Related papers: Conservative modified Serre-Green-Naghdi equations…
We develop structure-preserving numerical methods for the Serre-Green-Naghdi equations, a model for weakly dispersive free-surface waves. We consider both the classical form, requiring the inversion of a non-linear elliptic operator, and a…
The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is an extension of the well known shallow-water system to the situation where…
This paper presents an extended version of the celebrated Serre-Green-Naghdi (SGN) system. This extension is based on the well-known Bona-Smith-Nwogu trick which aims to improve the linear dispersion properties. We show that in the fully…
We derive here a variant of the 2D Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard $2D $ Green-Naghdi equations. Its…
The Serre-Green-Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre-Green-Naghdi system incorporating the effect of an artificial term that results in…
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-volume and finite-difference splitting approach recently…
We consider 2D free surface gravity waves in prismatic channels with bathymetric variations uniquely in the transverse direction. Starting from the Saint-Venant equations (shallow water equations) we derive a 1D transverse averaged model…
Serre-Green-Naghdi equations (SGN equations) is the most simple dispersive model of long water waves having "good" mathematical and physical properties. First, the model is a mathematically justified approximation of the exact water wave…
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 on reliable finite volume methods, proven to be very effective…
In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into…
We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. Contrarily to the classical Boussinesq-type models, it contains only first order derivatives, thus allowing to…
In this short note, we present a multi-symplectic structure of the Serre-Green-Naghdi (SGN) equations modelling nonlinear long surface waves in shallow water. This multi-symplectic structure allow the use of efficient finite difference or…
This manuscript is devoted to the modelling of water waves in the deep water regime with some emphasis on the underlying variational structures. The present article should be considered as a review of some existing models and modelling…
The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in…
The Green-Naghdi system is used to model highly nonlinear weakly dispersive waves propagating at the surface of a shallow layer of a perfect fluid. The system has three associated conservation laws which describe the conservation of mass,…
A novel method is developed for extending the Green-Naghdi (GN) shallow-water model equation to the general system which incorporates the arbitrary higher-order dispersive effects. As an illustrative example, we derive a model equation…
We introduce a new class of Green-Naghdi type models for the propagation of internal waves between two (1+1)-dimensional layers of homogeneous, immiscible, ideal, incompressible, irrotational fluids, vertically delimited by a flat bottom…
In this paper we study two multidimensional nonlinear dispersive systems: the Serre-Green-Naghdi (SGN) equations describing dispersive shallow water flows, and Iordanskii-Kogarko-Wijngaarden (IKW) equations describing fluids containing…
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 the Serre or Green Naghdi (S-GN) equations to reproduce…
The two-dimensional Green-Naghdi (GN) shallow-water model for surface gravity waves is extended to incorporate the arbitrary higher-order dispersive effects. This can be achieved by developing a novel asymptotic analysis applied to the…