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Séparation des échelles et schémas multiniveaux pour les équations d'ondes non-linéaires

Abstract : In this work, we point out and apply some ideas for the numerical simulation by multi- level schemes of several wave equations including dispersive (Korteweg de Vries) and dissipative ones (Kuramoto-Sivashinski). We start from the approach developed for dissipative equations decomposing the solution into large (Y) and small (Z) scales, and we show that it is necessary to have a regularization in time to allow stable numerical treatment of Y and Z which are here generated using hierarchical processes such as Wavelets, Incremental Unknowns or Fourier.
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https://hal.archives-ouvertes.fr/hal-00768332
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Caterina Calgaro, Jean-Paul Chehab, Jacques Laminie, Ezzeddine Zahrouni. Séparation des échelles et schémas multiniveaux pour les équations d'ondes non-linéaires. ESAIM: Proceedings, EDP Sciences, 2009, 27, pp.180-208. ⟨10.1051/proc/2009027⟩. ⟨hal-00768332⟩

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