In this paper, the development of a class of depth-integrated, phase-resolving models for
surface wave propagation, known as Boussinesq-type models (BTMs), is reviewed. This …

Page 1 Mathematical Surveys and Monographs Volume 188 The Water Waves Problem
Mathematical Analysis and Asymptotics David Lannes American Mathematical Society Page 2 …

The fully nonlinear and weakly dispersive Green–Naghdi model for shallow water waves of
large amplitude is studied. The original model is first recast under a new formulation more …

We investigate here the ability of a Green–Naghdi model to reproduce strongly nonlinear
and dispersive wave propagation. We test in particular the behavior of the new hybrid finite …

The accuracy and efficiency of two methods of resolving the exact potential flow problem for
nonlinear waves are compared using three different one horizontal dimension (1DH) test …

With the objective of modeling coastal wave dynamics taking into account nonlinear and
dispersive effects, a highly accurate nonlinear potential flow model was developed. The …

Nonlinear wave interactions and superpositions among the different wave components and
wave groups in a random sea sometimes produce rogue waves with extremely large wave …

A new multi-layer irrotational Boussinesq-type model is proposed for both linear and
nonlinear surface water waves over mildly sloping seabeds. The model is formulated in …

This article presents a semi-discrete, multilayer set of equations describing the three-
dimensional motion of an incompressible fluid bounded below by topography and above by …

Many of today's complex scientific applications now require a vast amount of computational
power. General purpose graphics processing units (GPGPUs) enable researchers in a …