ryujin::EquationOfStateLibrary::BumpyBarotropicPressure Class Reference

#include <source/euler_aeos/equation_of_state_bumpy_barotropic_pressure.h>

Inheritance diagram for ryujin::EquationOfStateLibrary::BumpyBarotropicPressure:

Collaboration diagram for ryujin::EquationOfStateLibrary::BumpyBarotropicPressure:

Public Member Functions
	BumpyBarotropicPressure (const std::string &subsection)
double	pressure (double rho, double e) const final
double	specific_internal_energy (double rho, double p) const final
double	temperature (double rho, double e) const final
double	cold_curve_bound (double rho) const final
double	specific_entropy (double rho, double e) const final
double	speed_of_sound (double rho, double e) const final
virtual double	pressure (double rho, double e) const=0
virtual double	specific_internal_energy (double rho, double p) const=0
virtual double	speed_of_sound (double, double) const
virtual double	temperature (double, double) const
Public Member Functions inherited from ryujin::EquationOfStateLibrary::EquationOfState
	EquationOfState (const std::string &name, const std::string &subsection)

Additional Inherited Members
Protected Attributes inherited from ryujin::EquationOfStateLibrary::EquationOfState
double	covolume_constant_
double	interpolation_pinfty_
double	interpolation_q_

Detailed Description

A composite equation of state of the form

\begin{align} p\;=\;p_{\text{h}}(\rho,e_{\text{h}})\,+\,p_{\text{b}}(\rho), \qquad e\;=\;e_{\text{h}}\,+\,e_{\text{b}}(\rho), \qquad p_{\text{b}}(\rho)\;=\;\rho^2\,\partial_\rho e_{\text{b}}(\rho), \end{align}

in which the hydrodynamical constituent \(p_{\text{h}},\,e_{\text{h}}\) is given by a Noble-Abel stiffened gas and the barotropic constituent \(p_{\text{b}},\,e_{\text{b}}\) is a synthetic "bump" that concentrates the barotropic speed of sound in a narrow interval of width \(\varepsilon\) centered at a reference density \(\rho_0\):

\begin{align} a_{\text{b}}^2(\rho)\;=\; \frac{c_0^2}{\big((\rho-\rho_0)^2+\varepsilon\big)^{3/2}}. \end{align}

The bump renders the total pressure \(p\) nonconvex so that the Riemann problem can develop composite shock-rarefaction waves, while hyperbolicity is maintained.

The barotropic constituent carries no entropy and no temperature: \(T\,\mathrm{d}s = \mathrm{d}e + p\,\mathrm{d}v = \mathrm{d}e_{\text{h}} + p_{\text{h}}\,\mathrm{d}v\), so that \(s=s_{\text{h}}\) and \(T=T_{\text{h}}\). Consequently the isentropes of the composite equation of state are the hydrodynamical isentropes and the total speed of sound is given by \(a^2=a_{\text{h}}^2+a_{\text{b}}^2\).

Note

All functions of this class take and return the total specific internal energy e and the total pressure p. The hydrodynamical constituents are recovered as \(e_{\text{h}}=e-e_{\text{b}}(\rho)\) and \(p_{\text{h}}=p-p_{\text{b}}(\rho)\).

Definition at line 55 of file equation_of_state_bumpy_barotropic_pressure.h.

Constructor & Destructor Documentation

BumpyBarotropicPressure()

ryujin::EquationOfStateLibrary::BumpyBarotropicPressure::BumpyBarotropicPressure ( const std::string &  subsection )

inline

Definition at line 63 of file equation_of_state_bumpy_barotropic_pressure.h.

References ryujin::EquationOfStateLibrary::EquationOfState::covolume_constant_, ryujin::EquationOfStateLibrary::EquationOfState::interpolation_pinfty_, and ryujin::EquationOfStateLibrary::EquationOfState::interpolation_q_.

Member Function Documentation

pressure() [1/2]

double ryujin::EquationOfStateLibrary::BumpyBarotropicPressure::pressure ( double  rho, double  e  ) const

inlinefinalvirtual

The total pressure is given by

\begin{align} p = p_{\text{h}}(\rho, e - e_{\text{b}}(\rho)) + p_{\text{b}}(\rho) \end{align}

Implements ryujin::EquationOfStateLibrary::EquationOfState.

Definition at line 155 of file equation_of_state_bumpy_barotropic_pressure.h.

specific_internal_energy() [1/2]

double ryujin::EquationOfStateLibrary::BumpyBarotropicPressure::specific_internal_energy ( double  rho, double  p  ) const

inlinefinalvirtual

The total specific internal energy is given by

\begin{align} e = e_{\text{h}}(\rho, p - p_{\text{b}}(\rho)) + e_{\text{b}}(\rho) \end{align}

Implements ryujin::EquationOfStateLibrary::EquationOfState.

Definition at line 168 of file equation_of_state_bumpy_barotropic_pressure.h.

temperature() [1/2]

double ryujin::EquationOfStateLibrary::BumpyBarotropicPressure::temperature ( double  rho, double  e  ) const

inlinefinalvirtual

The barotropic constituent is athermal, so that the temperature is the hydrodynamical one,

\begin{align} T = T_{\text{h}}(\rho, e - e_{\text{b}}(\rho)) \end{align}

Reimplemented from ryujin::EquationOfStateLibrary::EquationOfState.

Definition at line 182 of file equation_of_state_bumpy_barotropic_pressure.h.

cold_curve_bound()

double ryujin::EquationOfStateLibrary::BumpyBarotropicPressure::cold_curve_bound ( double  rho ) const

inlinefinalvirtual

The admissible set is characterized by \(e_{\text{h}}\ge e_{\text{h},\text{cold}}(\rho)\) and thus

\begin{align} e_{\text{cold}} = e_{\text{h},\text{cold}}(\rho) + e_{\text{b}}(\rho) \end{align}

Reimplemented from ryujin::EquationOfStateLibrary::EquationOfState.

Definition at line 196 of file equation_of_state_bumpy_barotropic_pressure.h.

specific_entropy()

double ryujin::EquationOfStateLibrary::BumpyBarotropicPressure::specific_entropy ( double  rho, double  e  ) const

inlinefinalvirtual

The barotropic constituent is isentropic, so that the specific entropy is the hydrodynamical one,

\begin{align} s = s_{\text{h}}(\rho, e - e_{\text{b}}(\rho)) \end{align}

Reimplemented from ryujin::EquationOfStateLibrary::EquationOfState.

Definition at line 209 of file equation_of_state_bumpy_barotropic_pressure.h.

speed_of_sound() [1/2]

double ryujin::EquationOfStateLibrary::BumpyBarotropicPressure::speed_of_sound ( double  rho, double  e  ) const

inlinefinalvirtual

The isentropes of the composite equation of state coincide with the hydrodynamical isentropes, so that the speed of sound is given by

\begin{align} a^2 = a_{\text{h}}^2(\rho, e - e_{\text{b}}(\rho)) + a_{\text{b}}^2(\rho) \end{align}

Reimplemented from ryujin::EquationOfStateLibrary::EquationOfState.

Definition at line 223 of file equation_of_state_bumpy_barotropic_pressure.h.

pressure() [2/2]

virtual double ryujin::EquationOfStateLibrary::EquationOfState::pressure ( double  rho, double  e  ) const

virtual

Return the pressure given density rho and specific internal energy e.

Note

This function is implemented for every equation of state.

Implements ryujin::EquationOfStateLibrary::EquationOfState.

specific_internal_energy() [2/2]

virtual double ryujin::EquationOfStateLibrary::EquationOfState::specific_internal_energy ( double  rho, double  p  ) const

virtual

Return the specific internal energy e for a given density rho and pressure p.

Note

This function is implemented for every equation of state.

Implements ryujin::EquationOfStateLibrary::EquationOfState.

speed_of_sound() [2/2]

virtual double ryujin::EquationOfStateLibrary::EquationOfState::speed_of_sound ( double  , double    ) const

inlinevirtual

Return the sound speed c for a given density rho and specific internal energy e.

Note

This function might not be implemented for a given equation of state.

Reimplemented from ryujin::EquationOfStateLibrary::EquationOfState.

Definition at line 123 of file equation_of_state.h.

temperature() [2/2]

virtual double ryujin::EquationOfStateLibrary::EquationOfState::temperature ( double  , double    ) const

inlinevirtual

Return the temperature T for a given density rho and specific internal energy e.

Note

This function might not be implemented for a given equation of state.

Reimplemented from ryujin::EquationOfStateLibrary::EquationOfState.

Definition at line 109 of file equation_of_state.h.

---

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

• source/euler_aeos/equation_of_state_bumpy_barotropic_pressure.h