Viscous Gubser flow with conserved charges (VGCC)

A Python implementation of semi-analytical solutions for Gubser flow with conserved charges (baryon number $B$, strangeness $S$, and electric charge $Q$) for benchmarking relativistic fluid simulations.

Overview

This repository provides tools to generate semi-analytical solutions for Gubser flow with conserved charges. These solutions can serve as benchmarks for relativistic viscous hydrodynamics codes.

For theoretical details, see:

• K. Ingles, J. Salinas San Martín, W. Serenone, and J. Noronha-Hostler, Viscous Gubser flow with conserved charges to benchmark fluid simulations, Phys. Rev. D <VOLUME NO.>, <IDENTIFIER> (2025), arXiv:2503.20021 [nucl-th].

Features

• Semi-analytical solutions for Gubser flow with BSQ conserved charges
• Compatible with the CCAKE hydrodynamics code; see details here
• Support for multiple equations of state
• Customizable parameters via YAML configuration

Installation

1. Clone the repository:

git clone git@github.com:the-nuclear-confectionery/viscous-gubser-with-conserved-charges.git
cd viscous-gubser-with-conserved-charges

2. Install dependencies:

pip install numpy matplotlib scipy pandas tqdm

Usage

To generate the solutions of Gubser flow with conserved charges, execute in the terminal the following command:

python vgcc.py [-h] [--config <FILE>] [--mode <{initial_condition,evolution}>] [--eos <{EoS1,EoS2}>]  [--debug]

where the default arguments are:

mode: initial_condition
eos: EoS2
config: config.yaml

Available Modes

1. initial_condition: Generates initial conditions for hydrodynamic simulations.
2. evolution: Solves hydrodynamic evolution equations until $\tau_f$ (defined on config.yaml).

Equation of State

The script provides the flexibility of changing and implementing different equations of state (EoS); please see PRD <VOLUME NO.>, <IDENTIFIER> (2025), arXiv:2503.20021 [nucl-th] for details.

Current options are EoS1 (massless QGP) and EoS2 (conformal plasma). The details of the equations of state included by default and instructions on how to implement a custom EoS are given in the eos folder.

Configuration

The parameters used for solving the hydrodynamics equations of viscous Gubser flow with conserved charges are defined in config.yaml.

Plotting tools

Visualization scripts used to generate the figures of PRD <VOLUME NO.>, <IDENTIFIER> (2025), arXiv:2503.20021 [nucl-th] are provided on the plots directory.

Citation

If you use this code, please cite:

@misc{ingles2025viscousgubserflowconserved,
      title={Viscous Gubser flow with conserved charges to benchmark fluid simulations}, 
      author={Kevin Ingles and Jordi Salinas San Martín and Willian Serenone and Jacquelyn Noronha-Hostler},
      year={2025},
      eprint={2503.20021},
      archivePrefix={arXiv},
      primaryClass={nucl-th},
      url={https://arxiv.org/abs/2503.20021}, 
}

Contributing

Contributions are welcome! Please feel free to submit a Pull Request. Additional equations of state can be included by creating the corresponding files inside the eos and eom directories.

Authorship

The content of this repository was developed by J. Salinas San Martín and K. Ingles at the University of Illinois.