Relativistic lattice Boltzmann model with improved dissipation

Abstract

We develop a relativistic lattice Boltzmann (LB) model, providing a more accurate description of dissipative phenomena in relativistic hydrodynamics than previously available with existing LB schemes. The procedure applies to the ultrarelativistic regime, in which the kinetic energy (temperature) far exceeds the rest mass energy, although the extension to massive particles and/or low temperatures is conceptually straightforward. In order to improve the description of dissipative effects, the Maxwell-J\"uttner distribution is expanded in a basis of orthonormal polynomials, so as to correctly recover the third-order moment of the distribution function. In addition, a time dilatation is also applied, in order to preserve the compatibility of the scheme with a Cartesian cubic lattice. To the purpose of comparing the present LB model with previous ones, the time transformation is also applied to a lattice model which recovers terms up to second order, namely up to the energy-momentum tensor. The approach is validated through quantitative comparison between the second- and third-order schemes with Boltzmann approach multiparton scattering (the solution of the full relativistic Boltzmann equation) for moderately high viscosity and velocities, and also with previous LB models in the literature. Excellent agreement with BAMPS and more accurate results than previous relativistic lattice Boltzmann models are reported.