**By Alessandro Gabbana Zoom ID: 896 2772 7941 Passcode: 809669**

The study of relativistic hydrodynamics has received renewed interest in recent years, as it has been realized that phenomena in diverse areas of physics, such as astrophysics, quark gluon plasma and even condensed matter physics can be studied via a hydrodynamic approach in the relativistic regime. For example, quark-gluon plasmas (QGP) created in heavy-ion collisions at RHIC or LHC or electron flow in 2D graphene sheets can be considered, in some cases, as relativistic fluids. For a long time, relativistic fluid dynamics has been hampered by several theoretical and computational shortcomings, since relativistic versions of Navier-Stokes equations suffer from causality problems linked to the order of the derivatives appearing in the dissipative terms. Some of these problems can be avoided by employing a lattice kinetic approach, that treats space and time on the same footing (i.e., via first-order derivatives).

This is one of the main reasons why Relativistic Lattice Boltzmann Methods (RLBMs), that discretize in coordinate and momentum space the Boltzmann equation, and yet ensure that the resulting synthetic dynamics retains all its hydrodynamic properties, have been recently proposed as effective computational tools to study relativistic flows.

This talk presents an overview of the formal algorithmic derivation of a RLBM capable of handling a wide range of physics parameters and kinematic regimes, from ultra-relativistic to mildly relativistic and eventually to the non-relativistic limit. Moreover, a few examples of applications will be discussed, including cross-comparisons with other numerical methods in the study of relativistic shock waves in QGP.