Numerical Methods for Two-phase Incompressible Flows
This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with models for
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Sven Gross
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Arnold Reusken
Numerical Methods for Two-phase Incompressible Flows
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Sven Gross Universit¨at Bonn Institut f¨ur Numerische Simulation Wegelerstrasse 6 53115 Bonn Germany [email protected]
Arnold Reusken RWTH Aachen Lehrstuhl f¨ur Numerische Mathematik Templergraben 55 52056 Aachen Germany [email protected]
ISSN 0179-3632 ISBN 978-3-642-19685-0 e-ISBN 978-3-642-19686-7 DOI 10.1007/978-3-642-19686-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011926983 Mathematics Subject Classification (2010): 35A35, 53A05, 76D05, 76D07, 65F08, 65F10, 65N22, 65N30, 65N75, 76M10, 76T10 c Springer-Verlag Berlin Heidelberg 2011 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. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to Agnes and Monique
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Preface
Numerical treatment of two-phase incompressible flow problems In the past few decades there has been tremendous progress in the development and analysis of numerical methods for one-phase incompressible Stokes and Navier-Stokes equations. There is an extensive literature on space- and time discretization methods, iterative solvers and other numerical issues, e.g., implementation aspects, related to this problem class. This literature comprises a huge number of papers and many monographs. The research activities resulted in output ranging from new fundamental mathematical insights to software packages that can be used for the simulation of incompressible flow problems. Nowadays open source and commercial software packages are available that perform satisfactory when used as black or gray box solvers for a fairly large class of incompressible one-phase flow problems. Although very big progress has been made, there are still important topics which require further research. For example, in the field of development and analysis of numerical methods for the simulation of turbulent flows, non-Newtonian flows and flows coupled with chemistry the state of the art is not satisfactory, yet. The work that has been done on numerical methods for one-phase incompressible Navier-Stoke
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