Three-Dimensional Numerical Model for Fully Nonlinear Waves Over Arbitrary Bottom

We present an accurate three-dimensional (3D) Numerical Wave Tank (NWT) solving the full equations in the potential ow formulation. The NWT is able to simulate wave propagation up to overturning over an arbitrary bottom topography. The model is based on a high-order 3D Boundary Element Method (BEM) with the Mixed Eulerian-Lagrangian (MEL) approach. The spatial discretization is third-order and ensures continuity of the inter-element slopes. Waves can be generated in the tank by wavemakers or they can be directly speci ed on the free surface. A node regridding can be applied at any time step over selected areas of the free surface. Results are presented for the computation of overturning waves over a ridge and their kinematics. INTRODUCTION Many numerical wave models solving Fully Nonlinear Potential Flow (FNPF) equations have been developed, mostly in two dimensions (2D), which have been shown to accurately simulate wave overturning in deep and intermediate water (Dommermuth et al. 1988) as well as wave shoaling and breaking over slopes (Grilli et al. 1997). In most recent 2D models, incident waves can be generated at one extremity and re ected, absorbed or radiated at the other extremity (Grilli and Horrillo 1997). In three dimensions (3D), only a few attempts have been reported of solving FNPF problems, for arbitrary transient nonlinear waves in a general propagation model, with the possibility of modeling overturning waves. Xu and Yue (1992) and Xue et al. (2001) calculated 3D overturning waves in a doubly periodic computational domain with in nite depth (i.e. only the free surface was discretized). In their case, progressive Stokes waves were led to breaking Dept. of Math. and Stat., McMaster Univ., Hamilton, ON L8S 4K1, Canada. E-mail: guyenne@math.mcmaster.ca. Ocean Engrg. Dept., Univ. of Rhode Island, Narragansett, RI 02882, USA. E-mail: grilli@oce.uri.edu. CMLA, ENS de Cachan, 94235 Cachan cedex, France. E-mail: dias@cmla.ens-cachan.fr. 1 Guyenne, Grilli and Dias