EOS_Hybrid

Harry Dimmelmeier, Ian Hawke, Christian Ott

Date

Abstract

EOS_Hybrid. The equation of state used for “simple” core collapse simulations.

1 The equations

This equation provides the hybrid polytropic / ideal gas equation of state used by Dimmelmeier et al. [1] for supernova collapse. A thorn wanting to use this needs to use the CactusEOS interface found in EOS_Base.

The equations are

P = Ppoly + Pth (1) P ρ = Ppoly ρ + Pth 1 ρ + Pth 2 ρ (2) P 𝜖 = (γth 1)ρ, (3)

where

Ppoly = Kργ (4) Pth = Kγth 1 γ 1 ργ + (γ th 1)ρ𝜖 (γth 1)γ γ1 γ2 1Kρnucγ11ρ (5) Ppoly ρ = γKργ1 (6) Pth 1 ρ = γKγth 1 γ 1 ργ1 (7) Pth 2 ρ = (γ 1)𝜖 (γth 1) γ γ1 (γ1 1)(γ2 1)Kρnuc(γ1 1). (8)

These expressions do not include the conversions between cgs and Cactus units that are necessary inside the code.

For more details, a recent paper to start with would be [1].

References

[1]   H. Dimmelmeier, J. Novak, A. Font, J. M. Ibanez, E. Mueller Combining spectral and shock-capturing methods: A new numerical approach for 3D relativistic core collapse simulations Phys. Rev. D71 064023 (2005)

2 Parameters




eos_gamma_supernuclear
Scope: restricted  REAL



Description: Gamma_2 for EOS



Range   Default: 1.66666666666666
:






eos_gamma_th
Scope: restricted  REAL



Description: Gamma_th for EOS



Range   Default: 1.5
:






rho_nuc
Scope: restricted  REAL



Description: Nuclear matter density



Range   Default: 1.e-10
:






eos_gamma
Scope: shared from EOS_2D_POLYTROPE REAL






eos_k
Scope: shared from EOS_2D_POLYTROPE REAL






gamma_ini
Scope: shared from EOS_2D_POLYTROPE REAL



3 Interfaces

General

Implements:

eos_hybrid

Inherits:

hydrobase

eos_2d_polytrope

Grid Variables

3.0.1 PRIVATE GROUPS




  Group Names     Variable Names    Details   




pressure_contributions   compact0
pressure_poly   descriptionPolytropic and thermal contributions to the pressure
pressure_th   dimensions3
  distributionDEFAULT
  group typeGF
  tagsProlongation=”None”
  timelevels1
 variable typeREAL




4 Schedule

This section lists all the variables which are assigned storage by thorn EinsteinEOS/EOS_Hybrid. 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.

Storage

NONE

Scheduled Functions

CCTK_STARTUP

  eos_hybrid_startup

  setup the eos used by dimmelmeier et al. in core collapse

 

 After: eos_polytrope_startup
 Language:fortran
 Type: function

CCTK_ANALYSIS

  check_poly_contrib

  output the polytropic and thermal contributions

 

 Language:fortran
 Storage: pressure_contributions
 Triggers: pressure_contributions
 Type: function