GRHayLib

Samuel Cupp
Leonardo Rosa Werneck
Terrence Pierre Jacques
Zachariah Etienne

\( \)Date\( \)

Abstract

Provides access to the General Relativistic Hydrodynamics Library (GRHayL). This library provides a suite of functions for GRMHD evolution codes based on the IllinoisGRMHD code.

1 Introduction

This thorn provides access to the General Relativistic Hydrodynamics Library (GRHayL) through the GRHayLib.h header file. The library contains all the core components necessary to produce an IllinoisGRMHD-like code in a modular, infrastructure-agnostic form. These functions are tested via unit tests using GitHub Actions in the GRHayL repository.

For comprehensive documentation of GRHayL’s features, please visit the GitHub wiki. As a brief overview, the library is split into several ‘gems’ which are entirely self-contained. These are Atmosphere, Con2Prim, EOS, Flux_Source, Induction, Neutrinos, and Reconstruction. The GRHayLib implementation provides access to all these gems in its header file. Additionally, the thorn automatically initializes an instance of the ghl_parameters and ghl_eos_parameters structs. The instances are named ghl_params and ghl_eos, and the pointers to these structs are provided by the GRHayLib.h header.

2 Equation of State

One of the more complicated part of GRMHD simulations is properly setting up the equation of state (EOS), especially for tabulated EOS. GRHayL provides both hybrid and tabulated EOS, and this information is passed to the library functions through ghl_eos. GRHayLib’s parameters control the initialization of this struct, so the user does not need to set any of the struct’s values unless they plan to manually adjust these parameters during the simulation. The EOS_type parameter chooses the type of EOS, and the thorn then sets up the struct using the other parameters associated with this choice.

For several variables, there are minimum, atmosphere, and maximum parameters. We will refer to these as collectively limit parameters. For the limit parameters a given EOS uses, the atmosphere parameter is required. The other parameters either have defaults or are ignored if unset.

2.1 Hybrid EOS

The hybrid EOS requires several parameters to function properly. First, it needs the number of elements in the polytropic approximation. This is currently limited by GRHayL to 10 pieces. The transition values of rho_b are set by rho_ppoly_in, and the associated Gamma values are stored in Gamma_ppoly_in. Note that for neos=1, only a single Gamma is necessary. Additionally, the parameter k_ppoly0 sets the polytropic constant for the first piece of the piecewise polytrope. The rest of the constanst are computed automatically.

In addition to the polytropic setup above, the value of the thermal Gamma Gamma_th must be set.

The hybrid EOS only uses the rho_b limit parameters. If unset, the minimum is set to 0, and the maximum is set to 1e300, effectively turning off both of these features.

2.2 Tabulated EOS

To properly configure for tabulated EOS, the most important parameter is the path to the EOS table, given by the EOS_tablepath parameter. GRHayLib automatically reads this table and makes it accessible to GRHayL functions through ghl_eos.

The tabulated EOS uses all the limit parameters (rho_b, Y_e, and T). If unset, the mimima and maxima are set to table bounds.

3 Conservative-to-Primitive Routines

GRHayL provides a selection of con2prim routines along with automated backup methods. ghl_params passes the information from the thorn parameters textttcon2prim_routine and textttcon2prim_backup_routines to the library’s multi-method functions. Of course, any of the routines can be called manually with logic dictated by the user. However, we provide functions for automatically calling the selected routine, as well as triggering the backup routines in the case of failure. The ghl_con2prim_hybrid_multi_method() and ghl_con2prim_tabulated_multi_method() functions implement this feature, and the ghl_con2prim_hybrid_select_method() and ghl_con2prim_tabulated_select_method() functions directly select a single method based on an input value. GRHayL supports up to three backups, but more complex behavior can be designed by the user using the core con2prim functions. Since the individual con2prim routines and the multi-method functions have identical argument lists, swapping routines is straightforward and requires little work from the user.

These routines are iterative solvers, so they require an initial guess. IllinoisGRMHD used always used default guess, which is also provided in GRHayL. The calc_primitive_guess parameter automatically sets the guess to this default in the multi-method function, so set this to ”no” to use a user-defined guess. Manual use of the con2prim routines require the user to either provide a guess or use the ghl_guess_primitives() function.

4 Changing parameters during a run

Cactus allows for changing parameters during a run using CCTK_ParameterSet(). However, this is only allowed for those with ”STEERABLE=ALWAYS” in the parfile. Those without this tag aren’t able to be steered during a run. Because GRHayLib stores this information inside GRHayL structs, the actual parameters are not steerable during a simulation. However, the parameters can be effectively steered by changing the values inside the structs. For the EOS struct, this can be dangerous since some elements are computed from the other parameters. To remedy this, the derived values need to also be recomputed. For the hybrid and simple EOS, we recommend running the appropriate ghl_initialize_EOSTYPE_eos() function to ensure that the elements are properly reinitialized. For tabulated EOS, initializing the struct involves allocating memory for the table. As such, just re-running the initialize function will not behave as desired. The simplest solution is to copy the needed code from the GRHayL function into a scheduled function and manage the elements values manually.

5 Parameters




calc_primitive_guess
Scope: restricted  BOOLEAN



Description: Do we want to calculate estimates for the primitives in Con2Prim?



Range   Default: yes
no
Uses the data currently in the primitive variables as the guess.
yes
Calculates primitive guesses from the current conservatives.






con2prim_backup_routines
Scope: restricted  KEYWORD



Description: We allow up to 3 backup routines



Range   Default: None
None
Don’t use backup routines
Noble2D
”2D routine in https://arxiv.org/pd f/astro-ph/0512420.p df”
Noble1D
”1Dw routine in https://arxiv.org/pd f/astro-ph/0512420.p df”
Noble1D_entropy
”1Dw routine in https://arxiv.org/pd f/astro-ph/0512420.p df, but uses the entropy”
Font1D
TODO
Palenzuela1D
”https://arxiv.org/p df/1505.01607.pdf (see also https://arxiv.org/pd f/1712.07538.pdf)”
Newman1D
”https://escholarshi p.org/content/qt0s53 f84b/qt0s53f84b.pdf (see also https://arxiv.org/pd f/1712.07538.pdf)”
see [1] below
”https://arxiv.org/p df/1505.01607.pdf (see also https://arxiv.org/pd f/1712.07538.pdf)”
Newman1D_entropy
”https://escholarshi p.org/content/qt0s53 f84b/qt0s53f84b.pdf (see also https://arxiv.org/pd f/1712.07538.pdf)”



[1]

Palenzuela1D\_entropy




con2prim_routine
Scope: restricted  KEYWORD



Description: What con2prim routine is used



Range   Default: Noble2D
Noble2D
”2D routine in https://arxiv.org/pd f/astro-ph/0512420.p df”
Noble1D
”1Dw routine in https://arxiv.org/pd f/astro-ph/0512420.p df”
Noble1D_entropy
”1Dw routine in https://arxiv.org/pd f/astro-ph/0512420.p df, but uses the entropy”
Font1D
TODO
Palenzuela1D
”https://arxiv.org/p df/1505.01607.pdf (see also https://arxiv.org/pd f/1712.07538.pdf)”
Newman1D
”https://escholarshi p.org/content/qt0s53 f84b/qt0s53f84b.pdf (see also https://arxiv.org/pd f/1712.07538.pdf)”
see [1] below
”https://arxiv.org/p df/1505.01607.pdf (see also https://arxiv.org/pd f/1712.07538.pdf)”
Newman1D_entropy
”https://escholarshi p.org/content/qt0s53 f84b/qt0s53f84b.pdf (see also https://arxiv.org/pd f/1712.07538.pdf)”



[1]

Palenzuela1D\_entropy




eos_tablepath
Scope: restricted  STRING



Description: Path to the EOS table



Range   Default: (none)
Forbidden, will error out
.+?
Any string






eos_type
Scope: restricted  KEYWORD



Description: The type of EOS for the simulation



Range   Default: (none)
Forbidden default; an EOS type must be specified
Simple
Simple EOS (often referred to as ’ideal fluid’ in literature)
Hybrid
Hybrid EOS
Tabulated
Tabulated EOS






evolve_entropy
Scope: restricted  BOOLEAN



Description: Do we want to evolve the entropy?



  Default: no






evolve_temperature
Scope: restricted  BOOLEAN



Description: Do we want to evolve the temperature?



  Default: no






gamma
Scope: restricted  REAL



Description: Gamma parameter



Range   Default: -1
0:*
Physical values
-1
forbidden value to make sure it is explicitly set in the parfile






gamma_ppoly_in
Scope: restricted  REAL



Description: Set polytropic Gamma parameters. Gamma_ppoly_in[0] goes from rho=0 to rho=rho_ppoly_in[0].



Range   Default: -1
0:*
value of Gamma for the polytropic rho in the bounds rho_ppoly[i-1] to rho_ppoly[i]
-1
forbidden value to make sure it is explicitly set in the parfile






gamma_th
Scope: restricted  REAL



Description: thermal Gamma parameter



Range   Default: -1
0:*
Physical values
-1
forbidden value to make sure it is explicitly set in the parfile






k_ppoly0
Scope: restricted  REAL



Description: Also known as k_ppoly[0], this is the polytropic constant for the lowest density piece of the piecewise polytrope. All other k_ppoly elements are set using rho_ppoly_in and enforcing continuity in the equation of state.



Range   Default: -1
0:*
Physical values
-1
forbidden value to make sure it is explicitly set in the parfile






lorenz_damping_factor
Scope: restricted  REAL



Description: Damping factor for the generalized Lorenz gauge. Has units of 1/length = 1/M. Typically set this parameter to 1.5/(maximum Delta t on AMR grids).



Range   Default: 0.0
*:*
any real






max_lorentz_factor
Scope: restricted  REAL



Description: Maximum Lorentz factor.



Range   Default: 10.0
1:*
Positive > 1, though you’ll likely have troubles far above 10.






neos
Scope: restricted  INT



Description: number of parameters in EOS table



Range   Default: 1
1:10
Any integer between 1 and 10






p_atm
Scope: restricted  REAL



Description: Atmospheric pressure (required)



Range   Default: -1
0:*
Should be non-negative
-1
Used to check if anything was given






p_max
Scope: restricted  REAL



Description: Maximum temperature allowed (disabled by default)



Range   Default: -1
0:*
Should be non-negative
-1
Used to check if anything was given






p_min
Scope: restricted  REAL



Description: Minimum temperature allowed (disabled by default)



Range   Default: -1
0:*
Should be non-negative
-1
Used to check if anything was given






ppm_flattening_epsilon
Scope: restricted  REAL



Description: Epsilon used for flattening in PPM algorithm



Range   Default: 0.33
:
Anything goes. Default is from Colella & Woodward






ppm_flattening_omega1
Scope: restricted  REAL



Description: Omega1 used for flattening in PPM algorithm



Range   Default: 0.75
:
Anything goes. Default is from Colella & Woodward






ppm_flattening_omega2
Scope: restricted  REAL



Description: Omega2 used for flattening in PPM algorithm



Range   Default: 10.0
:
Anything goes. Default is from Colella & Woodward






ppm_shock_epsilon
Scope: restricted  REAL



Description: Epsilon used for shock detection in steepen_rho algorithm



Range   Default: 0.01
:
Anything goes. Default is from Colella & Woodward






ppm_shock_eta1
Scope: restricted  REAL



Description: Eta1 used for shock detection in steepen_rho algorithm



Range   Default: 20.0
:
Anything goes. Default is from Colella & Woodward






ppm_shock_eta2
Scope: restricted  REAL



Description: Eta2 used for shock detection in steepen_rho algorithm



Range   Default: 0.05
:
Anything goes. Default is from Colella & Woodward






ppm_shock_k0
Scope: restricted  REAL



Description: K0 used for shock detection in steepen_rho algorithm



Range   Default: 0.1
:
Anything goes. Default suggested by Colella & Woodward is: (polytropic constant)/10.0






psi6threshold
Scope: restricted  REAL



Description: Where Psiˆ6  > Psi6threshold, we assume we’re inside the horizon in the primitives solver, and certain limits are relaxed or imposed



Range   Default: 1e100
*:*
Can set to anything






rho_b_atm
Scope: restricted  REAL



Description: Atmosphere value on the baryonic rest mass density rho_b (required). If this is unset, the run will die.



Range   Default: -1
0:*
Atmosphere density; must be positive
-1
Used to check if anything was given






rho_b_max
Scope: restricted  REAL



Description: Ceiling value on the baryonic rest mass density rho_b (disabled by default). Can help with stability to limit densities inside the BH after black hole formation.



Range   Default: -1
0:*
Maximum density; must be positive
-1
Used to check if anything was given






rho_b_min
Scope: restricted  REAL



Description: Floor value on the baryonic rest mass density rho_b (disabled by default).



Range   Default: -1
0:*
Minimum density; must be positive
-1
Used to check if anything was given






rho_ppoly_in
Scope: restricted  REAL



Description: Set polytropic rho parameters



Range   Default: -1
0:*
value of the density delimiters for the pieces of the piecewise polytrope
-1
forbidden value to make sure it is explicitly set in the parfile (only checked for neos > 1)






t_atm
Scope: restricted  REAL



Description: Atmospheric temperature (required)



Range   Default: -1
0:*
Should be non-negative
-1
Used to check if anything was given






t_max
Scope: restricted  REAL



Description: Maximum temperature allowed (optional; table bounds used by default)



Range   Default: -1
0:*
Should be non-negative
-1
Used to check if anything was given






t_min
Scope: restricted  REAL



Description: Minimum temperature allowed (optional; table bounds used by default)



Range   Default: -1
0:*
Should be non-negative
-1
Used to check if anything was given






y_e_atm
Scope: restricted  REAL



Description: Atmospheric electron fraction (required)



Range   Default: -1
0:1
Only makes sense if set to something between 0 and 1
-1
Used to check if anything was given






y_e_max
Scope: restricted  REAL



Description: Atmospheric electron fraction (optional; table bounds used by default)



Range   Default: -1
0:1
Only makes sense if set to something between 0 and 1
-1
Used to check if anything was given






y_e_min
Scope: restricted  REAL



Description: Atmospheric electron fraction (optional; table bounds used by default)



Range   Default: -1
0:1
Only makes sense if set to something between 0 and 1
-1
Used to check if anything was given



6 Interfaces

General

Implements:

grhaylib

Adds header:

GRHayLib.h

7 Schedule

This section lists all the variables which are assigned storage by thorn GRHayL/GRHayLib. 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_WRAGH (conditional)

  grhaylib_initialize

  set up the grhayl structs and read the table for tabulated eos.

 

 Language:c
 Options: global
 Type: function

CCTK_TERMINATE

  grhaylib_terminate

  free memory allocated for the grhayl structs.

 

 Language:c
 Options: global
 Type: function