A 2DH fully dispersive and weakly nonlinear Boussinesq-type model based on a finite-volume and finite-difference TVD-type scheme

Abstract

In this study, we developed a fully dispersive Boussinesq-type wave model in the modelling framework of the public-domain Boussinesq model, FUNWAVE-TVD. The model adopts the fully dispersive Boussinesq equations of Karambas and Memos (2009) and uses a finite-volume and finite-difference TVD-type scheme. A well-balanced conservative form of the governing equations is derived to facilitate the hybrid numerical scheme. Flux terms were computed by the MUSCL-TVD scheme up to the fourth-order accuracy within the Riemann solver. The third-order Strong Stability-Preserving (SSP) Runge–Kutta scheme was used for time stepping. The convolution integral terms were estimated by the numerical evaluation and the spatial derivative terms were computed by the finite difference scheme. Wave breaking is predicted by locally switching the Boussinesq equations to nonlinear shallow water equations with a Froude number criterion. The model is validated against the linear wave theory and various experiments to examine the capability of the model in simulating wave dispersion, shoaling, breaking, refraction, diffraction, and run-up.