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An Introduction
to Computational
Fluid Dynamics
THE FINITE VOLUME METHOD
Second Edition
H K Versteeg and W Malalasekera
ANIN_A01.qxd 29/12/2006 09:53 AM Page iii
An Introduction to Computational
Fluid Dynamics
Supporting resources
Visit www.pearsoned.co.uk/versteeg to find valuable online resources
For instructors
• PowerPoint slides that can be downloaded and used for presentations
For more information please contact your local Pearson Education sales
representative or visit www.pearsoned.co.uk/versteeg
ANIN_A01.qxd 29/12/2006 09:53 AM Page i
We work with leading authors to develop the
strongest educational materials in engineering,
bringing cutting-edge thinking and best
learning practice to a global market.
Under a range of well-known imprints, including
Prentice Hall, we craft high-quality print and
electronic publications which help readers to understand
and apply their content, whether studying or at work.
To find out more about the complete range of our
publishing, please visit us on the World Wide Web at:
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ANIN_A01.qxd 29/12/2006 09:53 AM Page ii
Pearson Education Limited
Edinburgh Gate
Harlow
Essex CM20 2JE
England
and Associated Companies throughout the world
Visit us on the World Wide Web at:
www.pearsoned.co.uk
First published 1995
Second edition published 2007
© Pearson Education Limited 1995, 2007
The rights of H K Versteeg and W Malalasekera to be identified as authors of this
work have been asserted by them in accordance with the Copyright, Designs and
Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored
in a retrieval system, or transmitted in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without either the prior
written permission of the publisher or a licence permitting restricted copying in the
United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House,
6–10 Kirby Street, London EC1N 8TS.
All trademarks used herein are the property of their respective owners. The use of
any trademark in this text does not vest in the author or publisher any trademark
ownership rights in such trademarks, nor does the use of such trademarks imply
any affiliation with or endorsement of this book by such owners.
ISBN: 978-0-13-127498-3
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
10987654321
10 09 08 07 06
Typeset by 35 in 10/11pt Ehrhardt MT
Printed and bound by Bell & Bain Limited, Glasgow
The publisher’s policy is to use paper manufactured from sustainable forests.
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Contents
Preface xi
Acknowledgements xiii
1
Introduction
1
1.1 What is CFD? 1
1.2 How does a CFD code work? 2
1.3 Problem solving with CFD 4
1.4 Scope of this book 6
2
Conservation laws of fluid motion and boundary
conditions 9
2.1 Governing equations of fluid flow and heat transfer 9
2.1.1 Mass conservation in three dimensions 10
2.1.2 Rates of change following a fluid particle and for
a fluid element 12
2.1.3 Momentum equation in three dimensions 14
2.1.4 Energy equation in three dimensions 16
2.2 Equations of state 20
2.3 Navier–Stokes equations for a Newtonian fluid 21
2.4 Conservative form of the governing equations of fluid flow 24
2.5 Differential and integral forms of the general transport equations 24
2.6 Classification of physical behaviours 26
2.7 The role of characteristics in hyperbolic equations 29
2.8 Classification method for simple PDEs 32
2.9 Classification of fluid flow equations 33
2.10 Auxiliary conditions for viscous fluid flow equations 35
2.11 Problems in transonic and supersonic compressible flows 36
2.12 Summary 38
3
Turbulence and its modelling 40
3.1 What is turbulence? 40
3.2 Transition from laminar to turbulent flow 44
3.3 Descriptors of turbulent flow 49
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