Uniformly valid approximation for singular perturbation problems and matching principleDéveloppements asymptotiques uniformément valables pour des problèmes de perturbations singulières et principe de raccordement |
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| Authors: | Jacques Mauss Jean Cousteix |
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| Institution: | 1. Institut de mécanique des fluides de Toulouse UMR-CNRS et Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France;2. Département modèles pour l''aérodynamique et l''énergétique, ONERA, 2, avenue Édouard Belin, BP 4025, 31055 Toulouse cedex 4, France;3. École nationale supérieure de l''aéronautique et de l''espace, 10, avenue Édouard Belin, 31055 Toulouse cedex, France |
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| Abstract: | After a brief reminder of the notion of asymptotic expansion, a counter-example of the Van Dyke matching principle is solved thanks to a modified form of this principle. This leads to a composite approximation to a given order. The proposed method of successive complementary expansions reverses the analysis by starting with a supposed form of the uniformly valid approximation. This method does not require any matching principle which, in fact, is a by-product. The method is illustrated with the very often studied one-dimensional model of Stokes–Oseen for the circular cylinder. To cite this article: J. Mauss, J. Cousteix, C. R. Mecanique 330 (2002) 697–702. |
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| Keywords: | fluid mechanics boundary layer differential equations asymptotic theory singular perturbations mécanique des fluides couche limite équations différentielles théorie asymptotique perturbations singulières |
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