A Splitting Method for Deep Water with Bathymetry
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.
Cite
@article{arxiv.1606.01630,
title = {A Splitting Method for Deep Water with Bathymetry},
author = {Afaf Bouharguane and Benjamin Melinand},
journal= {arXiv preprint arXiv:1606.01630},
year = {2017}
}