GRHayLID

Samuel Cupp
Leonardo Rosa Werneck

\( \)Date\( \)

Abstract

Provides simple magnetohydrodynamic (MHD) initial data for testing, as well as functionality for imposing beta equilibrium on initial hydrodynamic data and computing the initial entropy. The test data includes all five Balsara tests, equilibrium, sound-wave perturbations, and a shock tube. While some initial data requires EOS information provided by GRHayLib, the primitive data can be consumed with matching EOS and normalization conventions. Entropy representation requires the explicit agreement below.

1 Introduction

This thorn provides a variety of initial data setups for testing GRMHD evolution codes. For 1D, this includes all five Balsara tests, equilibrium initial data, a sound wave, and a shock tube. For 3D, we provide isotropic gas and constant-density sphere initial data. We also provide the option to impose beta-equilibrium on provided initial data.

The initial data is separated into magnetic and hydrodynamic parts, so the magnetic initial data can be turned off if desired. All settings use the HydroBase variables for compatibility with other thorns. Magnetic initialization writes both Avec and Bvec; Aphi is not set. Both magnetic selectors must name GRHayLID when this operation is enabled. Native tests require Cartesian coordinates and an identity spatial metric supplied by ADMBase. Curved metrics are rejected. For the normalized Balsara data imported into IllinoisGRMHD, set IllinoisGRMHD::rescale_magnetics=no.

2 Parameters

The parameters are mostly self-explanatory or just extensions of HydroBase keywords. The param.ccl is divided into sections based on which tests the parameters are for, but we explain them here. The type of test is controlled by initial_hydro from HydroBase. All the options for these parameters are explicitly listed by the autogenerated parameter documentation below.

Note that neither beta equilibrium nor entropy calculation are tied to initial_hydro, so they can be used even if the actual initial data is set by another thorn. Beta equilibrium is controlled by the impose_beta_equilibrium parameter, and entropy calculation is controlled by HydroBase::initial_entropy=GRHayLID. External producers must initialize the required fields in HydroBase_Initial; allocation alone is insufficient. Beta allocates Ye and temperature even when their selectors are none and intentionally replaces them after that group.

Some initial data is only valid for tabulated or hybrid EOS, and these check the EOS parameter from GRHayLib. If it is set incorrectly, the run will end with an error message stating the incompatibility. They will also check if HydroBase parameters are set in a compatible fashion (such as HydroBase::initial_temperature) and will also error out if these are set incorrectly.

2.1 HydroTest1D

This option is used for all the 1D tests we provide. The initial_data_1D parameter chooses the specific test and defaults to the Balsara1 test. For shocks and waves, the shock_direction parameter changes the direction of the shock, and the discontinuity_position parameter changes the location of the shock front. For the sound wave test, the amplitude can be set with wave_amplitude. It must be finite and in \([0,1)\). This setup perturbs the longitudinal velocity sinusoidally on \(\rho =P=1\); it is not a pure traveling acoustic eigenmode. Hybrid internal energy uses the cold-plus-thermal relation, and pressures below the cold curve are rejected.

2.2 IsotropicGas

This option sets the hydrodynamic variables to an isotropic gas using the tabulated equation of state and does not work with other EOS settings. It does not set magnetic quantities. The thorn checks to ensure parameters are set correctly in GRHayLiband HydroBaseso that the initial data works, and the run will end with an error message if the core parameters are misconfigured.

Specifically, the thorn checks the following parameters:

Thorn & Parameter Correct Setting


GRHayLib::EOS_type ”Tabulated”
HydroBase::initial_Y_e ”GRHayLID”
HydroBase::initial_temperature ”GRHayLID”

2.3 ConstantDensitySphere

This option sets the hydrodynamic variables to a sphere of constant density using the tabulated equation of state and does not work with other EOS settings. It does not set magnetic quantities. The thorn checks to ensure parameters are set correctly in GRHayLiband HydroBaseso that the initial data works, and the run will end with an error message if the core parameters are misconfigured.

Specifically, the thorn checks the following parameters:

Thorn & Parameter Correct Setting


GRHayLib::EOS_type ”Tabulated”
HydroBase::initial_Y_e ”GRHayLID”
HydroBase::initial_temperature ”GRHayLID”

2.4 Standalone beta equilibrium and entropy

Beta equilibrium solves \(\mu _e-\mu _n+\mu _p=0\) at the final density and requested temperature using base chemical potentials. The residual must satisfy beq_residual_tolerance in MeV (default \(10^{-8}\)). The search includes exact node roots and rejects missing brackets. It selects the first root in increasing Ye within the effective EOS bounds. This avoids reliance on a potentially shifted table munu field; table conventions and physical provenance still require separate validation. Atmosphere points (\(\rho \leq 1.01\rho _{\rm atm}\)) receive a complete atmosphere reset including density, and are deliberately exempt from equilibrium.

Tabulated entropy replaces pressure and specific internal energy as well as entropy. Without beta, it also clamps density, Ye, and temperature to effective bounds. With beta enabled, these three inputs are preserved and incompatible states are rejected. Every EOS return and output is checked before publication.

Simple and Hybrid entropy uses the native GRHayL proxy \(P/\rho ^{\Gamma _{\rm piece}-1}\), not physical specific entropy in \(k_b\)/baryon. Set allow_native_entropy_proxy=yes only when every entropy consumer agrees with that representation. The default rejects that route; use Tabulated EOS for physical table entropy. Native proxy inputs require positive finite density and nonnegative finite pressure. Vacuum and nonfinite states are rejected before evaluation.

The sphere checks finite, strictly subluminal Cartesian velocity. Native tests check the identity spatial metric. The thorn requires Cactus REAL_PRECISION=8, and does not produce HydroBase::w_lorentz; consumers must provide and order their own metric-consistent Lorentz-factor initializer.

3 Parameters




allow_native_entropy_proxy
Scope: restricted BOOLEAN



Description: Permit native Simple/Hybrid proxy in HydroBase entropy; only for compatible GRHayL consumers



Default: no






beq_residual_tolerance
Scope: restricted REAL



Description: Absolute tolerance in MeV for mu_e-mu_n+mu_p at the final beta state



Range Default: 1.0e-8
0:*
Must be finite and strictly positive (checked at initialization)






beq_temperature
Scope: restricted REAL



Description: Temperature used to impose beta-equilibrium



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






constantdensitysphere_rho_exterior
Scope: restricted REAL



Description: Exterior density in geometrized units



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






constantdensitysphere_rho_interior
Scope: restricted REAL



Description: Interior density in geometrized units



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






constantdensitysphere_sphere_radius
Scope: restricted REAL



Description: Sphere radius in geometrized units



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






constantdensitysphere_t_exterior
Scope: restricted REAL



Description: Exterior temperature in MeV



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






constantdensitysphere_t_interior
Scope: restricted REAL



Description: Interior temperature in MeV



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






constantdensitysphere_vx_interior
Scope: restricted REAL



Description: Interior x-velocity



Range Default: (none)
*:*
Anything goes






constantdensitysphere_vy_interior
Scope: restricted REAL



Description: Interior y-velocity



Range Default: (none)
*:*
Anything goes






constantdensitysphere_vz_interior
Scope: restricted REAL



Description: Interior z-velocity



Range Default: (none)
*:*
Anything goes






constantdensitysphere_y_e_exterior
Scope: restricted REAL



Description: Exterior electron fraction (dimensionless)



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






constantdensitysphere_y_e_interior
Scope: restricted REAL



Description: Interior electron fraction (dimensionless)



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






discontinuity_position
Scope: restricted REAL



Description: Set location of the shock discontinuity



Range Default: 0.0
*:*






impose_beta_equilibrium
Scope: restricted BOOLEAN



Description: Impose beta-equilibrium on initial data



Default: no






initial_data_1d
Scope: restricted KEYWORD



Description: Set initial data type for 1D tests



Range Default: Balsara1
equilibrium
initial data for the equilibrium test
sound wave
initial data for the sound wave test
shock tube
initial data for the shock tube test
Balsara1
initial data for the Balsara1 test
Balsara2
initial data for the Balsara2 test
Balsara3
initial data for the Balsara3 test
Balsara4
initial data for the Balsara4 test
Balsara5
initial data for the Balsara5 test






initialize_magnetic_quantities
Scope: restricted BOOLEAN



Description: Initialize both Avec and Bvec for HydroTest1D



Default: yes






isotropicgas_rho
Scope: restricted REAL



Description: Gas density in geometrized units



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






isotropicgas_temperature
Scope: restricted REAL



Description: Gas temperature in MeV



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






isotropicgas_y_e
Scope: restricted REAL



Description: Gas electron fraction (dimensionless)



Range Default: -1
0:*
Non-negative values
-1
Forbidden value






shock_direction
Scope: restricted KEYWORD



Description: Set direction for shock in test data



Range Default: x
x
Test data will have discontinuities along x direction
y
Test data will have discontinuities along y direction
z
Test data will have discontinuities along z direction






stagger_a_fields
Scope: restricted BOOLEAN



Description: Sets whether Avec is staggered to +1/2 (following IllinoisGRMHD convention)



Default: yes






wave_amplitude
Scope: restricted REAL



Description: Wave amplitude for sound wave initial data



Range Default: 1.0e-3
0.0:1.0
Runtime check requires amplitude strictly below one






initial_avec
Scope: shared from HYDROBASE KEYWORD



Extends ranges:



GRHayLID
Initial vector potential set by GRHayLID






initial_bvec
Scope: shared from HYDROBASE KEYWORD



Extends ranges:



GRHayLID
Initial magnetic fields set by GRHayLID






initial_entropy
Scope: shared from HYDROBASE KEYWORD



Extends ranges:



GRHayLID
Initial entropy set by GRHayLID






initial_hydro
Scope: shared from HYDROBASE KEYWORD



Extends ranges:



HydroTest1D
Initial data set by 1D test; see initial_data_1D parameter for options
IsotropicGas
Initial data set to isotropic gas
see [1] below
Initial data set to constant density sphere



[1]

ConstantDensitySphere




initial_temperature
Scope: shared from HYDROBASE KEYWORD



Extends ranges:



GRHayLID
Initial temperature set by GRHayLID






initial_y_e
Scope: shared from HYDROBASE KEYWORD



Extends ranges:



GRHayLID
Initial Y_e set by GRHayLID



4 Interfaces

General

Implements:

grhaylid

Inherits:

grhaylib

grid

hydrobase

admbase

Uses header:

GRHayLib.h

5 Schedule

This section lists all the variables which are assigned storage by thorn GRHayLET/GRHayLID. 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

 

  Conditional:
  HydroBase::Y_e[1] HydroBase::temperature[1]
   

Scheduled Functions

CCTK_PARAMCHECK

  grhaylid_paramcheck

  validate grhaylid producer, selector, eos, and representation contracts

 

  Language: c
  Type: function

HydroBase_Initial (conditional)

  grhaylid_1d_tests_hydro_data

  set initial hydrodynamic data for 1d test

 

  Language: c
  Reads: grid::coordinates
    admbase::metric
  Type: function
  Writes: hydrobase::rho(everywhere)
    hydrobase::press(everywhere)
    hydrobase::eps(everywhere)
    hydrobase::vel(everywhere)

HydroBase_Initial (conditional)

  grhaylid_1d_tests_magnetic_data

  set initial magnetic data for 1d test

 

  After: grhaylid_1d_tests_hydro_data
  Language: c
  Reads: grid::coordinates
    admbase::metric
  Type: function
  Writes: hydrobase::avec(everywhere)
    hydrobase::bvec(everywhere)

HydroBase_Initial (conditional)

  grhaylid_isotropicgas

  set three-dimensional isotropic gas initial data

 

  Language: c
  Reads: grid::coordinates
    admbase::metric
  Type: function
  Writes: hydrobase::rho(everywhere)
    hydrobase::press(everywhere)
    hydrobase::eps(everywhere)
    hydrobase::vel(everywhere)
    hydrobase::y_e(everywhere)
    hydrobase::temperature(everywhere)

HydroBase_Initial (conditional)

  grhaylid_constantdensitysphere

  set three-dimensional constant-density sphere initial data

 

  Language: c
  Reads: grid::coordinates
    admbase::metric
  Type: function
  Writes: hydrobase::rho(everywhere)
    hydrobase::press(everywhere)
    hydrobase::eps(everywhere)
    hydrobase::vel(everywhere)
    hydrobase::y_e(everywhere)
    hydrobase::temperature(everywhere)

CCTK_INITIAL (conditional)

  grhaylid_betaequilibrium

  set beta-equilibrium primitives with a complete atmosphere density reset

 

  After: hydrobase_initial
  Before: hydrobase_prim2coninitial
  Language: c
  Reads: hydrobase::rho
  Type: function
  Writes: hydrobase::rho(everywhere)
    hydrobase::press(everywhere)
    hydrobase::eps(everywhere)
    hydrobase::y_e(everywhere)
    hydrobase::temperature(everywhere)

CCTK_INITIAL (conditional)

  grhaylid_compute_entropy_hybrid

  computes entropy from density and pressure using simple/hybrid native proxy

 

  After: hydrobase_initial
    impose_beta_equilibrium
  Before: hydrobase_prim2coninitial
  Language: c
  Reads: hydrobase::rho
    hydrobase::press
  Type: function
  Writes: hydrobase::entropy(everywhere)

CCTK_INITIAL (conditional)

  grhaylid_compute_entropy_tabulated

  computes entropy from density, y_e, and temperature using tabulated eos

 

  After: hydrobase_initial
    impose_beta_equilibrium
  Before: hydrobase_prim2coninitial
  Language: c
  Reads: hydrobase::rho
    hydrobase::y_e
    hydrobase::temperature
  Type: function
  Writes: hydrobase::rho(everywhere)
    hydrobase::press(everywhere)
    hydrobase::eps(everywhere)
    hydrobase::entropy(everywhere)
    hydrobase::y_e(everywhere)
    hydrobase::temperature(everywhere)

Aliased Functions

 

Alias Name:         Function Name:
GRHayLID_BetaEquilibrium impose_beta_equilibrium