The RAM Approach in Aerodynamics
First, in Sect. 7.1.1, we again consider the simple case examined in Veuillot’s thesis [140] devoted to turbomachinery fluid flow, simulated in Sect. 6.3.1; then, in Sect. 7.1.2, the more sophisticated G–Z RAM Approach [141].
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Radyadour Kh. Zeytounian
Navier–Stokes–Fourier Equations A Rational Asymptotic Modelling Point of View
R. Kh. Zeytounian Universite´ des Sciences et Technologies de Lille LML – cite´ Scientifique 59655 Villeneuve d’Ascq Ce´dex France [email protected]
ISBN 978-3-642-20745-7 e-ISBN 978-3-642-20746-4 DOI 10.1007/978-3-642-20746-4 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011943087 # 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)
Preface
Rationality and Asymptotics are the two main concepts associated with the Modelling in Fluid Dynamics, which have completely changed our look on the Understanding of Navier–Stokes–Fourier (NS-F) equations, governing the viscous, compressible and heat conducting Newtonian baroclinic and non-adiabatic fluid flows.1 This Rational Asymptotic Modelling (RAM) Approach have raised, on the one hand, further new interesting questions and potentialities for Applied Mathematicians, in their quest of rigorous existence and uniqueness results for the Fluid Flow problems. On the other hand, this RAM Approach have opening up of new vistas for the derivation, by Fluid Dynamicians, various consistent simplified models related with real stiff fluid flow problems, as an assistance to Numericians embarked on a computational simulations of complex problems of engineering interest with the help of high speed computers. In this book we touch (see, in particular, the Chap. 6) the “crucial” problem of a practical (rather than formal, abstract) “Mathematics” for a consistent RAM Approach, via a “Postulate” and, some “key rules” inspired from asymptotics. This “mathematics for the RAM” is applied in a consistent way to modelling of various stiff problems of the: aerodynamics (Chap. 7), Be´nard thermal convection (Chap. 8) and atmospheric motions (Chap. 9). The main lignes of the aims of this book are set out in the “Prologue”, and in the “Overview” a brief outline of the events related with my rather long “RAM Adventure”, during the years 1968–2009, is given. The book is divided into nine Chapters, an Epilogue, a list of References, and a
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