Related papers: On the blow-up scenario for some modified Serre-Gr…
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…
We perform numerical experiments on the Serre-Green-Naghdi (SGN) equations and a fully dispersive "Whitham-Green-Naghdi" (WGN) counterpart in dimension 1. In particular, solitary wave solutions of the WGN equations are constructed and their…
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…
For surface gravity waves propagating in shallow water, we propose a variant of the fully nonlinear Serre-Green-Naghdi equations involving a free parameter that can be chosen to improve the dispersion properties. The novelty here consists…
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…
The Serre-Green-Naghdi (SGN) equations provide a valuable framework for modelling fully nonlinear and weakly dispersive shallow-water flows. However, their elliptic formulation can considerably increase the computational cost compared to…
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…
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 present an algorithm to solve the dispersive depth-averaged Serre-Green-Naghdi (SGN) equations using patch-based adaptive mesh refinement. These equations require adding additional higher derivative terms to the nonlinear shallow water…
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…
The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations (also known as the fully non-linear Boussinesq equations) with full topography effects introduced in Green, A.E. and…
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…
The (Serre-)Green-Naghdi system is a non-hydrostatic model for the propagation of surface gravity waves in the shallow-water regime. Recently , Favrie and Gavrilyuk proposed in [Nonlinearity, 30(7) (2017)] an efficient way of numerically…
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…
We consider in this paper the Serre--Green--Naghdi equations with surface tension. Smooth solutions of this system conserve an $H^1$-equivalent energy. We prove the existence of global weak dissipative solutions for any relatively…
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…
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 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…
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…
New evidence of surprising robustness of solitary-wave solutions of the Serre-Green-Naghdi (SGN) equations is presented on the basis of high-resolution numerical simulations conducted using a novel well-balanced finite-volume method. SGN…