Quadrature-based Lattice Boltzmann Model for Relativistic Flows

TL;DR

This paper introduces a quadrature-based lattice Boltzmann model tailored for simulating relativistic massless particle flows, accurately capturing behaviors across different regimes from hydrodynamic to ballistic.

Contribution

The paper develops a novel quadrature-based finite-difference lattice Boltzmann model for relativistic flows, capable of high-order extensions and accurate across various relaxation regimes.

Findings

Successfully simulates relativistic flows in the Sod shock tube problem

Accurately captures behavior across relaxation times from hydrodynamic to ballistic regimes

Model's high-order extendability is crucial for recovering analytical results in ballistic regime

Abstract

A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.