This review focuses on recent advances in process-based numerical models of the impact of
extreme storms on sandy coasts. Driven by larger-scale models of meteorology and …

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 …

Abstract The Serre–Green–Naghdi (SGN) equations, also known as the fully-nonlinear
Boussinesq wave equations, accurately describe the behaviour of dispersive shoaling water …

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 …

A general method for the derivation of asymptotic nonlinear models in shallow and deep
water is presented. Starting from a general dimensionless version of the water wave …

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 new methodology is presented to handle wave breaking over complex bathymetries in
extended two-dimensional Boussinesq-type (BT) models which are solved by an …

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 …

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 …

Finite volume schemes are commonly used to construct approximate solutions to
conservation laws. In this study we extend the framework of the finite volume methods to …