Review of Numerical Modeling of Water Waves by Pengzhi Lin: Taylor & Francis, Oxford, England; 2008; ISBN: 9780415415781; 504 pp. Price: $170.

 In the last two decades, myriad numerical models and modeling techniques have been developed for simulating the properties and behavior of ocean waves under a variety of conditions. These include models for coastal wave propagation, wave agitation in harbors, overtopping of seawalls, wave-structure interaction, etc. Thanks to recent advances that have occurred in the past $20\text{years}$ in computing power, both large-scale (ocean) and refined local-scale (coastal) wave modeling can now be performed. The modeling techniques are based on a variety of governing equations, including Laplace equation, Boussinesq equations, Navier-Stokes equations, energy-balance equations, etc., involving either the steady or the unsteady mode, and either one, two, or three dimensions as well as numerous approximations. The numerical techniques also display wide variation: finite differences, finite elements, boundary elements, volume of fluid, meshless computations, etc. This explosion of modeling methods is certainly admirable and attests to the dynamism of the field; however, it sometimes confronts practitioners (engineers needing models for project applications), researchers, model developers, and managers with confusion, because the pros and cons of certain models vis-a-vis others are infrequently discussed.

This issue has occasionally been addressed in brief review papers (Panchang et al. 1999; Isobe 1999), but Professor Pengzhi Lin’s recent book Numerical Modeling of Water Waves is, simply stated, a superb contribution. It is comprehensive and authoritative, covering practically the entire spectrum of modeling applications and methodologies that one encounters in this field. It is a systematic compilation of knowledge associated with wave models. And while one may think that such a book would be full of arcane mathematical derivations, it is, despite the obviously large number of equations, very readable.

The first three chapters, totaling 127 pages, contain an introduction to water waves, a review of hydrodynamics, and a discussion of the frequently used wave theories and wave phenomena. While these topics are similar to the first few chapters in many other textbooks on water waves, they are presented with an elegant combination of intuition, assumed background preparation (perhaps of the order of a first course in wave mechanics), and mathematics; and the emphasis of the presentation seems to be on material that is needed later for modeling purposes. For instance, one will have to look elsewhere for the deri-vation of the Airy solution. We were particularly impressed by the succinct discussions of turbulence in Chapter 2 and individual wave phenomena in Chapter 3. These chapters are followed by a well-crafted chapter covering numerous numerical solution methods. While entire textbooks have been devoted to the solution of partial differential equations by the finite-difference method alone, for instance, we like the concise presentation of this chapter (56 pages), which provides the reader with a fundamental understanding of the procedures through a combination of intuitive reasoning and a nominal amount of mathematics: even if all the details are not provided, one learns enough to become an educated user or researcher for a particular method. We were pleased to see sections on mesh generation and on topics like stability, convergence, consistency, truncation errors, etc., which, in spite of their importance for successful simulations, seem to receive relatively little attention these days.

The next two chapters (“Water Wave Models” and “Modeling Wave-Structure Interaction”) provide details of various modeling schemes used in coastal and ocean engineering. In addition to mathematical details, reference is made to numerous widely used packages like FLOW3D, FLUENT, PHAROS, CGWAVE, COBRAS, WAMIT, WAM, DELFT3D, MIKE21, BOUSS-2D, and a whole host of other models, and, importantly, examples of many applications (with black and white photographs) are provided. Also of interest is a set of benchmark tests that not only help the reader to understand the theory but also provide solutions that a modeler should reproduce to invest confidence in solutions to real-life applications that he may obtain later (for which the solutions may not be known). The final chapter is a 30-page summary of the numerous modeling methods along with the author’s assessment of the suitability (using a star-based rating system), of a particular method for various phenomena. Although we were surprised that wave reflection was not one of the criteria used, the summary table would be valuable to those uninitiated wave modeling. This chapter also contains a list of areas deserving of attention for future developments.

Professor Lin has taken the sometimes chaotic and certainly voluminous body of research and development work in this field and presented it in a very systematic and elegant manner. The writing and the figures are clean, and the book contains 38 pages of references as well as a few Fortran source codes (in the appendix) for selected problems, making it a comprehensive resource and, in our opinion, one of the best textbooks on water waves published in recent years. The purpose of this book as stated in the preface by Professor Lin is twofold: (1) to introduce readers to the basic wave theories and wave models so that readers are able to choose appropriate existing models for different physical problems, and (2) to provide adequate details of numerical techniques so that advanced readers can construct their own wave models and test models against the benchmark tests provided. Professor Lin has met this objective with distinction. We highly recommend this book for those involved in the practice of coastal, ocean, marine, and civil engineering and naval architecture, and also for introductory and intermediate graduate students.