The book under review is intended to be a two-volume textbook to provide students of engineering, science and applied mathematics with specific techniques which have proved effective in computational fluid dynamics (CFD). It is written by an expert in the field in a remarkably direct, jargon-free and clear style with a wealth of examples chosen from a wide-ranging set of applications. A very useful set of references and indices are also provided. All people involved in the production of this excellent textbook, the author, the publishers and the series editors are to be congratulated for their efforts. I am fairly certain that this text is likely to become the standard one in this extremely rapidly growing and important subject.
The first of the two volumes deals with "Fundamental and General Techniques". There are ten chapters and two appendices. Chapter 1 gives a brief but readable introduction to the subject of CFD. This includes a discussion of the cost-effectiveness and power of numerical simulations, especially with modern computers. Chapter 2 is an introduction to partial differential equations as they are usually encountered in fluid dynamics. The coverage here is traditional and more in the nature of a quick recapitulation of the essentials of pde's than an in-depth treatment. An unwary student might get the (wrong) impression that the author's classification is complete. There follow three chapters on computational techniques, theoretical background, and Galerkin type methods (collectively called weighted residual methods by the author). The final four chapters provide applications of the techniques introduced. They deal, respectively, with steady problems, diffusion problems in one or more space dimensions and convection-dominated problems (linear and nonlinear).
The second volume is more specialised and is aimed at the advanced graduate student and the research worker. Chapters 11, 12 and 13 are concerned with general matters such as th~derivation of the equations of fluid flow and various flow categories, a treatment of curvilinear co-ordinates and grid-generation. Chapter 14 treats inviscid supersonic and transomc flows. Both potential and direct solutions of the Euler equations are discussed. Chapter 15 is devoted to boundary-layer flow. The last three chapters treat various types of flows governed by the full or reduced Navier-Stokes equations.
It is apparent from the above description that the coverage of these volumes is little short of encyclopaedic! The author has made his treatment particulary accessible to students by including many interesting and challenging problems. It would have been helpful to include hjnts for their solution. There are several fully written-out computer programs getting right down to the 'nuts and bolts' of CFD. Considering the size of the work, it was pleasant to find that there were relatively few errors. I list the very few I noticed: In problem 2.15, the fundamental solution of the heat equation is confused with its Green's function for a certain initial-boundary value problem. Equation 6.12 has a m~sprintinvolving a sign. The discussion in 17.4 of the vorticity formulation does not mention that a "gauge" condition can always be imposed on the velocity vector-potential and that only two components of Such potentials are actually independent functions. If a code solves for the three components as implied in this section, convergence would be a rare event! Incidentally, no discussion is given of what it means (if at all) to have a well-posed