Basic Control Volume Finite Element Methods for Fluids and Solids

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. For photocopying of material in this volume, please pay a copying fee through the Copyright In this case permission to photocopy is not required from the publisher. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. will co-publish a series of prestigious lectures delivered during IISc's centenary year (2008-09), and a series of textbooks and monographs, by prominent scientists and engineers from IISc and other institutions. This pioneering collaboration will contribute significantly in disseminating current Indian scientific advancement worldwide. In addition, the collaboration also proposes to bring the best scientific ideas and thoughts across the world in areas of priority to India through specially designed Indian editions. The " IISc Research Monographs Series " will comprise state-of-the-art monographs written by experts in specific areas. They will include, but not be limited to, the authors' own research work. This page intentionally left blank This page intentionally left blank vii To my mentors, advisors, colleagues, and students This page intentionally left blank This page intentionally left blank ix Preface The advent of the digital computer in the middle of the last century initiated a rapid and continued growth in the development of computational tools for solving field problems. In the early days of these developments, researchers worked on a relatively small set of methods, applying them to a broad range of mechanics problems from stress and strain in solids through to fluid flow. As the field matured, however, distinct camps of researches based around methods and problems were formed. In extremely broad terms, the development of methods were split between those based on finite difference approaches and those based on finite element approaches; likewise applications were split between solids and fluids. As the computational modeling field moved forward, other classes of solution methods were developed. Of particular note were control volume/finite volume methods. An immediate appeal of such methods was their obvious connection, through explicit discrete balance equations, to the physics of the problem at hand. Early control volume developments used finite difference methods to arrive at appropriate discrete equations. It was rapidly realized, however, that control volume solutions could also …