zbMATH — the first resource for mathematics

Numerical computation of internal and external flows. Volume 1: Fundamentals of numerical discretization. (English) Zbl 0662.76001
Wiley Series in Numerical Methods in Engineering; Wiley-Interscience Publication. Chichester (UK) etc.: Wiley. xiv, 515 p. £60.00 (1988).
The first volume of Prof. Hirsch’s book deals with the fundamentals of fluid flow simulation on the theoretical level, that is, without entering into the details of real flow computations. It is a well structured introduction to Numerical Fluid Mechanics that demands few prerequesites from the students.
The book is divided into 4 parts, each containing two or more chapters. The first part, consisting of 3 chapters, treats mathematical models for fluid flow simulation. The first chapter sketches the basic equations of Fluid Dynamics, the second discusses the different types of approximations used in Fluid Dynamics (inviscid flows, irrotational flows, boundary layer approximation, etc.), the third discusses characteristic in order to classify second-order partial differential equations. The second part, called Basic Discretization Techniques, treats Finite Differences, Finite Elements and Finite Volumes in three different chapters. The Finite Element Method is dealt with on 35 pages.
The third part treats the Analysis of Numerical Schemes in 4 chapters. The concepts of consistency, stability and convergence of a numerical scheme are defined and several methods to analyse the stability of a scheme are discussed. I have found this 4 chapters very suitable to introduce the subject to Engineering students.
Finally, the forth part of the book deals, in 2 chapters, with solution of the discretized equations. One chapter gives integration methods for systems of ordinary differential equations and the other iterative methods for the solution of algebraic systems.
Reviewer: R.Sampaio

76-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
76M99 Basic methods in fluid mechanics