This paper is on arbitrary high order fully discrete one-step ADER discontinuous Galerkin
schemes with subcell finite volume limiters applied to a new class of first order hyperbolic …

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 …

This review paper describes a class of scheme named “residual distribution schemes” or
“fluctuation splitting schemes”. They are a generalization of Roe's numerical flux in …

In this paper we propose a novel set of first-order hyperbolic equations that can model
dispersive non-hydrostatic free surface flows. The governing PDE system is obtained via a …

We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An
efficient formally second-order well-balanced hybrid finite volume finite difference numerical …

In this paper, we propose a novel first-order reformulation of the most well-known
Boussinesq-type systems that are used in ocean engineering. This has the advantage of …

We study here Green–Naghdi type equations (also called fully nonlinear Boussinesq, or
Serre equations) modelling the propagation of large-amplitude waves in shallow water …

We describe fully explicit residual based discretizations of the shallow water equations with
friction on unstructured grids. The schemes are obtained by properly adapting the explicit …

In this paper we evaluate hybrid strategies for the solution of the Green–Naghdi system of
equations for the simulation of fully nonlinear and weakly dispersive free surface waves. We …

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 …