Beyond moments: relativistic Lattice-Boltzmann methods for radiative transport in computational astrophysics

TL;DR

This paper introduces a relativistic Lattice-Boltzmann method for solving the radiative transfer equation in astrophysics, demonstrating improved accuracy and efficiency over traditional moment-based schemes across various optical regimes.

Contribution

The paper develops a novel relativistic Lattice-Boltzmann approach for radiative transfer, capable of handling complex regimes and coupling with hydrodynamics, outperforming existing methods in accuracy and computational cost.

Findings

Accurately models radiative transfer in all optical regimes

Outperforms the M1 scheme in accuracy for free-streaming and intermediate regimes

Provides self-consistent solutions coupled with relativistic hydrodynamics

Abstract

We present a new method for the numerical solution of the radiative-transfer equation (RTE) in multidimensional scenarios commonly encountered in computational astrophysics. The method is based on the direct solution of the Boltzmann equation via an extension of the Lattice Boltzmann (LB) equation and allows to model the evolution of the radiation field as it interacts with a background fluid, via absorption, emission, and scattering. As a first application of this method, we restrict our attention to a frequency independent ("grey") formulation within a special-relativistic framework, which can be employed also for classical computational astrophysics. For a number of standard tests that consider the performance of the method in optically thin, optically thick and intermediate regimes with a static fluid, we show the ability of the LB method to produce accurate and convergent results matching the analytic solutions. We also contrast the LB method with commonly employed moment-based schemes for the solution of the RTE, such as the M1 scheme. In this way, we are able to highlight that the LB method provides the correct solution for both non-trivial free-streaming scenarios and the intermediate optical-depth regime, for which the M1 method either fails or provides inaccurate solutions. When coupling to a dynamical fluid, on the other hand, we present the first self-consistent solution of the RTE with LB methods within a relativistic-hydrodynamic scenario. Finally, we show that besides providing more accurate results in all regimes, the LB method features smaller or comparable computational costs compared to the M1 scheme.