Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics

TL;DR

This paper presents a detailed derivation and validation of a Lattice Boltzmann model tailored for relativistic hydrodynamics, demonstrating its effectiveness in simulating shock waves in quark-gluon plasmas and supernova impacts.

Contribution

The paper introduces a novel derivation of the Lattice Boltzmann scheme specifically for relativistic fluids, with validation on complex astrophysical and high-energy physics problems.

Findings

Close to second order convergence with grid resolution

Linear computational time dependence on grid points and time-steps

Successful application to shock-wave and supernova simulations

Abstract

A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic fluids recently proposed in Ref. [1], is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast-wave on massive interstellar clouds. Close to second order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time-steps, are reported.