A Lattice Boltzmann Method for relativistic rarefied flows in (2+1) dimensions

L. Bazzanini; A. Gabbana; D. Simeoni; S. Succi; R. Tripiccione

doi:10.1016/j.jocs.2021.101320

A Lattice Boltzmann Method for relativistic rarefied flows in (2+1) dimensions

L. Bazzanini, A. Gabbana, D. Simeoni (Corresponding author), S. Succi, R. Tripiccione

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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 Ambruş and Blaga (2018), we use product quadrature rules and select weights and nodes by separately discretizing 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 discretization 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.

Original language	English
Article number	101320
Number of pages	9
Journal	Journal of Computational Science
Volume	51
DOIs	https://doi.org/10.1016/j.jocs.2021.101320
Publication status	Published - Apr 2021

Bibliographical note

Funding Information:
The authors would like to thank Luciano Rezzolla and Lukas Weih for useful discussions. DS has been supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 765048 . SS acknowledges funding from the European Research Council under the European Union’s Horizon 2020 framework programme (No. P/2014-2020 )/ERC Grant Agreement No. 739964 (COPMAT). AG would like to thank professor Michael Günther and professor Matthias Ehrhardt for their kind hospitality at Wuppertal University. All numerical work has been performed on the COKA computing cluster at Università di Ferrara.

Funding

The authors would like to thank Luciano Rezzolla and Lukas Weih for useful discussions. DS has been supported by the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 765048. SS acknowledges funding from the European Research Council under the European Union's Horizon 2020 framework programme (No. P/2014-2020)/ERC Grant Agreement No. 739964 (COPMAT). AG would like to thank professor Michael G?nther and professor Matthias Ehrhardt for their kind hospitality at Wuppertal University. All numerical work has been performed on the COKA computing cluster at Universit? di Ferrara. The authors would like to thank Luciano Rezzolla and Lukas Weih for useful discussions. DS has been supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 765048 . SS acknowledges funding from the European Research Council under the European Union’s Horizon 2020 framework programme (No. P/2014-2020 )/ERC Grant Agreement No. 739964 (COPMAT). AG would like to thank professor Michael Günther and professor Matthias Ehrhardt for their kind hospitality at Wuppertal University. All numerical work has been performed on the COKA computing cluster at Università di Ferrara.

Funders	Funder number
European Union's Horizon 2020 - Research and Innovation Framework Programme
Università di Ferrara
European Union's Horizon 2020 - Research and Innovation Framework Programme	739964
Marie Skłodowska‐Curie	765048
University of Wuppertal
H2020 European Research Council
European Union's Horizon 2020 - Research and Innovation Framework Programme

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title = "A Lattice Boltzmann Method for relativistic rarefied flows in (2+1) dimensions",

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 Ambru{\c s} and Blaga (2018), we use product quadrature rules and select weights and nodes by separately discretizing 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 discretization 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.",

author = "L. Bazzanini and A. Gabbana and D. Simeoni and S. Succi and R. Tripiccione",

note = "Funding Information: The authors would like to thank Luciano Rezzolla and Lukas Weih for useful discussions. DS has been supported by the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 765048 . SS acknowledges funding from the European Research Council under the European Union{\textquoteright}s Horizon 2020 framework programme (No. P/2014-2020 )/ERC Grant Agreement No. 739964 (COPMAT). AG would like to thank professor Michael G{\"u}nther and professor Matthias Ehrhardt for their kind hospitality at Wuppertal University. All numerical work has been performed on the COKA computing cluster at Universit{\`a} di Ferrara. ",

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AU - Tripiccione, R.

N1 - Funding Information: The authors would like to thank Luciano Rezzolla and Lukas Weih for useful discussions. DS has been supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 765048 . SS acknowledges funding from the European Research Council under the European Union’s Horizon 2020 framework programme (No. P/2014-2020 )/ERC Grant Agreement No. 739964 (COPMAT). AG would like to thank professor Michael Günther and professor Matthias Ehrhardt for their kind hospitality at Wuppertal University. All numerical work has been performed on the COKA computing cluster at Università di Ferrara.

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N2 - 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 Ambruş and Blaga (2018), we use product quadrature rules and select weights and nodes by separately discretizing 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 discretization 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.

AB - 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 Ambruş and Blaga (2018), we use product quadrature rules and select weights and nodes by separately discretizing 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 discretization 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.

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A Lattice Boltzmann Method for relativistic rarefied flows in (2+1) dimensions

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