Extended Galerkin–Eckhaus Method in Nonlinear Thermoconvection
We propose an extension of the Galerkin–Eckhaus method in order to study thermoconvective instabilities not only in the weakly nonlinear régime, but also farther from the threshold. This extension consists in an appropriate choice of the basis functions used to expand the unknowns and in an increase...
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Published in | Journal of non-equilibrium thermodynamics Vol. 32; no. 2; pp. 155 - 179 |
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Main Authors | , , |
Format | Journal Article Web Resource |
Language | English |
Published |
Walter de Gruyter
23.05.2007
Walter de Gruyter GmbH & Co. KG |
Subjects | |
Online Access | Get full text |
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Summary: | We propose an extension of the Galerkin–Eckhaus method in order to study thermoconvective instabilities not only in the weakly nonlinear régime, but also farther from the threshold. This extension consists in an appropriate choice of the basis functions used to expand the unknowns and in an increase of the number of amplitude equations taken into account. The rigid-free Rayleigh–Bénard problem with heat-conducting boundaries and the Marangoni–Bénard problem are considered in detail before generalizing to all thermoconvective instabilities. The validity of our approach is proven by comparing its results with a multiple scale method and with a finite element method. A very good agreement between all methods is found in the weakly nonlinear regime. Farther from the threshold, the agreement between our extended Galerkin–Eckhaus method and the finite element approach is also obtained with appropriate basis functions whose choice depends crucially on the value of the Prandtl number and also on the boundary conditions imposed at the top and bottom of the system. |
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Bibliography: | jnetdy.2007.007.pdf istex:8449850BB1A99BE2C99F92D2910F61445EE90E7C ArticleID:jnet.32.2.155 ark:/67375/QT4-L9MKL8Q4-V scopus-id:2-s2.0-34249681806 |
ISSN: | 0340-0204 1437-4358 1437-4358 |
DOI: | 10.1515/JNETDY.2007.007 |