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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 11, Pages 1949–1957 (Mi zvmmf226)  
This article is cited in 1 scientific paper (total in 1 paper)

Conservative numerical method for solving the averaged Boltzmann equation

V. A. Rykov, D. A. Shil'tsov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
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Abstract: A method is proposed for averaging the Boltzmann kinetic equation with respect to transverse velocities. A system of two integro-differential equations for two desired functions depending only on the longitudinal velocity is derived. The gas particles are assumed to interact as absolutely hard spheres. The integrals in the equations are double. The reduction in the number of variables in the desired functions and the low multiplicity of the integrals ensure the computational efficiency of the averaged equations. A numerical method of discrete ordinates is developed that effectively solves the gas relaxation problem based on the averaged equations. The method is conservative, and the number of particles, momentum, and energy are conserved automatically at every time step.
Key words: кинетическое уравнение Больцмана, осреднение кинетического уравнения, консервативная разностная схема.
Received: 11.01.2007
Revised: 25.04.2007
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 11, Pages 1867–1874
DOI: https://doi.org/10.1134/S0965542507110115
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: V. A. Rykov, D. A. Shil'tsov, “Conservative numerical method for solving the averaged Boltzmann equation”, Zh. Vychisl. Mat. Mat. Fiz., 47:11 (2007), 1949–1957; Comput. Math. Math. Phys., 47:11 (2007), 1867–1874
Citation in format AMSBIB
\Bibitem{RykShi07}
\by V.~A.~Rykov, D.~A.~Shil'tsov
\paper Conservative numerical method for solving the averaged Boltzmann equation
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 11
\pages 1949--1957
\mathnet{http://mi.mathnet.ru/zvmmf226}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2405036}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 11
\pages 1867--1874
\crossref{https://doi.org/10.1134/S0965542507110115}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36448946200}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Full-text PDF :119
    References:49
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