[« Les fleurs du MAL » – une méthode d'ondelettes adaptive de lignes arbitraires I : problèmes de convection–diffusion]
« Les fleurs du MAL » font allusion aux quelques nouveaux développements ( « les fleurs ») de la méthode des lignes arbitraires (MAL), obtenus depuis la première publication (dans C. R. Acad. Sci. Paris, Sér. I, dans 1991). Ici nous rappelons les bases de la méthodologie MAL (semi-discrétisation) appliquée aux problèmes de convection–diffusion stationnaire. Nous développons aussi un programme de résolution adaptatif, basé sur une analyse en ondelettes, capable de capter les situations avec des couches minces, apparaissant dans ce type de problèmes. Nous démontrons l'efficacité et la haute précision de ce programme de résolution par ondelettes, en l'appliquant à un problème bidimensionnel qui pose un vrai défi, traitant à la fois les couches limites et intérieures.
Baudelaire's ‘les fleurs du mal’ refers to various new developments (‘les fleurs’) of the method of arbitrary lines (mal), since it was first published (in C. R. Acad. Sci. Paris, Sér. I, in 1991). Here we revisit the basic mal (semi-discretization) methodology for stationary convection–diffusion problems and develop an adaptive, wavelet-based solver that is capable of capturing the thin layers that arise in such problems. We show the efficacy and high accuracy of the wavelet-mal solver by applying it to a challenging 2D problem involving both boundary and interior layers.
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Mot clés : Mécanique des fluides numérique, Problèmes singulièrement perturbés, Réduction dimensionelle, Semi-discrétisation, Programme de résolution adaptatif par ondelettes, Couches frontières et intérieurs
@article{CRMECA_2004__332_1_23_0,
author = {Xiaoan Ren and Leonidas S. Xanthis},
title = {{\textquoteleft}Les fleurs du mal{\textquoteright} {\textendash} an adaptive wavelet method of arbitrary lines {I:} convection{\textendash}diffusion problems},
journal = {Comptes Rendus. M\'ecanique},
pages = {23--29},
publisher = {Elsevier},
volume = {332},
number = {1},
year = {2004},
doi = {10.1016/j.crme.2003.10.004},
language = {en},
}
TY - JOUR AU - Xiaoan Ren AU - Leonidas S. Xanthis TI - ‘Les fleurs du mal’ – an adaptive wavelet method of arbitrary lines I: convection–diffusion problems JO - Comptes Rendus. Mécanique PY - 2004 SP - 23 EP - 29 VL - 332 IS - 1 PB - Elsevier DO - 10.1016/j.crme.2003.10.004 LA - en ID - CRMECA_2004__332_1_23_0 ER -
Xiaoan Ren; Leonidas S. Xanthis. ‘Les fleurs du mal’ – an adaptive wavelet method of arbitrary lines I: convection–diffusion problems. Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 23-29. doi : 10.1016/j.crme.2003.10.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.10.004/
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