A splitting method for deep water with bathymetry
Afaf Bouharguane, Benjamin Melinand · IMA Journal of Numerical Analysis · 2017
In this article, we derive and prove the well-posedness 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 1 in time. Then, we perform some numerical experiments that 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 and the homogenization effect of rapidly varying topographies on water waves.