A Splitting Method for Deep Water with Bathymetry

Afaf Bouharguane; Benjamin Melinand

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arXiv · 1606.01630

A Splitting Method for Deep Water with Bathymetry

Afaf Bouharguane·Benjamin Melinand

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Abstract

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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Afaf Bouharguane, Benjamin Melinand. 2016-06-06. A Splitting Method for Deep Water with Bathymetry. https://arxiv.org/abs/1606.01630

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