[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
@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/
[1] Drag due to lift: Concepts for prediction and reduction, Annual Review of Fluid Mechanics, Volume 33 (2001), pp. 587-617
[2] Boundary Element Methods in Acoustics (C.A. Brebbia; R.D. Ciskowski, eds.), Computational Mechanics Publications and Elsevier Applied Sciences, 1991
[3] Boundary Integral Equation Methods for Solids and Fluids, Wiley, London, 1999
[4] Calculation of potential flows about arbitrary bodies, Progress in Aeronautical Sciences, Volume 8 (1966), pp. 1-138
[5] Low Speed Aerodynamics, McGraw-Hill, 1991
[6] F.T. Johnson, A general panel method for the analysis and design of arbitrary configurations in incompressible flows, NASA Report 3079, 1980
[7] B. Maskew, Prediction of subsonic aerodynamics characteristics: A case for low order panel methods, AIAA Paper 81-0252, 1981
[8] A.E. Magnus, M.A. Epton, PAN AIR-A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method, vol. 1, NASA CR-3251, 1980
[9] B. Hunt, The panel method for subsonic aerodynamic flows: A survey of mathematical formulations and numerical models and an outline of the new British aerospace scheme, Von Karman Institute for Fluid Dynamics, Lecture Series 1978-4, 1978
[10] Aérodynamique Subsonique, Editions de l'Ecole Polytechnique de Montréal, 1998
[11] M. Mudry, La théorie générale des nappes et filaments tourbillonnaires et ses applications à l'aérodynamique instationnaire, Thèse d'Etat, Paris VI, 1982
[12] Theoretical Hydrodynamics, MacMillan and Co, 1962 (pp. 186–191)
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