On a model to propagate surface waves — A second order approach

Abstract

Surface water waves can travel large distances with negligible energy dissipation. The description of such waves is therefore often done using the Laplace equation with suitable boundary conditions. In most cases linear models can give reasonable descriptions of the wave transformation and good values of design parameters. However there is a growing interest on non-linear models since the magnitude of non-linear effects should be considered for certain wave conditions. In this paper the development of a time dependent Boundary Integral Element Model, which includes significant non-linear effects at an affordable computational time, is reported. The savings in CPU time where achieved mostly because it was possible to set-up and invert the coefficient matrix only once. The free-surface equations are established using a Taylor series expansion and an analysis using dimensionless parameters is done to retain the most important terms. The formulation is presented in some detail and computational aspects are also referred. Results for different types of wave generation and propagation are presented. The applicability of the model to irregular wave propagation is also illustrated.