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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». 2022. Vol 41

Two-dimensional Thermocapillary Fluid Motion in an Open Channel

Author(s)
Elena N. Lemeshkova1

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

Abstract
The problem of two-dimensional thermocapillary fluid motion in a flat channel is studied. The temperature in the liquid is distributed according to the quadratic law, which is consistent with the velocity field of the Himentz type. At the bottom of the channel, the temperature depends on the time, which allows you to control the movement inside the layer. The Oberbeck-Boussinesq equations are taken as a mathematical model. The resulting initial - boundary value problem is highly nonlinear and inverse with respect to the pressure gradient along the channel. To solve it, a modified Galerkin method was used, where Legendre polynomials were chosen as the basis functions. The expansion coefficients are functions of time for which a system of nonlinear ODES was obtained. As a result of the application of the Runge-Kutta-Felberg method, a solution was found that, with increasing time, tends to solve a stationary problem if the temperature at the bottom of the channel stabilizes.
About the Authors
Elena N. Lemeshkova, Cand. Sci. (Phys.-Math.), Researcher, Institute of Computational Modelling SB RAS, Krasnoyarsk, 630036, Russian Federation, elena cher@icm.krasn.ru
For citation
Lemeshkova E. N. Two–dimensional Thermocapillary Fluid Motion in an Open Channel. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 41, pp. 121–130. (in Russian) https://doi.org/10.26516/1997-7670.2022.41.121
Keywords
free boundary, thermocapillarity, inverse problem, Oberbeck-Boussinesq equations, Galerkin method
UDC
517.957, 517.958, 532.5.032
MSC
76D05, 45K05, 76D45
DOI
https://doi.org/10.26516/1997-7670.2022.41.121
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