Finite volume schemes for Boussinesq type equations

TL;DR

This paper extends finite volume schemes to Boussinesq type dispersive water wave models, enabling accurate simulation of nonlinear phenomena like solitary wave interactions in one dimension.

Contribution

It introduces a finite volume framework tailored for Boussinesq systems, addressing dispersive effects in nonlinear water wave modeling.

Findings

Effective simulation of solitary wave interactions

Extension of finite volume methods to dispersive systems

Potential for improved water wave modeling

Abstract

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 dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions.