Numerical methods in fluid dynamics: Initial and initial boundary-value problems.

*(English)*Zbl 0592.76001
Cambridge etc.: Cambridge University Press. IX, 446 p. £30.00; $ 44.50 (1985).

This book is intended to be a first book on numerical fluid dynamics for graduate students in engineering and physical sciences. The finite difference method is used throughout the book and this volume deals with initial and initial boundary-value problems. A basic knowledge of partial differential equations is required.

The overall appearance of the manuscript is very good. Illustrations are neatly done, well labelled and appear close to the point where they are first referenced. The type used is quite readable. The equations are typed clearly and no ambiguity is detected. Notation is introduced along the test, allowing an easy reading.

A review of the table of contents reveals that the author organized the subjects in the text in an increasing complexity order. The proof of some of the classical theorems involving a lot of knowledge, is left on appendices, ensuring continuity of the subject. The book is divided into five chapters and references are gathered at the end of each chapter.

Chapter I provides a very good introduction on the basis of finite difference approximations and the Lax’s theorem. Chapter II is completely devoted to parabolic equations, presenting a very interesting discussion, beginning with a finite difference approximation for a linear parabolic equation in a one space dimension until the nonlinear case with irregular boundaries. Chapters III and IV are concerned with hyperbolic equations. Chapter IV follows the same scheme of Chapter II, but presenting an introductory discussion on the accuracy of finite difference approximations. Chapter IV introduces the hyperbolic conservation laws and chapter V deals with the stability of the solution in the presence of boundaries. Along all the book the numerical methods are discussed in detail and the numerical examples, gathered at the end of each chapter, are intended to clarify and to stress the main features of the preceeding theory.

This book should be of value to a wide segment of the scientific community related to fluid dynamics.

The overall appearance of the manuscript is very good. Illustrations are neatly done, well labelled and appear close to the point where they are first referenced. The type used is quite readable. The equations are typed clearly and no ambiguity is detected. Notation is introduced along the test, allowing an easy reading.

A review of the table of contents reveals that the author organized the subjects in the text in an increasing complexity order. The proof of some of the classical theorems involving a lot of knowledge, is left on appendices, ensuring continuity of the subject. The book is divided into five chapters and references are gathered at the end of each chapter.

Chapter I provides a very good introduction on the basis of finite difference approximations and the Lax’s theorem. Chapter II is completely devoted to parabolic equations, presenting a very interesting discussion, beginning with a finite difference approximation for a linear parabolic equation in a one space dimension until the nonlinear case with irregular boundaries. Chapters III and IV are concerned with hyperbolic equations. Chapter IV follows the same scheme of Chapter II, but presenting an introductory discussion on the accuracy of finite difference approximations. Chapter IV introduces the hyperbolic conservation laws and chapter V deals with the stability of the solution in the presence of boundaries. Along all the book the numerical methods are discussed in detail and the numerical examples, gathered at the end of each chapter, are intended to clarify and to stress the main features of the preceeding theory.

This book should be of value to a wide segment of the scientific community related to fluid dynamics.

Reviewer: N.F.F.Ebecken

##### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

35Q30 | Navier-Stokes equations |

76Dxx | Incompressible viscous fluids |

76M99 | Basic methods in fluid mechanics |