Multiscale Modeling And Simulation In Science

Lecture Notes in Computational Science and Engineering Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick 66 Björn Engquist • Per Lötstedt • Olof Runborg Editors Multiscale Modeling and Simulation in Science With 109 Figures and 4 Tables ABC Björn Engquist Per Lötstedt Department of Information Technology Uppsala University 751 05 Uppsala Sweden [email protected] Department of Mathematics The University of Texas at Austin 1 University Station C1200 Austin, TX 78712-0257 USA [email protected] Olof Runborg Department of Numerical Analysis and Computer Science Royal Institute of Technology 100 44 Stockholm Sweden [email protected] ISBN 978-3-540-88856-7 e-ISBN 978-3-540-88857-4 Lecture Notes in Computational Science and Engineering ISSN 1439-7358 Library of Congress Control Number: 2008939216 Mathematics Subject Classification (2000): 65-01, 65P99, 35B27, 65R20, 70-08, 42C40, 76S05, 76T20 © 2009 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: deblik, Berlin Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com Preface Most problems in science involve many scales in time and space. An example is turbulent flow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundary layer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common difficulty with the simulation of these problems and many others in physics, chemistry and biology