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.

While there are several excellent books dealing with numerical analysis and analytical theory, students and faculty in numerical applications to ocean dynamics have to sift through hundreds of references. This monograph is an attempt to partly rectify this situation. Major chapters (II, III and IV) deal first with the basics and then go on to various applications. Instead of covering the vast field of ocean dynamics, this book focuses on transport equations (diffusion and advection), shallow water phenomena - tides, storm surges and tsunamis; three-dimensional time dependent oceanic motion; natural oscillations; and steady state phenomena. The aim of this book is two-fold; it gives an introduction to the application of finite-difference methods to ocean dynamics, and it also reviews more complex methods.

While there are several excellent books dealing with numerical analysis and analytical theory, one has to practically sift through hundreds of references. This monograph is an attempt to partly rectify this situation. It aims to introduce the application of finite-difference methods to ocean dynamics as well as review other complex methods. Systematically presented, the monograph first gives a detailed account of the basics and then go on to discuss the various applications. Recognising the impossibility of covering the entire field of ocean dynamics, the writers have chosen to focus on transport equations (diffusion and advection), shallow water phenomena - tides, storm surges and tsunamis, three-dimensional time dependent oceanic motion, natural oscillations, and steady state phenomena. The many aspects covered by this book makes it an indispensable handbook and reference source to both professionals and students of this field.