A Lattice Boltzmann Method for Relativistic Rarefied Flows in (2 + 1) Dimensions

TL;DR

This paper introduces an advanced Relativistic Lattice Boltzmann method that enhances simulation accuracy for relativistic rarefied flows by employing improved quadrature rules, enabling better modeling of flows near the free streaming limit.

Contribution

The paper develops a new quadrature-based RLBM with increased isotropy, improving accuracy for relativistic flows beyond the hydrodynamic regime.

Findings

Enhanced accuracy in shock wave simulations across kinetic regimes

Improved isotropy in the numerical scheme

Effective modeling of flows near the free streaming limit

Abstract

We propose an extension to recently developed Relativistic Lattice Boltzmann solvers (RLBM), which allows the simulation of flows close to the free streaming limit. Following previous works [Phys. Rev. C 98 (2018) 035201], we use product quadrature rules and select weights and nodes by separately discretising the radial and the angular components. This procedure facilitates the development of quadrature-based RLBM with increased isotropy levels, thus improving the accuracy of the method for the simulation of flows beyond the hydrodynamic regime. In order to quantify the improvement of this discretisation procedure over existing methods, we perform numerical tests of shock waves in one and two spatial dimensions in various kinetic regimes across the hydrodynamic and the free-streaming limits.