[Développements asymptotiques uniformément valables pour des problèmes de perturbations singulières et principe de raccordement]
Après un bref rappel de la notion de développement asymptotique, un contre-exemple du principe de raccordement de Van Dyke est levé grâce à une forme modifiée de ce principe. Ceci conduit à une approximation composite à un ordre donné. La méthode des développements successifs complémentaires proposée renverse l'analyse en partant d'une forme supposée d'une approximation uniformément valable. Cette méthode ne fait appel à aucun principe de raccordement. En fait, un tel principe apparaı̂t comme un résultat. La méthode est illustrée avec le modèle unidimensionnel souvent étudié de Stokes–Oseen pour le cylindre circulaire.
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.
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Mots-clés : mécanique des fluides, couche limite, équations différentielles, théorie asymptotique, perturbations singulières
Jacques Mauss 1 ; Jean Cousteix 2, 3
@article{CRMECA_2002__330_10_697_0,
author = {Jacques Mauss and Jean Cousteix},
title = {Uniformly valid approximation for singular perturbation problems and matching principle},
journal = {Comptes Rendus. M\'ecanique},
pages = {697--702},
publisher = {Elsevier},
volume = {330},
number = {10},
year = {2002},
doi = {10.1016/S1631-0721(02)01522-X},
language = {en},
}
TY - JOUR AU - Jacques Mauss AU - Jean Cousteix TI - Uniformly valid approximation for singular perturbation problems and matching principle JO - Comptes Rendus. Mécanique PY - 2002 SP - 697 EP - 702 VL - 330 IS - 10 PB - Elsevier DO - 10.1016/S1631-0721(02)01522-X LA - en ID - CRMECA_2002__330_10_697_0 ER -
Jacques Mauss; Jean Cousteix. Uniformly valid approximation for singular perturbation problems and matching principle. Comptes Rendus. Mécanique, Volume 330 (2002) no. 10, pp. 697-702. doi : 10.1016/S1631-0721(02)01522-X. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01522-X/
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