The solution of problems of the stability of three-dimensional convective flows in a closed rectangular cavity by the collocation method |
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Authors: | DYe Pivovarov |
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Institution: | Moscow, Russia |
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Abstract: | The use of the collocation method, with collocation points at the zeroes of a Chebyshev polynomial, to solve spatial problems of the stability of convective flows, is described. The fluid occupies a closed rectangular cavity on the boundaries of which conditions of the first, second and third kind can be specified. Using a differential matrix constructed at the collocation points, the spectral problem is transformed into an extended eigenvector problem that is solved numerically. The Rayleigh problem in a closed layer is solved for different values of the ratio of the sides of the rectangular cavity. The calculations presented are compared with the results of the solution of non-linear equations and also with the experimental and theoretical data of other authors. |
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