Lattice Boltzmann study of the one-dimensional boost-invariant expansion with anisotropic initial conditions

TL;DR

This paper introduces a lattice Boltzmann numerical scheme for simulating anisotropic relativistic fluids, validated on one-dimensional boost-invariant expansion scenarios with massless particles and varying viscosity-to-entropy ratios.

Contribution

It develops a novel lattice Boltzmann algorithm for anisotropic distributions in relativistic kinetic theory, specifically tailored for boost-invariant flows.

Findings

The scheme accurately reproduces known solutions of Bjorken flow.

Validation shows robustness across different shear viscosity to entropy density ratios.

The method is limited to massless particles with Maxwell-Jüttner statistics.

Abstract

A numerical algorithm for the implementation of anisotropic distributions in the frame of the relativistic Boltzmann equation is presented. The implementation relies on the expansion of the Romatschke-Strickland distribution with respect to orthogonal polynomials, which is evolved using the lattice Boltzmann algorithm. The validation of our proposed scheme is performed in the context of the one-dimensional boost invariant expansion (Bjorken flow) at various values of the ratio $\eta / s$ of the shear viscosity to the entropy density. This study is limited to the case of massless particles obeying Maxwell-J\"uttner statistics.