er &) override
virtual auto	get_clone () const -> std::unique_ptr< InitialData >=0

Static Public Attributes
static constexpr Options::String	help

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

Detailed Description

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

Smooth density wave advecting across the domain.

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 NewtonianEuler::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 NewtonianEuler::Solutions::SmoothFlow< Dim >::help

staticconstexpr

Initial value:

= {
      "Smooth density wave advecting across a domain."}

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

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