Relativistic lattice gas hydrodynamics

Non-relativistic cellular automata can model non-relativistic hydrodynamical flows. In this article we show that if the hopping occurs on a space-time lattice which is generated by discrete subgroups of the Poincaré group and if the collision rules embody the relativistic conservation laws, we can modelrelativistic flows. The simplest version of the relativistic model is formally isomorphic with the non-relativistic Hardy, de Pazzis and Pomeau (HPP) lattice model, provided we reinterpret the various quantities that appear there. This observation explains the non-Galilean invariant results of HPP.