@note this repository is a copy of Camelio (2022), "hydro-bulk-1D", zenodo, https://doi.org/10.5281/zenodo.6478022

hydro-bulk-1D

1-dimensional general relativistic hydrodynamic code with bulk viscosity.

hydro-bulk-1D tests the correspondence between the bulk viscous formulation of the multi-component fluid and that of the Israel-Stewart theories (see Gavassino, Antonelli, and Haskell, 2021, CQG 38:075001) in the context of neutron stars.

The theory and the code are described in the following papers:

• [1] Camelio, Gavassino, Antonelli, Bernuzzi, and Haskell, "Simulating bulk viscosity in neutron stars. I. Formalism", PRD 107:103031 (2023).
• [2] Camelio, Gavassino, Antonelli, Bernuzzi, and Haskell, "Simulating bulk viscosity in neutron stars. II. Evolution in spherical symmetry", PRD 107:103032 (2023).

hydro-bulk-1D is released under the MIT License.

If you use hydro-bulk-1D in your research, please cite Refs. [1] and [2].

EDIT 2023-05-19: code updated during peer-review of Refs. [1] and [2].

Content

• README.md -- this file
• hydro-bulk-1D.c -- the hydrodynamic code
• parameters.h -- parameter file included in hydro-bulk-1D.c
• par/par-*.h -- parameter files used in [2]
• Doxyfile -- Doxygen configuration file
• LICENSE.txt -- the MIT License

Usage

The program is the file hydro-bulk-1D.c, which directly include the parameter file parameters.h.

The parameter files for the simulations and tests presented in Ref. [2] are par/par-*.h.

For example, to simulate the shocktube test using the gcc compiler, execute on a Linux terminal:

$ cp par/par-shocktube.h parameters.h
$ gcc hydro-bulk-1D.c -O2 -lm -o shocktube.x
$ ./shocktube.x

In order to generate the automatic documentation using Doxygen, run:

$ doxygen

You can read the automatic documentation openening html/index.html in a browser. Note that I have set HAVE_DOT = YES in the Doxygen configuration file; this option requires the dot program from the graphviz package.

Output

hydro-bulk-1D generates in output a profile file and a log file.

The profile file name can be set with the OUTPUT_FILE macro. It is a gnuplot-friendly text file, which means that each time snapshot is separated by two blank lines. The format of the output is the following:

• r|x -- radial or Cartesian coordinate,
• ρ -- rest mass density,
• Wv -- Lorentz factor times velocity,
• u -- internal specific (per unit mass) energy density,
• [Ye|Π] -- electron fraction or bulk stress (optional),
• [Yμ] -- muon fraction (optional),
• [mg] -- enclosed gravitational mass (optional),
• cs -- speed of sound.

The log file name can be set with the LOG_FILE macro. It is a text file, and its format is the following:

• t -- time,
• ρ -- rest mass density in the first non-ghost cell,
• Wv -- Lorentz factor times velocity in the first non-ghost cell,
• u -- internal specific (per unit mass) energy density in the first non-ghost cell,
• [Ye|Π] -- electron fraction or bulk stress in the first non-ghost cell (optional),
• [Yμ] -- muon fraction in the first non-ghost cell (optional),
• cs -- speed of sound in the first non-ghost cell,
• [Mg] -- total gravitational mass (optional),
• [Mb] -- total baryon mass (optional),
• ρend -- rest mass density in the last non-ghost cell.

Unless otherwise specified, all quantities in the code, in the parameter files, and in the output files, are in code units: c = G = M☉ = kB = 1.

Acknowledgments

This work was supported by the Polish National Science Centre (NCN) grant number OPUS 2019/33/B/ST9/00942.

I am grateful to Sebastiano Bernuzzi, Lorenzo Gavassino, Marco Antonelli, and Brynmor Haskell for useful discussions.