A parametric finite-difference method for shallow sea waves

This paper presents a parametric finite-difference scheme concerning the numerical solution of the one-dimensional Boussinesq-type set of equations, as they were introduced by Peregrine (J. Fluid Mech. 1967; 27(4)) in the case of waves relatively long with small amplitudes in water of varying depth. The proposed method, which can be considered as a generalization of the Crank-Nickolson method, aims to investigate alternative approaches in order to improve the accuracy of analogous methods known from bibliography. The resulting linear finite-difference scheme, which is analysed for stability using the Fourier method, has been applied successfully to a problem used by Beji and Battjes (Coastal Eng. 1994; 23: 1-16), giving numerical results which are in good agreement with the corresponding results given by MIKE 21 BW (User Guide. In: MIKE 21, Wave Modelling, User Guide. 2002; 271-392) developed by DHI Software. Copyright (c) 2006 John Wiley & Sons, Ltd.