BOUHARGUANE, Afaf; MELINAND, Benjamin

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Licence d’utilisation du document

BOUHARGUANE, Afaf
Modeling Enablers for Multi-PHysics and InteractionS [MEMPHIS]
Institut de Mathématiques de Bordeaux [IMB]

MELINAND, Benjamin
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

IMA Journal of Numerical Analysis. 2017-07-29

Oxford University Press (OUP)

Résumé en anglais

In this paper we derive and prove the wellposedness of a deep water model that generalizes the Saut-Xu system for nonflat bottoms. Then, we present a new numerical method based on a splitting approach for studying this system. The advantage of this method is that it does not require any low pass filter to avoid spurious oscillations. We prove a local error estimate and we show that our scheme represents a good approximation of order one in time. Then, we perform some numerical experiments which confirm our theoretical result and we study three physical phenomena : the evolution of water waves over a rough bottom; the evolution of a KdV soliton when the shallowness parameter increases; the homogenization effect of rapidly varying topographies on water waves.< Réduire

Mots clés en anglais

deep water

splitting scheme

URI

https://oskar-bordeaux.fr/handle/20.500.12278/193728

Project ANR

DYnamique des Fluides, Couches Limites, Tourbillons et Interfaces - ANR-13-BS01-0003

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251