In developing this book, we decided to emphasize applications and to provide methods for solving problems. As a result, we limited the mathematical devel opments and we tried as far as possible to get insight into the behavior of numerical methods by considering simple mathematical models. The text contains three sections. The first is intended to give the fundamen tals of most types of numerical approaches employed to solve fluid-mechanics problems. The topics of finite differences, finite elements, and spectral meth ods are included, as well as a number of special techniques. The second section is devoted to the solution of incompressible flows by the various numerical approaches. We have included solutions of laminar and turbulent-flow prob lems using finite difference, finite element, and spectral methods. The third section of the book is concerned with compressible flows. We divided this last section into inviscid and viscous flows and attempted to outline the methods for each area and give examples.

High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.

This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean

This well-known 2-volume textbook provides senior undergraduate and postgraduate engineers, scientists and applied mathematicians with the specific techniques, and the framework to develop skills in using the techniques in the various branches of computational fluid dynamics. A solutions manual to the exercises is in preparation.

As indicated in Vol. 1, the purpose of this two-volume textbook is to pro vide students of engineering, science and applied mathematics with the spe cific techniques, and the framework to develop skill in using them, that have proven effective in the various branches of computational fluid dy namics Volume 1 describes both fundamental and general techniques that are relevant to all branches of fluid flow. This volume contains specific tech niques applicable to the different categories of engineering flow behaviour, many of which are also appropriate to convective heat transfer. The contents of Vol. 2 are suitable for specialised graduate courses in the engineering computational fluid dynamics (CFD) area and are also aimed at the established research worker or practitioner who has already gained some fundamental CFD background. It is assumed that the reader is famil iar with the contents of Vol. 1. The contents of Vol. 2 are arranged in the following way: Chapter 11 de velops and discusses the equations governing fluid flow and introduces the simpler flow categories for which specific computational techniques are considered in Chaps. 14-18. Most practical problems involve computational domain boundaries that do not conveniently coincide with coordinate lines. Consequently, in Chap. 12 the governing equations are expressed in generalised curvilinear coordinates for use in arbitrary computational domains. The corresponding problem of generating an interior grid is considered in Chap. 13.

This book leads directly to the most modern numerical techniques for compressible fluid flow, with special consideration given to astrophysical applications. Emphasis is put on high-resolution shock-capturing finite-volume schemes based on Riemann solvers. The applications of such schemes, in particular the PPM method, are given and include large-scale simulations of supernova explosions by core collapse and thermonuclear burning and astrophysical jets. Parts two and three treat radiation hydrodynamics. The power of adaptive (moving) grids is demonstrated with a number of stellar-physical simulations showing very crispy shock-front structures.