Optimized Green-Naghdi Equations for the Modelling of Waves Nearshore Transformations

Discontinuous-Galerkin discretization of a new class of Green-Naghdi equations

We describe in this work a discontinuous-Galerkin Finite-Element method to approximate the solutions of a new family of 1d Green-Naghdi models. These new models are shown to be more computationally efficient, while being asymptotically equivalent to the initial formulation with regard to the shallowness parameter. Using the free surface instead of the water height as a conservative variable, th...

Large Time Existence for 1d Green-naghdi Equations

We consider here the 1D Green-Naghdi equations that are commonly used in coastal oceanography to describe the propagation of large amplitude surface waves. We show that the solution of the Green-Naghdi equations can be constructed by a standard Picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition.

Derivation and Analysis of a New 2d Green-naghdi System

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 GreenNaghdi equations. Its mathematical interest is that it allows a control of the rotational part of the (vertically averaged) horizontal velocity, which is not the case for the usual Green...

The Eigenvalue Problem for Solitary Waves of the Green-Naghdi Equations

High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model

In this paper, we consider a one-dimensional fully nonlinear weakly dispersive Green-Naghdi model for shallow water waves over variable bottom topographies. Such model describes a large spectrum of shallow water waves, and it is thus of great importance to design accurate and robust numerical methods for solving it. The governing equations contain mixed spatial and temporal derivatives of the u...