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 …

After we derive the Serre system of equations of water wave theory from a generalized
variational principle, we present some of its structural properties. We also propose a robust …

We develop a general framework for designing conservative numerical methods based on
summation by parts operators and split forms in space, combined with relaxation Runge …

This paper is devoted to the derivation and mathematical analysis of a wave-structure
interaction problem which can be reduced to a transmission problem for a Boussinesq …

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 …

The present book is entirely devoted to the development of mathematical models and
numerical algorithms to simulate the generation and propagation of long surface water …

We review here the derivation of many of the most important models that appear in the
literature (mainly in coastal oceanography) for the description of waves in shallow water. We …

Considered here is a class of Boussinesq systems of Nwogu type. Such systems describe
propagation of nonlinear and dispersive water waves of significant interest such as solitary …

In this paper we consider the one-parameter family of Bona–Smith systems, which belongs
to the class of Boussinesq systems modelling two-way propagation of long waves of small …

This paper is devoted to the theoretical and numerical investigation of the initial boundary
value problem for a system of equations used for the description of waves in coastal areas …