Dispersive wave runup on non-uniform shores

TL;DR

This paper applies finite volume methods to dispersive PDEs, specifically Boussinesq-type equations, to simulate wave runup on non-uniform shores, demonstrating their effectiveness in coastal hydrodynamics modeling.

Contribution

It introduces recent numerical results for dispersive wave runup using finite volume schemes on non-uniform beaches, advancing computational approaches in coastal hydrodynamics.

Findings

Successful numerical simulation of wave runup on non-uniform beaches.

Finite volume methods effectively solve dispersive Boussinesq-type equations.

Results align with expected physical wave behaviors.

Abstract

Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically a representative of Boussinesq type equations in view of important applications to the coastal hydrodynamics. Numerical results of the runup of a moderate wave onto a non-uniform beach are presented along with great lines of the employed numerical method (see D. Dutykh et al. (2011) for more details).