https://doi.org/10.1140/epjst/e2014-02257-0
Review
Relativistic lattice kinetic theory: Recent developments and future prospects
1 ETH Zürich, Department of Mechanical and Process Engineering, Sonneggstrasse 3, ML K 20, 8092 Zürich, Switzerland
2 ETH Zürich, Computational Physics for Engineering Materials, Institute for Building Materials, Wolfgang-Pauli-Strasse 27, HIT, 8093 Zürich, Switzerland
3 Istituto per le Applicazioni del Calcolo C.N.R., via dei Taurini 19, 00185 Rome, Italy
Received: 27 April 2014
Revised: 18 August 2014
Published online: 24 October 2014
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.
© EDP Sciences, Springer-Verlag, 2014
