A splitting method for deep water with bathymetry

Afaf Bouharguane (1, 2) , Benjamin Melinand (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS

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 two physical phenomena : the evolution of a KdV soliton when the shallowness parameter increases; the homogenization effect of rapidly varying topographies on water waves.

Mots clés: deep water; splitting scheme

Domaines: Equations aux dérivées partielles [math.AP]

Afaf Bouharguane, Benjamin Melinand. A splitting method for deep water with bathymetry. 2016. ⟨hal-01326794v1⟩