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

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.