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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 52

The Spectrum of the Boundary Value Problem of Two-dimensional Thermal Convection

Author(s)
Viktor K. Andreev1, Elena N. Lemeshkova1

1Institute of Computational Modeling SB RAS, Krasnoyarsk, Russian Federation

Abstract
The problem of two-dimensional fluid flow in a layer with a heated bottom is investigated. A seepage condition is set on the upper wall for the velocity. The velocity field is linear in the longitudinal coordinate, and the temperature and pressure fields are quadratic functions of the same coordinate. The analysis of the compatibility of the Navier-Stokes equations and thermal conductivity leads to a nonlinear eigenvalue problem for finding the flow field in the layer. The spectrum of this problem is constructed numerically for any permeability rates. The uniqueness of the solution, which is typical for problems of this kind, has been established. The structure of the flow in the layer is analyzed depending on the values of the Reynolds number.
About the Authors

Victor K. Andreev, Dr. Sci. (Phys.–Math.), Prof., Chief Research Scientist, Institute of Computational Modeling SB RAS, Krasnoyarsk, 660036, Russian Federation, andr@icm.krasn.ru

Elena N. Lemeshkova, Cand. Sci. (Phys.Math.), Research Scientist, Institute of Computational Modeling SB RAS, Krasnoyarsk, 660036, Russian Federation, elena cher@icm.krasn.ru

For citation
Andreev V. K., Lemeshkova E. N. The Spectrum of the Boundary Value Problem of Two-dimensional Thermal Convection. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 52, pp. 34–43. (in Russian)

https://doi.org/10.26516/1997-7670.2025.52.34

Keywords
thermal convection, viscous heat-conducting liquid equations, inverse problem, spectrum of the boundary value problem
UDC
517.956: 532.5.032
MSC
31B20, 76D05
DOI
https://doi.org/10.26516/1997-7670.2025.52.34
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