Comptes Rendus
Influence of boundary layers over the rate of convergence in a penalization method for a 1-D wave equation
Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 454-457.

For domain penalization methods, there can be a gap between the expected speed of convergence and the observed one, by numerical means. Such a gap has been observed by Paccou, et al. [A. Paccou, G. Chiavassa, J. Liandrat, K. Schneider, A penalization method applied to the wave equation, C. R. Mecanique 333 (2005) 79–85], concerning the penalization of a wave equation. We answer here one of their questions by proving that the observed lack in convergence speed is clearly related to the formation of boundary layers on one side of the boundary.

Pour les méthodes de pénalisation de domaine, il est possible qu'il y ait un écart entre la vitesse de convergence attendue et celle observée numériquement. Un tel écart a été mis en évidence par Paccou, et al. [A. Paccou, G. Chiavassa, J. Liandrat, K. Schneider, A penalization method applied to the wave equation, C. R. Mecanique 333 (2005) 79–85], lors de la pénalisation d'une équation des ondes. On répond ici à une question posée dans, en prouvant que le défaut de vitesse de convergence observé est clairement provoqué par la formation de couches limites, localisées d'un seul côté du bord.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2008.01.009
Keywords: Computational fluid mechanics, Domain penalization method, Boundary layers, Wave equation
Mot clés : Mécanique des fluides numérique, Méthode de pénalisation de domaine, Couches limites, Équation des ondes

Bruno Fornet 1, 2

1 LATP, université de Provence, 39, rue Joliot-Curie, 13453 Marseille cedex 13, France
2 LMRS, université de Rouen, avenue de l'université, B.P. 12, 76801 Saint Étienne du Rouvray, France
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Bruno Fornet. Influence of boundary layers over the rate of convergence in a penalization method for a 1-D wave equation. Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 454-457. doi : 10.1016/j.crme.2008.01.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.01.009/

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