**NUMERICAL
MODELING OF WATER WAVES**

SECOND
EDITION

by

Dr. Charles
L. Mader

ISBN -
0-8493-2311-8, **CRC Press, Boca Raton, Florida**

Review
of the Book by:

Dr. George Pararas-Carayannis

Retired Director of The International Tsunami Information Center

Honolulu, Hawaii

**The
second edition of the book entitled Numerical Modeling of Water
Waves is a well-written, comprehensive treatise of the evolving
science of computer modeling of waves.**

**Its author,
Dr. Charles Mader - a pioneering researcher and a world authority
on numerical modeling - presents an all-encompassing treatment
based on his life-long research on the subject, conducted mainly
at the Los Alamos National Laboratory.**

**In this
second edition however - and in a very skillful and methodical
manner - the author provides new insights on the subject and
updates the reader with what is being done with state-of-the-art,
high-performance computers which allow for the adaptation of
new codes that can result in even more accurate simulations of
waves generated from a variety of source mechanisms - whether
earthquakes, landslides, explosions, or the impact of asteroids.**

The discussions in the second edition include thorough reviews
of theoretical principles and of the development of codes for
specific applications to computer modeling of real and theoretical
data sets, as well of examples from the literature specific to
the methodology used.

**The new
codes allow the rapid solution of highly complex equations that
describe wave generation, wave energy propagation, and allow
the prediction of near and far field wave characteristics. In
addition to validating the results with historical and hydraulic
modeling data, the new edition of the book provides several conclusions
concerning the effects of various source characteristics on wave
generation, propagation and termination.**

These characteristics relate to the unique mechanisms of wave
generation from dierent sources and the effects on the distribution
of wave energy and its attenuation across a body of water. The
modeling described is based on finite discretization in space
and time using structured rectangular meshes with codes using
finite difference schemes. However, the codes that are used for
the calculations have been modified or extended to allow for
mesh refinements.

By far, the greater part of the second edition of the book is
devoted to selected applications of codes for wave computer modeling
used in simulating various historical tsunamis and in developing
animations from a variety of other actual or postulated wave
generative mechanisms.

**Specifically
in the Second Edition, Dr. Mader does a remarkable job in summarizing
succinctly the principles of water wave theory and the governing
mathematical equations of Eulerian conservation of mass, momentum
and energy which are used to describe different forms of water
waves.**

**Subsequently,
he explains the classical theory of the shallow water model and
the mathematical equations that describe wave motions - thus
leading to the development of the finite-difference equations
that he used with dierent codes to model waves including those
of historical tsunamis.**

**Through
such skillful and methodical presentation and examples - ensuring
that every aspect of modeling receives appropriate consideration
- the author not only explains how the basic theory is applied,
but also introduces several new important ideas, procedures and
concepts in tsunami science**

that can be used as the fundamental basis for the simulations
of such waves.

More specifically in the second edition, Dr. Mader describes
in detail:

**a) the WAVE
code which solves the equations for Airy, third-order Stokes
and the Laitone solitary gravity waves;**

**b) the shallow-water
SWAN code which solves the long wave, shallow water, nonlinear
equations of fluid flow;**

**c) the two-dimensional
ZUNI code which solves the incompressible, viscous fluid flows
with a free surface using the Navier-Stokes equations;**

**d) the threedimensional
ZUNI code (SOLA) that solves the incompressible viscous fluid
flows with a free surface, also using the full Navier-Stokes
equations;**

**e) the Carrier
linear gravity wave LGW code which uses analytical methods to
solve the linear gravity model; and**

**f) TIDE,
a classic computer program used for calculating tides.**

**Additionally
he furnishes on the book's CD-ROM the FORTRAN source and the
executable codes which he uses to generate realistic graphic
animations showing the result of finite dierences at every time
step.**

**With all
of these code descriptions, the author provides examples of wave
propagation from analytical,**

postulated and historical wave source mechanisms - such as those
of the 1994 Skagway tsunami as well as for other north Pacific
historical tsunamis.

The most remarkable part of the book is the use, for the first
time, of compressible numerical modeling methodologies to model,
in two and three dimensions, the generation of water waves by
explosions, projectile and asteroid impacts and their propagation
from the source. These include modeling of the KT Chicxulub asteroid
impact and the modeling of the impact landslide that generated
the largest historical tsunami which flooded to 520 meter altitude
in Lituya Bay, Alaska in 1958.

In summary, the Second Edition of Numerical Modeling of Water
Waves by Dr.

Charles Mader represents an outstanding work of of scholarship
and a valuable reference for any researcher involved in numerical
modeling of waves.