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Zh. Vychisl. Mat. Mat. Fiz., 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:11, 1867–1874

Bibliographic databases:

Document Type: Article
UDC: 519.634
Received: 11.01.2007
Revised: 25.04.2007

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://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36448946200}


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    This publication is cited in the following articles:
    1. Yang T. Kwon O.J., “Numerical Simulation of Heat Transfer Flows By a Direct Solution of Generalized Kinetic Models”, Comput. Fluids, 164 (2018), 114–118  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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