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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2017

A Splitting Method for Deep Water with Bathymetry

Résumé

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.
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Dates et versions

hal-01326794 , version 1 (05-06-2016)
hal-01326794 , version 2 (14-02-2017)

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Afaf Bouharguane, Benjamin Melinand. A Splitting Method for Deep Water with Bathymetry. IMA Journal of Numerical Analysis, 2017. ⟨hal-01326794v2⟩
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