Mathematics of Large Eddy Simulation of Turbulent Flows
Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. Since its birth in 1970, LES has undergone an explosive deve
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L. C. Berselli
T. Iliescu
W. J. Layton
Mathematics of Large Eddy Simulation of Turbulent Flows With 32 Figures
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Dr. Luigi C. Berselli
Dr. William J. Layton
University of Pisa Department of Applied Mathematics “U. Dini” Via Bonanno 25/b I-56126 Pisa, Italy e-mail: [email protected]
University of Pittsburgh Department of Mathematics Thackeray Hall 301 Pittsburgh, PA 15260, USA e-mail: [email protected]
Dr. Traian Iliescu Virginia Polytechnic Institute and State University Department of Mathematics 456 McBryde Hall Blacksburg, VA 24061, USA e-mail: [email protected]
Library of Congress Control Number: 2005930495
ISSN 1434-8322 ISBN-10 3-540-26316-0 Springer Berlin Heidelberg New York ISBN-13 978-3-540-26316-6 Springer Berlin Heidelberg New York 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. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany 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. Typesetting: Data conversion by LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig, Germany Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
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To Lucia, Raffaella, and Annette
Preface
Turbulence is ubiquitous in nature and central to many applications important to our life. (It is also a ridiculously fascinating phenomenon.) Obtaining an accurate prediction of turbulent flow is a central difficulty in such diverse problems as global change estimation, improving the energy efficiency of engines, controlling dispersal of contaminants and designing biomedical devices. It is absolutely fundamental to understanding physical processes of geophysics, combustion, forces of fluids upon elastic bodies, drag, lift and mixing. Decisions that affect our life must be made daily based on predictions of turbulent flows. Direct numerical simulation of turbulent flows is not feasible for the foreseeable future in many of these applications. Even for those flows for which it is currently feasible, it is filled with uncertainties due to the sensitivity of the flow to factors such as incomplete initial conditions, body forces, and surface roughness. It is also expensive and time consuming–far too time consuming to use as a design tool. Storing, manipulating and post-processing the m
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