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
using	source_term_type = Sources::NoSource

Public Member Functions
	SmoothFlow (const SmoothFlow &)=delete
SmoothFlow &	operator= (const SmoothFlow &)=delete
	SmoothFlow (SmoothFlow &&) noexcept=default
SmoothFlow &	operator= (SmoothFlow &&) noexcept=default
	SmoothFlow (const std::array< double, Dim > &mean_velocity, const std::array< double, Dim > &wavevector, double pressure, double adiabatic_index, double perturbation_size) noexcept
	SmoothFlow (CkMigrateMessage *msg) noexcept
template<typename DataType >
tuples::TaggedTuple< Tags::MassDensity< DataType > >	variables (const tnsr::I< DataType, Dim > &x, const double t, tmpl::list< Tags::MassDensity< DataType > >) const noexcept
template<typename DataType >
tuples::TaggedTuple< Tags::Velocity< DataType, Dim > >	variables (const tnsr::I< DataType, Dim > &x, const double t, tmpl::list< Tags::Velocity< DataType, Dim > >) const noexcept
template<typename DataType >
tuples::TaggedTuple< Tags::Pressure< DataType > >	variables (const tnsr::I< DataType, Dim > &x, const double t, tmpl::list< Tags::Pressure< DataType > >) const noexcept
template<typename DataType >
tuples::TaggedTuple< Tags::SpecificInternalEnergy< DataType > >	variables (const tnsr::I< DataType, Dim > &x, const double t, tmpl::list< Tags::SpecificInternalEnergy< DataType > >) const noexcept
template<typename DataType , typename... Tags>
tuples::TaggedTuple< Tags... >	variables (const tnsr::I< DataType, Dim > &x, const double t, tmpl::list< Tags... >) const noexcept
	Retrieve a collection of hydro variables at (x, t)
void	pup (PUP::er &) noexcept

Static Public Attributes
static constexpr Options::String	help

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

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 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."}