  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.
