Finite volume schemes for dispersive wave propagation and runup

TL;DR

This paper extends finite volume schemes to dispersive water wave models, specifically Boussinesq systems, to accurately simulate complex phenomena like solitary waves, shock formation, and wave runup in one-dimensional bidirectional nonlinear dispersive waves.

Contribution

It introduces a finite volume framework tailored for dispersive water waves, enhancing the modeling of nonlinear phenomena and wave interactions.

Findings

Effective simulation of solitary wave interactions

Accurate modeling of dispersive shock waves

Successful application to wave runup scenarios

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, dispersive shock wave formation and the runup of breaking and non-breaking long waves.