Dissipative hydrodynamics of relativistic shock waves in a quark gluon plasma: Comparing and benchmarking alternate numerical methods

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 Monte Carlo test-particle methods. Lacking any realistic option for accurate validation vis-á-vis experimental data, we check the consistency of our results against established simulation packages available in the literature. We successfully 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 of 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.