SpECTRE  v2022.09.02
EquationsOfState::Spectral Class Reference

A spectral equation of state. More...

#include <Spectral.hpp>

Classes

struct  Coefficients
 
struct  ReferenceDensity
 
struct  ReferencePressure
 
struct  UpperDensity
 

Public Types

using options = tmpl::list< ReferenceDensity, ReferencePressure, Coefficients, UpperDensity >
 

Public Member Functions

 Spectral (const Spectral &)=default
 
Spectraloperator= (const Spectral &)=default
 
 Spectral (Spectral &&)=default
 
Spectraloperator= (Spectral &&)=default
 
 Spectral (double reference_density, double reference_pressure, std::vector< double > coefficients, double upper_density)
 
std::unique_ptr< EquationOfState< true, 1 > > get_clone () const override
 
bool operator== (const Spectral &rhs) const
 
bool operator!= (const Spectral &rhs) const
 
bool is_equal (const EquationOfState< true, 1 > &rhs) const override
 
 WRAPPED_PUPable_decl_base_template (SINGLE_ARG(EquationOfState< true, 1 >), Spectral)
 
double rest_mass_density_lower_bound () const override
 The lower bound of the rest mass density that is valid for this EOS.
 
double rest_mass_density_upper_bound () const override
 The upper bound of the rest mass density that is valid for this EOS.
 
double specific_internal_energy_lower_bound (const double) const override
 The lower bound of the specific internal energy that is valid for this EOS at the given rest mass density \(\rho\).
 
double specific_internal_energy_upper_bound (const double) const override
 The upper bound of the specific internal energy that is valid for this EOS at the given rest mass density \(\rho\).
 
double specific_enthalpy_lower_bound () const override
 The lower bound of the specific enthalpy that is valid for this EOS.
 

Static Public Attributes

static constexpr size_t thermodynamic_dim = 1
 
static constexpr bool is_relativistic = true
 
static constexpr Options::String help
 

Detailed Description

A spectral equation of state.

This equation of state is determined as a function of \(x = \ln(\rho/\rho_0)\) where \(\rho\) is the rest mass density and \(\rho_0\) is the provided reference density. The adiabatic index \(\Gamma(x)\) is defined such that

\begin{equation} \frac{d \ln p}{dx} = \Gamma(x) = \sum_{n=0}^N \gamma_n x^n \end{equation}

for the set of spectral coefficinets \(\gamma_n\) when \(0 < x < x_u = \ln(\rho_u/\rho_0)\), where \(\rho_u\) is the provided upper density.

For \( x < 0 \), \( \Gamma(x) = \gamma_0 \).

For \( x > x_u \), \( \Gamma(x) = \Gamma(x_u) \)

Member Data Documentation

◆ help

constexpr Options::String EquationsOfState::Spectral::help
staticconstexpr
Initial value:
= {
"A spectral equation of state. Defining x = log(rho/rho_0), Gamma(x) = "
"Sum_i gamma_i x^i, then the pressure is determined from d(log P)/dx = "
"Gamma(x) for x > 0. For x < 0 the EOS is a polytrope with "
"Gamma(x)=Gamma(0). For x > x_u = log(rho_u/rho_0), Gamma(x) = "
"Gamma(x_u).\n"
"To get smooth equations of state, it is recommended that the second "
"and third supplied coefficient should be 0. It is up to the user to "
"choose coefficients that are physically reasonable, e.g. that "
"satisfy causality."}

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