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Matem. Mod., 2016, Volume 28, Number 2, Pages 65–85 (Mi mm3700)  

This article is cited in 4 scientific papers (total in 4 papers)

Micro-macro Fokker–Planck–Kolmogorov models for a gas of rigid spheres

S. V. Bogomolov, N. B. Esikova, A. E. Kuvshinnikov

Lomonosov Moscow State University

Abstract: Macroscopic system of gas dynamic equations, differing from Navier–Stokes and quasi gas dynamic ones, is derived from a stochastic microscopic model of a hard sphere gas in a phase space. The model is diffusive in velocity space and valid for moderate Knudsen numbers. The main pecularity of our derivation is more accurate velocity averaging due to analitical solving stochastic differential equations with respect to Wiener mesure which describe our original meso model. It is shown at an example of a shock wave front structure that our approach leads to larger than NavierStokes front widening that corresponds to reality. The numerical solution is performed by a well suited to super computer applications special discontinious particle method.

Keywords: Boltzmann equation, Kolmogorov–Fokker–Planck equation, Navier–Stokes equation; random processes, stochastic differential equations with respect to Poisson and Wiener measures, particle method.

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English version:
Mathematical Models and Computer Simulations, 2016, 8:5, 533–547

Received: 25.05.2015

Citation: S. V. Bogomolov, N. B. Esikova, A. E. Kuvshinnikov, “Micro-macro Fokker–Planck–Kolmogorov models for a gas of rigid spheres”, Matem. Mod., 28:2 (2016), 65–85; Math. Models Comput. Simul., 8:5 (2016), 533–547

Citation in format AMSBIB
\Bibitem{BogEsiKuv16}
\by S.~V.~Bogomolov, N.~B.~Esikova, A.~E.~Kuvshinnikov
\paper Micro-macro Fokker--Planck--Kolmogorov models for a gas of rigid spheres
\jour Matem. Mod.
\yr 2016
\vol 28
\issue 2
\pages 65--85
\mathnet{http://mi.mathnet.ru/mm3700}
\elib{https://elibrary.ru/item.asp?id=25707625}
\transl
\jour Math. Models Comput. Simul.
\yr 2016
\vol 8
\issue 5
\pages 533--547
\crossref{https://doi.org/10.1134/S2070048216050069}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84987941316}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Sadr, M. H. Gorji, “A continuous stochastic model for non-equilibrium dense gases”, Phys. Fluids, 29:12 (2017), 122007  crossref  isi  scopus
    2. S. V. Bogomolov, A. E. Kuvshinnikov, “Razryvnyi metod chastits na gazodinamicheskikh primerakh”, Matem. modelirovanie, 31:2 (2019), 63–77  mathnet  crossref  elib
    3. S. V. Bogomolov, N. B. Esikova, “Stokhasticheskaya magnitogidrodinamicheskaya ierarkhiya v silnom vneshnem magnitnom pole”, Matem. modelirovanie, 31:8 (2019), 120–142  mathnet  crossref  elib
    4. S. V. Bogomolov, T. V. Zakharova, “Uravnenie Boltsmana bez gipotezy molekulyarnogo khaosa”, Matem. modelirovanie, 33:1 (2021), 3–24  mathnet  crossref
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