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This monograph aims at presenting a unified approach to numerical
modeling of tsunami as long waves based on finite difference
methods for 1D, 2D and 3D generation processes, propagation, and
runup. Many practical examples give insight into the relationship
between long wave physics and numerical solutions and allow readers
to quickly pursue and develop specific topics in greater depth. The
aim of this book is to start from basics and then continue into
applications. This approach should serve well the needs of
researchers and students of physics, physical oceanography,
ocean/civil engineers, computer science, and emergency management
staff. Chapter 2 is particularly valuable as it fully describes the
application of finite-difference methods to the study of long waves
by demonstrating how physical properties of water waves, especially
phase velocity, are connected to the chosen numerical algorithm.
Basic notions of numerical methods, i.e. approximation of the
relevant differential equations, stability of the numerical scheme,
and computational errors are explained through application to long
waves. Finite-difference methods are further developed in major
chapters to deal with complex problems that arise in the study of
recent tsunamis.
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