Relativistic lattice kinetic theory: Recent developments and future prospects

In this paper, we review recent progress in relativistic lattice kinetic theory and its applications to relativistic hydrodynamics. Two methods for constructing the discretised distribution function, moment matching and projection onto orthogonal polynomials, are described. Extensions to ultra-high velocities as well as improved dissipation models are discussed. We show that the existing models can successfully cover a wide range of velocities (from weak-relativistic to ultra-relativistic) and viscous regimes. Various applications, from quark-gluon plasma and relativistic Richtmyer-Meshkov instability to flows in curved manifolds are also explored. Finally, potential developments for general relativity are outlined along with future prospects for solving the full set of Einstein equations of general relativity.