"This book is a well-written graduate level text in computational fluid dynamics. The text begins with a rather thorough discussion and derivation of the equations of fluid dynamics, followed by a review of topics in the theory of partial differential equations. There is a good introduction to the two numerical methods, finite volume and finite difference, that are treated in this text. The material is well-organized, starting with simple one-dimensional equations and moving to numerical methods for two-dimensional and three-dimensional problems. Grids are treated in some detail. In addition to simple colocated grids, there is discussion of non-uniform, staggered, and unstructured grids. There is a good mixture of theoretical and computational topics. This text should be of value to all researchers interested in computational fluid dynamics." -- MATHEMATICAL REVIEWS
From the Back Cover
The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state-of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov's order barrier and how to overcome it by means of slope-limited schemes is discussed. An introduction is given to efficient iterative solution methods, using Krylov subspace and multigrid acceleration. Many pointers are given to current literature, to help the reader to quickly reach the current research frontier.