EquationsOfState::EquationOfState< IsRelativistic, 3 > Class Template Reference

Base class for equations of state which need three independent thermodynamic variables in order to determine the pressure. More...

#include <EquationOfState.hpp>

Public Types
using	creatable_classes = implementation defined

Public Member Functions
	EquationOfState (const EquationOfState &)=default
EquationOfState &	operator= (const EquationOfState &)=default
	EquationOfState (EquationOfState &&)=default
EquationOfState &	operator= (EquationOfState &&)=default
	EquationOfState (CkMigrateMessage *msg)
	WRAPPED_PUPable_abstract (EquationOfState)
virtual std::unique_ptr< EquationOfState< IsRelativistic, 3 > >	get_clone () const =0
virtual bool	is_equal (const EquationOfState< IsRelativistic, 3 > &rhs) const =0
virtual std::unique_ptr< EquationOfState< IsRelativistic, 3 > >	promote_to_3d_eos () const
virtual bool	is_barotropic () const =0
	Returns true if the EOS is barotropic. More...
virtual bool	is_equilibrium () const =0
	Returns true if the EOS is in beta-equilibrium. More...
virtual double	electron_fraction_lower_bound () const =0
	The lower bound of the electron fraction that is valid for this EOS. More...
virtual double	electron_fraction_upper_bound () const =0
	The upper bound of the electron fraction that is valid for this EOS. More...
virtual double	rest_mass_density_lower_bound () const =0
	The lower bound of the rest mass density that is valid for this EOS. More...
virtual double	rest_mass_density_upper_bound () const =0
	The upper bound of the rest mass density that is valid for this EOS. More...
virtual double	specific_internal_energy_lower_bound (const double rest_mass_density, const double electron_fraction) const =0
	The lower bound of the specific internal energy that is valid for this EOS at the given rest mass density $\rho$ and electron fraction $Y_e$. More...
virtual double	specific_internal_energy_upper_bound (const double rest_mass_density, const double electron_fraction) const =0
	The upper bound of the specific internal energy that is valid for this EOS at the given rest mass density $\rho$ and electron fraction $Y_e$. More...
virtual double	specific_enthalpy_lower_bound () const =0
	The lower bound of the specific enthalpy that is valid for this EOS. More...
virtual double	temperature_lower_bound () const =0
	The lower bound of the temperature that is valid for this EOS. More...
virtual double	temperature_upper_bound () const =0
	The upper bound of the temperature that is valid for this EOS. More...
virtual double	baryon_mass () const
	The vacuum mass of a baryon for this EOS. More...
virtual Scalar< double >	equilibrium_electron_fraction_from_density_temperature (const Scalar< double > &, const Scalar< double > &) const =0
virtual Scalar< DataVector >	equilibrium_electron_fraction_from_density_temperature (const Scalar< DataVector > &, const Scalar< DataVector > &) const =0
virtual Scalar< double >	pressure_from_density_and_energy (const Scalar< double > &, const Scalar< double > &, const Scalar< double > &) const =0
virtual Scalar< DataVector >	pressure_from_density_and_energy (const Scalar< DataVector > &, const Scalar< DataVector > &, const Scalar< DataVector > &) const =0
virtual Scalar< double >	pressure_from_density_and_temperature (const Scalar< double > &, const Scalar< double > &, const Scalar< double > &) const =0
virtual Scalar< DataVector >	pressure_from_density_and_temperature (const Scalar< DataVector > &, const Scalar< DataVector > &, const Scalar< DataVector > &) const =0
virtual Scalar< double >	temperature_from_density_and_energy (const Scalar< double > &, const Scalar< double > &, const Scalar< double > &) const =0
virtual Scalar< DataVector >	temperature_from_density_and_energy (const Scalar< DataVector > &, const Scalar< DataVector > &, const Scalar< DataVector > &) const =0
virtual Scalar< double >	specific_internal_energy_from_density_and_temperature (const Scalar< double > &, const Scalar< double > &, const Scalar< double > &) const =0
virtual Scalar< DataVector >	specific_internal_energy_from_density_and_temperature (const Scalar< DataVector > &, const Scalar< DataVector > &, const Scalar< DataVector > &) const =0
virtual Scalar< double >	sound_speed_squared_from_density_and_temperature (const Scalar< double > &, const Scalar< double > &, const Scalar< double > &) const =0
virtual Scalar< DataVector >	sound_speed_squared_from_density_and_temperature (const Scalar< DataVector > &, const Scalar< DataVector > &, const Scalar< DataVector > &) const =0

Static Public Attributes
static constexpr bool	is_relativistic = IsRelativistic
static constexpr size_t	thermodynamic_dim = 3

Detailed Description

template<bool IsRelativistic>
class EquationsOfState::EquationOfState< IsRelativistic, 3 >

Base class for equations of state which need three independent thermodynamic variables in order to determine the pressure.

The template parameter IsRelativistic is true for relativistic equations of state and false for non-relativistic equations of state.

Member Function Documentation

baryon_mass()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::baryon_mass ( ) const

inlinevirtual

The vacuum mass of a baryon for this EOS.

Reimplemented in EquationsOfState::Tabulated3D< IsRelativistic >.

electron_fraction_lower_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::electron_fraction_lower_bound ( ) const

pure virtual

The lower bound of the electron fraction that is valid for this EOS.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

electron_fraction_upper_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::electron_fraction_upper_bound ( ) const

pure virtual

The upper bound of the electron fraction that is valid for this EOS.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

equilibrium_electron_fraction_from_density_temperature() [1/2]

template<bool IsRelativistic>

virtual Scalar< DataVector > EquationsOfState::EquationOfState< IsRelativistic, 3 >::equilibrium_electron_fraction_from_density_temperature ( const Scalar< DataVector > &  , const Scalar< DataVector > &    ) const

pure virtual

Computes the electron fraction in beta-equilibrium $Y_e^{\mathrm{e}\mathrm{q}}$ from the rest mass density $\rho$ and the temperature $T$.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

equilibrium_electron_fraction_from_density_temperature() [2/2]

template<bool IsRelativistic>

virtual Scalar< double > EquationsOfState::EquationOfState< IsRelativistic, 3 >::equilibrium_electron_fraction_from_density_temperature ( const Scalar< double > &  , const Scalar< double > &    ) const

pure virtual

Computes the electron fraction in beta-equilibrium $Y_e^{\mathrm{e}\mathrm{q}}$ from the rest mass density $\rho$ and the temperature $T$.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

is_barotropic()

template<bool IsRelativistic>

virtual bool EquationsOfState::EquationOfState< IsRelativistic, 3 >::is_barotropic ( ) const

pure virtual

Returns true if the EOS is barotropic.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

is_equilibrium()

template<bool IsRelativistic>

virtual bool EquationsOfState::EquationOfState< IsRelativistic, 3 >::is_equilibrium ( ) const

pure virtual

Returns true if the EOS is in beta-equilibrium.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

pressure_from_density_and_energy() [1/2]

template<bool IsRelativistic>

virtual Scalar< DataVector > EquationsOfState::EquationOfState< IsRelativistic, 3 >::pressure_from_density_and_energy ( const Scalar< DataVector > &  , const Scalar< DataVector > &  , const Scalar< DataVector > &    ) const

pure virtual

Computes the pressure $p$ from the rest mass density $\rho$, the specific internal energy $ϵ$ and electron fraction $Y_e$.

pressure_from_density_and_energy() [2/2]

template<bool IsRelativistic>

virtual Scalar< double > EquationsOfState::EquationOfState< IsRelativistic, 3 >::pressure_from_density_and_energy ( const Scalar< double > &  , const Scalar< double > &  , const Scalar< double > &    ) const

pure virtual

Computes the pressure $p$ from the rest mass density $\rho$, the specific internal energy $ϵ$ and electron fraction $Y_e$.

pressure_from_density_and_temperature() [1/2]

template<bool IsRelativistic>

virtual Scalar< DataVector > EquationsOfState::EquationOfState< IsRelativistic, 3 >::pressure_from_density_and_temperature ( const Scalar< DataVector > &  , const Scalar< DataVector > &  , const Scalar< DataVector > &    ) const

pure virtual

Computes the pressure $p$ from the rest mass density $\rho$, the temperature $T$, and electron fraction $Y_e$.

pressure_from_density_and_temperature() [2/2]

template<bool IsRelativistic>

virtual Scalar< double > EquationsOfState::EquationOfState< IsRelativistic, 3 >::pressure_from_density_and_temperature ( const Scalar< double > &  , const Scalar< double > &  , const Scalar< double > &    ) const

pure virtual

Computes the pressure $p$ from the rest mass density $\rho$, the temperature $T$, and electron fraction $Y_e$.

rest_mass_density_lower_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::rest_mass_density_lower_bound ( ) const

pure virtual

The lower bound of the rest mass density that is valid for this EOS.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

rest_mass_density_upper_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::rest_mass_density_upper_bound ( ) const

pure virtual

The upper bound of the rest mass density that is valid for this EOS.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

sound_speed_squared_from_density_and_temperature() [1/2]

template<bool IsRelativistic>

virtual Scalar< DataVector > EquationsOfState::EquationOfState< IsRelativistic, 3 >::sound_speed_squared_from_density_and_temperature ( const Scalar< DataVector > &  , const Scalar< DataVector > &  , const Scalar< DataVector > &    ) const

pure virtual

Computes adiabatic sound speed squared

$$c_s^2\equiv \frac{\partial p}{\partial e}{|}_{s,Y_e}=\frac{\rho }{h}\frac{\partial p}{\partial \rho }{|}_{e,Y_e}+\frac{\partial p}{\partial e}{|}_{\rho ,Y_e}$$

. With $p,e$ the pressure and energy density respectively, $s$ the entropy density, $Y_e$ the electron fraction $\rho$ the rest-mass density, and $h$ the enthalpy density. Note that $e$ is the total energy density and not the internal energy, therefore

$$\frac{\partial p}{\partial \rho }{|}_{e,Y_e}\ne \chi \equiv \frac{\partial p}{\partial \rho }{|}_{ϵ,Y_e}$$

as defined in the 2-d EoS above. By definition $e=(1+ϵ)\rho$ so holding $e$ constant

$$0=\frac{de}{d\rho }=\frac{\partial e}{\partial \rho }+\frac{\partial e}{\partial ϵ}\frac{\partial ϵ}{\rho }.$$

(where we have suppressed $Y_e$ dependence) So $\partial ϵ/\partial \rho {|}_e=(1+ϵ)/\rho$ and we can expand

$$\frac{\partial p}{\partial \rho }{|}_{e,Y_e}={\frac{\partial e}{\partial \rho }}_{ϵ,Y_e}+\frac{(1+ϵ)}{\rho }\frac{\partial e}{\partial ϵ}{|}_{\rho ,Y_e}$$

Finally, we can rewrite the entire sound speed using only the rest-mass density, specific internal energy, and electron fraction as variables, by using $\frac{\partial e}{\partial ϵ}{|}_{\rho ,Y_e}=1$

$$c_s^2=\frac{\rho }{h}\frac{\partial p}{\partial \rho }{|}_{ϵ,Y_e}+\frac{1}{\rho }\frac{\partial p}{\partial ϵ}{|}_{\rho ,Y_e}(1-\frac{(1+ϵ)\rho }{h})$$

Which reduces to our preferred form

$$c_s^2=\frac{\rho }{h}(\chi +\kappa )$$

Computed as a function of temperature, rest-mass density and electron fraction. Note that this will break thermodynamic consistency if the pressure and internal energy interpolated separately. The precise impact of this will depend on the EoS and numerical scheme used for the evolution.

sound_speed_squared_from_density_and_temperature() [2/2]

template<bool IsRelativistic>

virtual Scalar< double > EquationsOfState::EquationOfState< IsRelativistic, 3 >::sound_speed_squared_from_density_and_temperature ( const Scalar< double > &  , const Scalar< double > &  , const Scalar< double > &    ) const

pure virtual

Computes adiabatic sound speed squared

$$c_s^2\equiv \frac{\partial p}{\partial e}{|}_{s,Y_e}=\frac{\rho }{h}\frac{\partial p}{\partial \rho }{|}_{e,Y_e}+\frac{\partial p}{\partial e}{|}_{\rho ,Y_e}$$

. With $p,e$ the pressure and energy density respectively, $s$ the entropy density, $Y_e$ the electron fraction $\rho$ the rest-mass density, and $h$ the enthalpy density. Note that $e$ is the total energy density and not the internal energy, therefore

$$\frac{\partial p}{\partial \rho }{|}_{e,Y_e}\ne \chi \equiv \frac{\partial p}{\partial \rho }{|}_{ϵ,Y_e}$$

as defined in the 2-d EoS above. By definition $e=(1+ϵ)\rho$ so holding $e$ constant

$$0=\frac{de}{d\rho }=\frac{\partial e}{\partial \rho }+\frac{\partial e}{\partial ϵ}\frac{\partial ϵ}{\rho }.$$

(where we have suppressed $Y_e$ dependence) So $\partial ϵ/\partial \rho {|}_e=(1+ϵ)/\rho$ and we can expand

$$\frac{\partial p}{\partial \rho }{|}_{e,Y_e}={\frac{\partial e}{\partial \rho }}_{ϵ,Y_e}+\frac{(1+ϵ)}{\rho }\frac{\partial e}{\partial ϵ}{|}_{\rho ,Y_e}$$

Finally, we can rewrite the entire sound speed using only the rest-mass density, specific internal energy, and electron fraction as variables, by using $\frac{\partial e}{\partial ϵ}{|}_{\rho ,Y_e}=1$

$$c_s^2=\frac{\rho }{h}\frac{\partial p}{\partial \rho }{|}_{ϵ,Y_e}+\frac{1}{\rho }\frac{\partial p}{\partial ϵ}{|}_{\rho ,Y_e}(1-\frac{(1+ϵ)\rho }{h})$$

Which reduces to our preferred form

$$c_s^2=\frac{\rho }{h}(\chi +\kappa )$$

Computed as a function of temperature, rest-mass density and electron fraction. Note that this will break thermodynamic consistency if the pressure and internal energy interpolated separately. The precise impact of this will depend on the EoS and numerical scheme used for the evolution.

specific_enthalpy_lower_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::specific_enthalpy_lower_bound ( ) const

pure virtual

The lower bound of the specific enthalpy that is valid for this EOS.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

specific_internal_energy_from_density_and_temperature() [1/2]

template<bool IsRelativistic>

virtual Scalar< DataVector > EquationsOfState::EquationOfState< IsRelativistic, 3 >::specific_internal_energy_from_density_and_temperature ( const Scalar< DataVector > &  , const Scalar< DataVector > &  , const Scalar< DataVector > &    ) const

pure virtual

Computes the specific internal energy $ϵ$ from the rest mass density $\rho$, the temperature $T$, and electron fraction $Y_e$.

specific_internal_energy_from_density_and_temperature() [2/2]

template<bool IsRelativistic>

virtual Scalar< double > EquationsOfState::EquationOfState< IsRelativistic, 3 >::specific_internal_energy_from_density_and_temperature ( const Scalar< double > &  , const Scalar< double > &  , const Scalar< double > &    ) const

pure virtual

Computes the specific internal energy $ϵ$ from the rest mass density $\rho$, the temperature $T$, and electron fraction $Y_e$.

specific_internal_energy_lower_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::specific_internal_energy_lower_bound ( const double  rest_mass_density, const double  electron_fraction  ) const

pure virtual

The lower bound of the specific internal energy that is valid for this EOS at the given rest mass density $\rho$ and electron fraction $Y_e$.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

specific_internal_energy_upper_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::specific_internal_energy_upper_bound ( const double  rest_mass_density, const double  electron_fraction  ) const

pure virtual

The upper bound of the specific internal energy that is valid for this EOS at the given rest mass density $\rho$ and electron fraction $Y_e$.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

temperature_from_density_and_energy() [1/2]

template<bool IsRelativistic>

virtual Scalar< DataVector > EquationsOfState::EquationOfState< IsRelativistic, 3 >::temperature_from_density_and_energy ( const Scalar< DataVector > &  , const Scalar< DataVector > &  , const Scalar< DataVector > &    ) const

pure virtual

Computes the temperature $T$ from the rest mass density $\rho$, the specific internal energy $ϵ$, and electron fraction $Y_e$.

temperature_from_density_and_energy() [2/2]

template<bool IsRelativistic>

virtual Scalar< double > EquationsOfState::EquationOfState< IsRelativistic, 3 >::temperature_from_density_and_energy ( const Scalar< double > &  , const Scalar< double > &  , const Scalar< double > &    ) const

pure virtual

Computes the temperature $T$ from the rest mass density $\rho$, the specific internal energy $ϵ$, and electron fraction $Y_e$.

temperature_lower_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::temperature_lower_bound ( ) const

pure virtual

The lower bound of the temperature that is valid for this EOS.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

temperature_upper_bound()

template<bool IsRelativistic>

virtual double EquationsOfState::EquationOfState< IsRelativistic, 3 >::temperature_upper_bound ( ) const

pure virtual

The upper bound of the temperature that is valid for this EOS.

Implemented in EquationsOfState::Tabulated3D< IsRelativistic >.

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

• src/PointwiseFunctions/Hydro/EquationsOfState/EquationOfState.hpp