On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization
Résumé
In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplectic and Hamiltonian formulations, well-posedness and existence of solitary-wave solutions) were previously analyzed by the authors in Part I. As a second part of the study, considered here is the construction of geometric schemes for the numerical integration. By using the method of lines, the geometric properties, based on the multi-symplectic and Hamiltonian structures, of different strategies for the spatial and time discretizations are discussed and illustrated.
Domaines
Mécanique des fluides [physics.class-ph] Dynamique des Fluides [physics.flu-dyn] Equations aux dérivées partielles [math.AP] Analyse numérique [math.NA] Physique Atmosphérique et Océanique [physics.ao-ph] Physique Numérique [physics.comp-ph] Formation de Structures et Solitons [nlin.PS] Systèmes Solubles et Intégrables [nlin.SI]Origine | Fichiers produits par l'(les) auteur(s) |
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