Beyond moments: Relativistic lattice Boltzmann methods for radiative transport in computational astrophysics
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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.
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Lattice Boltzmann methods have been developed to solve the RTE, and some models are included in open software codes.
“Recently, lattice Boltzmann methods as another class of methods were developed to solve the Radiative transfer equation [13,21,209-212] and some models are included in open software codes [213].”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [212]
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Self-citation
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Cited by
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Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review
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- Authors
- Weih, L. R., Gabbana, A., Simeoni, D., Rezzolla, L., Succi, S., & Tripiccione, R.
- Affiliations
- Goethe University Frankfurt (DE)
- Istituto Nazionale di Fisica Nucleare (IT)
- Center for Life Nano Science @ La Sapienza, Italian Institute of Technology, Viale Regina Elena 295, I-00161 Roma, Italy
- Corresponding author
- Weih, L R
- Venue
- Monthly Notices of the Royal Astronomical Society
- Publisher
- Oxford University Press (OUP)
- Published
- 2020-08-24
- Volume
- 498
- Issue
- 3
- Pages
- 3374-3394
- ISSN
- 0035-8711 (ISSN-L)
- 1365-2966
- OpenAlex
- W3041708317
- Cited by
- 34
- References
- 139
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 6 · 2023: 5 · 2022: 8 · 2021: 5 · 2020: 1
- FWCI
- 2.93
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Monthly Notices of the Royal Astronomical Society (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- Institutional Research Information System University of Ferrara (University of Ferrara) (submittedVersion, other-oa)
- Institutional Research Information System University of Ferrara (University of Ferrara) (submittedVersion, cc-by)
- arXiv (Cornell University)
- Funders
- European Commission (765048)
- H2020 European Research Council (739964)
- European Cooperation in Science and Technology (CA16214)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › Radiative Heat Transfer Studies
- Physical Sciences › Engineering › Computational Mechanics › Lattice Boltzmann Simulation Studies
- Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
- Keywords
- radiative transfer, lattice Boltzmann method, relativistic Boltzmann equation, method of moments, free streaming, radiation hydrodynamics, computational astrophysics
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