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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 11, Pages 1883–1894
DOI: https://doi.org/10.31857/S0044466922110059 (Mi zvmmf11474) 		 
Mathematical physics

Efficient method for solving the Boltzmann equation on a uniform mesh

A. D. Beklemishevab, È. A. Fedorenkovab

a Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
b Novosibirsk State University, 630090, Novosibirsk, Russia
DOI: https://doi.org/10.31857/S0044466922110059
Abstract: A new numerical method for solving the Boltzmann equation on a uniform mesh in velocity space is proposed. The asymptotic complexity of the method is $O(N^3)$, where $N$ is the total number of nodes on a three-dimensional mesh. The algorithm is efficient on relatively small meshes due to the simplicity of its operations and easy parallelization. The method preserves the most important properties of the solution, such as nonnegativity and conservation of total energy, momentum, and the number of particles.
Key words: kinetic equation, Boltzmann equation, discrete-velocity models, $O(N^3)$ kinetic code.
Received: 05.02.2022
Revised: 06.06.2022
Accepted: 07.07.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 11, Pages 1900–1911
DOI: https://doi.org/10.1134/S0965542522110045
Bibliographic databases:
Document Type: Article
UDC: 519.635
Language: Russian
Citation: A. D. Beklemishev, È. A. Fedorenkov, “Efficient method for solving the Boltzmann equation on a uniform mesh”, Zh. Vychisl. Mat. Mat. Fiz., 62:11 (2022), 1883–1894; Comput. Math. Math. Phys., 62:11 (2022), 1900–1911
Citation in format AMSBIB
\Bibitem{BekFed22}
\by A.~D.~Beklemishev, \`E.~A.~Fedorenkov
\paper Efficient method for solving the Boltzmann equation on a uniform mesh
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 11
\pages 1883--1894
\mathnet{http://mi.mathnet.ru/zvmmf11474}
\crossref{https://doi.org/10.31857/S0044466922110059}
\elib{https://elibrary.ru/item.asp?id=49455082}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 11
\pages 1900--1911
\crossref{https://doi.org/10.1134/S0965542522110045}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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