Spectral Methods for Uncertainty Quantification With Applications to
This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on
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Scientific Computation Editorial Board J.-J. Chattot, Davis, CA, USA P. Colella, Berkeley, CA, USA W. E, Princeton, NJ, USA R. Glowinski, Houston, TX, USA Y. Hussaini, Tallahassee, FL, USA P. Joly, Le Chesnay, France J.E. Marsden, Pasadena, CA, USA D.I. Meiron, Pasadena, CA, USA O. Pironneau, Paris, France A. Quarteroni, Lausanne, Switzerland and Politecnico of Milan, Milan, Italy J. Rappaz, Lausanne, Switzerland R. Rosner, Chicago, IL, USA P. Sagaut, Paris, France J.H. Seinfeld, Pasadena, CA, USA A. Szepessy, Stockholm, Sweden M.F. Wheeler, Austin, TX, USA
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O.P. Le Maître O.M. Knio
Spectral Methods for Uncertainty Quantification With Applications to Computational Fluid Dynamics
Prof. Dr. O.P. Le Maître LIMSI-CNRS Université Paris-Sud XI 91403 Orsay cedex France [email protected]
Prof. Dr. O.M. Knio Department of Mechanical Engineering The Johns Hopkins University 3400 North Charles Street 223 Latrobe Hall Baltimore MD 21218-2682 USA [email protected]
ISBN 978-90-481-3519-6 e-ISBN 978-90-481-3520-2 DOI 10.1007/978-90-481-3520-2 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010921813 © Springer Science+Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To the Ladies, certainly, Marie-Christine & May
Preface
This book deals with the application of spectral methods to problems of uncertainty propagation and quantification in model-based computations. It specifically focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special attention to models arising in simulations of fluid flows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated flows and compressible flows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only alludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or fluid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-depende
