1. INTRODUCTION

One of the most outstanding characteristics of the development of coastal water wave mechanics during the last decades is probably the ever-increasing importance of numerical models. The background of this situation, which has much in common with many other branches of applied physics, is twofold. First, differential or integral representation of the physical reality is generally well established, but not in a form suitable for general analytical treatment, particularly when practical problems with complex geometry of the solution domain are concerned. Second, significant progress in computational methods for differential and integral equations with complicated properties has been made in the recent years, and the accessibility of high-speed computers to practicing engineers has been remarkably improved. The objective in writing this chapter is to provide a state-of-the-art review of the theories and applications of the various numerical models that have been distributed in the various publication media. Owing to the rapid expansion of the literature, a relatively complete review would be voluminous and will not be performed here. Instead, the focus will concentrate on the models that are widely applicable to coastal and ocean engineering practice. Some emphasis will be given to the high-resolution methods.

A numerical model in this chapter must be understood as any algebraic representation of a differential equation or an equation system that depicts the whole or some aspects of...