Approximate Deconvolution Models of Turbulence Analysis, Phenomenolo
This volume presents a mathematical development of a recent approach to the modeling and simulation of turbulent flows based on methods for the approximate solution of inverse problems. The resulting Approximate Deconvolution Models or ADMs have some adva
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2042
William J. Layton
•
Leo G. Rebholz
Approximate Deconvolution Models of Turbulence Analysis, Phenomenology and Numerical Analysis
123
William J. Layton University of Pittsburgh Dept. Mathematics Pittsburgh Pennsylvania USA
Leo G. Rebholz Clemson University Department of Mathematical Sciences Clemson South Carolina USA
ISBN 978-3-642-24408-7 e-ISBN 978-3-642-24409-4 DOI 10.1007/978-3-642-24409-4 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2011943497 Mathematics Subject Classification (2010): 65-XX, 76-XX c Springer-Verlag Berlin Heidelberg 2012 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 to 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The Navier–Stokes Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Integral Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 The K41 Theory of Homogeneous, Isotropic Turbulence.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Large Eddy Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Eddy Viscosity Closures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Closure by van Cittert Approximate Deconvolution . . . . . . . . . . 1.4.1 The Bardina Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 The Accuracy of van Cittert Deconvolution .. . . . . . . . . . 1.5 Approximate Deconvolution Regularizations . . . . . . . . . . . . . . . . . . 1.5.1 Time Relaxation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.2 The Leray-Deconvolution Regularization . . . . . . . . . . . . . 1.5.3 The NS-Alpha Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5.4 The NS-Omega Regularization . . . . . . . . . . . . . . . . . . . . . . .
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