Partial Differential Equations/Numerical Analysis
A smooth extension method
Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 361-366.

In this note, we present a smooth extension method for the simulation of the motion of immersed rigid bodies. It is a method of the fictitious domain type, which uses Cartesian meshes and recovers the optimal order of the error by finding a smooth extension of the exact solution defined in the domain with holes. We first present the method with a Poisson problem and show next how it can be adapted to the case of immersed rigid bodies. Finally, the method is validated in both the scalar and the vector cases.

Nous présentons dans cette note une méthode de prolongement régulier pour simuler le mouvement de particules rigides immergées dans un fluide incompressible. Cʼest une méthode de type domaine fictif sur maillage cartésien permettant de retrouver lʼordre optimal de lʼerreur en espace, en trouvant un prolongement régulier de la solution exacte définie sur le domaine perforé. Nous présentons tout dʼabord la méthode sur un problème scalaire, puis nous lʼadaptons au cas des équations de Stokes incompressibles et des particules rigides. Elle est ensuite validée sur différents cas de test.

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DOI: 10.1016/j.crma.2013.05.011
Fabrèges, Benoit 1; Gouarin, Loïc 2; Maury, Bertrand 2

1 INRIA Paris–Rocquencourt, BP 105, Project team REO, Building 16, 78153 Le Chesnay cedex, France
2 Université Paris-Sud 11, laboratoire de mathématiques, Bat. 425, 91405 Orsay cedex, France
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Fabrèges, Benoit; Gouarin, Loïc; Maury, Bertrand. A smooth extension method. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 361-366. doi : 10.1016/j.crma.2013.05.011. http://www.numdam.org/articles/10.1016/j.crma.2013.05.011/

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