[Une procédure nodale de résolution numérique de l'équation de Laplace. Application aux écoulements à potentiel de vitesse]
La Note présente une méthode non-conventionnelle de calcul de l'écoulement de fluide parfait incompressible autour de corps portants. D'abord l'équation de Laplace régissant le potentiel de la vitesse est résolue avec des conditions de Dirichlet internes exprimées aux nœuds du maillage plutôt que sur des parties lisses de la surface. La méthode est applicable moyennant l'utilisation de répartitions surfaciques continues de couches de doublets, avec lesquelles l'obtention du champ de vitesse pariétale devient trivial. Ensuite une formulation originale de type Neumann des conditions de Kutta est proposée. Exprimée sous forme d'une minimisation du flux pariétal de la vitesse, elle entraîne une réduction sensible de l'impact de la discrétisation sur l'estimation des efforts globaux par rapport aux formulations locales. La méthode est applicable aux écoulements bi ou tri-dimensionnels, stationnaires ou non.
The Note presents an unconventional computational method for irrotational and incompressible fluid flows over lifting bodies. At first, Laplace's equation for the velocity potential is solved with internal Dirichlet conditions expressed at the nodes of the mesh rather than at smooth surface positions. Continuous distributions of surface normal doublets are used, and obtaining the surface velocity field with such distributions becomes straightforward. Secondly, an original Neumann type formulation of the Kutta conditions is proposed. Expressing the minimization of the velocity flux across the wall shows a significant reduction of the discretization impact upon the computed global efforts when compared to local no-load conditions. The method can be applied to 2 or 3-dimensional flows, steady or not.
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Mot clés : Mécanique des fluides, Dirichlet, Doublets, Écoulement, Kutta, Laplace, Nœuds, Potentiel
Pascal Ardonceau 1
@article{CRMECA_2009__337_4_208_0,
author = {Pascal Ardonceau},
title = {A nodal boundary elements formulation. {Application} to the solution of the {Laplace} equation for irrotational flows},
journal = {Comptes Rendus. M\'ecanique},
pages = {208--217},
publisher = {Elsevier},
volume = {337},
number = {4},
year = {2009},
doi = {10.1016/j.crme.2009.05.004},
language = {en},
}
TY - JOUR AU - Pascal Ardonceau TI - A nodal boundary elements formulation. Application to the solution of the Laplace equation for irrotational flows JO - Comptes Rendus. Mécanique PY - 2009 SP - 208 EP - 217 VL - 337 IS - 4 PB - Elsevier DO - 10.1016/j.crme.2009.05.004 LA - en ID - CRMECA_2009__337_4_208_0 ER -
Pascal Ardonceau. A nodal boundary elements formulation. Application to the solution of the Laplace equation for irrotational flows. Comptes Rendus. Mécanique, Volume 337 (2009) no. 4, pp. 208-217. doi : 10.1016/j.crme.2009.05.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.05.004/
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