Lattice Boltzmann model for ultra-relativistic flows

TL;DR

This paper introduces a novel relativistic lattice Boltzmann model capable of simulating ultra-high velocity relativistic flows, validated through shock wave simulations in quark-gluon plasmas and astrophysical scenarios.

Contribution

The paper presents the first successful simulation of viscous shock waves in highly relativistic regimes using a new lattice Boltzmann approach with flux limiting and bulk viscosity.

Findings

Accurately simulates shock waves in viscous quark-gluon plasmas.

Validates the model against existing relativistic flow models.

Demonstrates applicability to astrophysical phenomena like supernova shocks.

Abstract

We develop a relativistic lattice Boltzmann model capable of describing relativistic fluid dynamics at ultra-high velocities, with Lorentz factors up to $\gamma \sim 10$. To this purpose, we first build a new lattice kinetic scheme by expanding the Maxwell-J\"uttner distribution function in an orthogonal basis of polynomials and applying an appropriate quadrature, providing the discrete versions of the relativistic Boltzmann equation and the equilibrium distribution. To achieve ultra-high velocities, we include a flux limiter scheme, and introduce the bulk viscosity by a suitable extension of the discrete relativistic Boltzmann equation. The model is validated by performing simulations of shock waves in viscous quark-gluon plasmas and comparing with existing models, finding very good agreement. To the best of our knowledge, we for the first time successfully simulate viscous shock waves in the highly relativistic regime. Moreover, we show that our model can also be used for near-inviscid flows even at very high velocities. Finally, as an astrophysical application, we simulate a relativistic shock wave, generated by, say, a supernova explosion, colliding with a massive interstellar cloud, e.g. molecular gas.