Dissipative hydrodynamics of relativistic shock waves in a Quark Gluon Plasma: comparing and benchmarking alternate numerical methods

TL;DR

This paper compares two numerical methods for simulating relativistic dissipative hydrodynamics in quark-gluon plasmas, validating their consistency and providing benchmark results to aid future research in the field.

Contribution

It introduces a cross-comparison and benchmarking of relativistic lattice Boltzmann and Montecarlo Test-Particle methods for quark-gluon plasma simulations.

Findings

Both methods produce consistent pressure and flow profiles.

Results validate the robustness of the numerical approaches.

Benchmark data is provided for future method validation.

Abstract

This paper presents numerical cross-comparisons and benchmark results for two different kinetic numerical methods, capable of describing relativistic dissipative fluid dynamics in a wide range of kinematic regimes, typical of relevant physics applications, such as transport phenomena in quark-gluon plasmas. We refer to relativistic lattice Boltzmann versus Montecarlo Test-Particle methods. Lacking any realistic option for accurate validation vis-a-vis experimental data, we check the consistency of our results against established simulation packages available in the literature. We successfully cross-compare the results of the two aforementioned numerical approaches for momentum integrated quantities like the hydrostatic and dynamical pressure profiles, the collective flow and the heat flux. These results corroborate the confidence on the robustness and correctness of these computational methods and on the accurate calibration of their numerical parameters with respect to the physical transport coefficients. Our numerical results are made available as supplemental material, with the aim of establishing a reference benchmark for other numerical approaches.