Relativistic flows on a spacetime lattice

Abstract

The relativistic extension of non-relativistic hydrodynamics suffers from notorious difficulties. In non-relativistic hydrodynamics where difficulties also abound, it has proved a useful supplement to study lattice models which can imitate viscous fluid flow. In this paper we construct a relativistic spacetime lattice and construct a dynamics of points, thus a relativistic cellular automaton over it, to model relativistic fluid flow. A simple example is also explicitly studied, and some numerical results with figures are shown in the last section.