INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2007; 53:129–147 Published online 19 June 2006 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/fld.1252 A parametric finite-difference method for shallow sea waves A. G. Bratsos 1, ∗, † , I. Th. Famelis 1, ‡ and A. M. Prospathopoulos 2, § 1 Department of Mathematics, Technological Educational Institution (T.E.I.) of Athens, GR 122 10 Egaleo, Athens, Greece 2 Hellenic Center for Marine Research (HCMR), Institute of Oceanography, P.O. Box 712, GR-190 13 Anavyssos, Greece SUMMARY 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 2006 John Wiley & Sons, Ltd. Received 2 January 2005; Revised 10 April 2006; Accepted 11 April 2006 KEY WORDS: shallow water waves; Boussinesq equations; numerical modelling; finite-difference method 1. INTRODUCTION During the last three decades a lot of effort has been put by the scientific community on numerical modelling of short waves in shallow water. Most of the phase-resolving models dealing with this research aspect and used in practical applications are based either on the mild-slope equation, ∗ Correspondence to: A. G. Bratsos, Department of Mathematics, Technological Educational Institution (T.E.I.) of Athens, GR 122 10 Egaleo, Athens, Greece. † E-mail: bratsos@teiath.gr ‡ E-mail: ifamelis@teiath.gr § E-mail: aprosp@ath.hcmr.gr Contract/grant sponsor: E.E. Contract/grant sponsor: Greek Government Copyright 2006 John Wiley & Sons, Ltd.