To describe the strongly nonlinear dynamics of waves propagating in the final stages of
shoaling and in the surf and swash zones, fully nonlinear models are required. The ability of …

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 …

In this paper, a new method to handle wave breaking in fully non-linear Boussinesq-type
models is presented. The strategy developed to treat wave breaking is based on a …

We introduce a new class of two-dimensional fully nonlinear and weakly dispersive Green–
Naghdi equations over varying topography. These new Green–Naghdi systems share the …

A novel tool for tsunami wave modeling is presented. This tool has the potential of being
used for operational purposes: indeed, the numerical code VOLNA is able to handle the …

In this paper, we present an original derivation process of a non-hydrostatic shallow water-
type model which aims at approximating the incompressible Euler and Navier-Stokes …

After we derive the Serre system of equations of water wave theory from a generalized
variational principle, we present some of its structural properties. We also propose a robust …

In this paper, a non-reflection internal wave maker algorithm is included in the
incompressible Smoothed Particle Hydrodynamics (ISPH) model for the wave simulations. A …

In this paper, we describe a numerical method to solve numerically the weakly dispersive
fully nonlinear Serre-Green-Naghdi (SGN) celebrated model. Namely, our scheme is based …