22/4/2002

Abstract

EOS_Polytrope

This equation provides a polytropic equation of state to thorns using the CactusEOS interface found in EOS_Base. As such it’s a fake, as EOS_Base assumes that, e.g., the pressure is a function of both density and specific internal energy. Here the pressure is just a function of the density, and is set appropriately (the specific internal energy is always ignored).

The two fluid constants are \(K\) (eos_k) and \(\Gamma \) (eos_gamma), which default to 100 and 2 respectively. The formulas that are applied under the appropriate EOS_Base function calls are

\begin {eqnarray} \label {eq:eosformulas} P & = & K \rho ^{\Gamma } \\ \epsilon & = & \frac {K \rho ^{\Gamma -1}}{\Gamma - 1} \\ \rho & = & \frac {P}{(\Gamma - 1) \epsilon } \\ \frac {\partial P}{\partial \rho } & = & K \Gamma \rho ^{\Gamma -1} \\ \frac {\partial P}{\partial \epsilon } & = & 0. \end {eqnarray}

To calculate the units of the Cactus quantities and back, remember that \(G=c=M_{\odot }=1\) in
Cactus.

Here is one example how to calculate densities: \begin {equation} \rho _{\mbox {\tiny Cactus}}=\frac {G^3M_{\odot }^2}{c^6}\cdot \rho \approx 1.6167\cdot 10^{-21}\frac {\mbox {m}^3}{\mbox {kg}}\cdot \rho = 1.6167\cdot 10^{-18}\frac {\mbox {cm}^3}{\mbox {g}}\cdot \rho \end {equation}
and one example for calculating \(K\) (for \(\Gamma =2\)): \begin {equation} K_{\mbox {\tiny Cactus}}=\frac {c^4}{G^3M_{\odot }^2}\cdot K \approx 6.8824\cdot 10^{-11}\frac {\mbox {m}^5}{\mbox {kg}\cdot \mbox {s}^2}\cdot K= 6.8824\cdot 10^{-4}\frac {\mbox {cm}^5}{\mbox {g}\cdot \mbox {s}^2}\cdot K \end {equation}

eos_gamma | Scope: restricted | REAL |

Description: Adiabatic Index for Ideal Fluid
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Range | Default: 2.0 | |

: | ||

eos_k | Scope: restricted | REAL |

Description: Polytropic constant
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Range | Default: 80.0 | |

: | ||

gamma_ini | Scope: restricted | REAL |

Description: Polytropic Gamma used for the initial model (e.g., by RNSID)
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Range | Default: 2.0 | |

: | ||

use_cgs | Scope: restricted | BOOLEAN |

Description: Use the CGS units
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Default: no | ||

Implements:

eos_2d_polytrope

Inherits:

eos_base

Uses header:

EOS_Base.h

EOS_Base.inc

This section lists all the variables which are assigned storage by thorn EinsteinEOS/EOS_Polytrope. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

NONE

CCTK_STARTUP

eos_polytrope_startup

setup the polytropic eos

Language: | fortran | |

Type: | function | |