Numerical verification of a two-layer Boussinesq-type model for surface gravity wave evolution

Abstract

A vertical two-dimensional numerical model is developed to demonstrate the application potential of the recently proposed two-layer Boussinesq-type equations, which have been theoretically shown to exhibit high accuracy in both linear and nonlinear properties, by the authors (Liu and Fang, 2016). Numerical implementation is established on a regular uniform grid, combined with finite differencing of the spatial derivatives and a composite fourth-order Adams–Bashforth–Moulton time integration. Initially, some idealized numerical experiments are designed to examine the fundamental aspects of the model, including the linear dispersion, linear shoaling gradient and highly nonlinear velocity profile. Next, challenging numerical experiments for the regular wave evolution over a submerged breakwater, bichromatic wave evolution in a long flume and focused wave group evolution in a short flume are carried out. The computed results are consistent with the experimental data. By simulating moderately and highly nonlinear wave propagation in deep water, we further investigate the effect of nonlinear terms in the governing equations on the numerical performance. The numerical test of the evolution process of highly nonlinear regular water waves shows that retaining third-order nonlinear terms in the governing equations can provide more accurate computational results.