Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 491, Pages 38–43
DOI: https://doi.org/10.31857/S2686954320020113 (Mi danma46) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Numerical analysis of laminar–turbulent transition by methods of chaotic dynamics

N. M. Evstigneev, N. A. Magnitskii

Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S2686954320020113
Abstract: This paper summarizes the results of studies of the laminar–turbulent transition in some fluid and gas dynamics problems obtained by applying numerical methods and methods of chaotic dynamics. The following problems are analyzed: 2D and 3D Kolmogorov problems in a periodic domain, 3D Rayleigh–Benard convection in rectangular domains, 3D backward-facing step flow, and development of 3D Rayleigh–Taylor and Kelvin–Helmholtz instabilities in viscous compressible flows. An analysis confirms that instabilities develop via cascades of subcritical or supercritical bifurcations. In all systems, a universal scenario of the transition to chaos (Feigenbaum–Sharkovskii–Magnitskii scenario) is found along with other scenarios of chaotization of dynamical systems.
Keywords: laminar–turbulent transition, chaotic dynamics, numerical methods, bifurcation analysis, Navier–Stokes equations.
Funding agency Grant number
Russian Foundation for Basic Research 18–29–10008 ěę
20–07–00066
This work was supported by the Russian Foundation for Basic Research, grant nos. 18-29-10008 mk and 20-07-00066.
Presented: Yu. S. Popkov
Received: 05.06.2019
Revised: 05.06.2019
Accepted: 18.02.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 2, Pages 110–114
DOI: https://doi.org/10.1134/S1064562420020118
Bibliographic databases:
Document Type: Article
UDC: 519.635.8
Language: Russian
Citation: N. M. Evstigneev, N. A. Magnitskii, “Numerical analysis of laminar–turbulent transition by methods of chaotic dynamics”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 38–43; Dokl. Math., 101:2 (2020), 110–114
Citation in format AMSBIB
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