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Theoretical Issues Arising in the Modeling of Viscous Free-Surface Flows

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Free Boundaries in Viscous Flows

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 61))

Abstract

This paper discusses theoretical and computational issues regarding viscous flows which have a free surface. A number of mathematical models for a particular flow are described and compared, both with one another and with some physical experiments. We consider some approximate models based both on lubrication theory and finite element methods. The importance of the choice of boundary conditions in modeling practical flow phenomena is discussed, and some related open theoretical questions regarding the well-posedness of mathematical models for such phenomena are presented. The discussion also touches upon the role that surface tension has so far played in the mathematical theory of free-surface flows and in many numerical calculations. Briefly outlined is some preliminary work related to convergence estimates for finite-element methods for free-boundary problems.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Penn State University, USA

    W. G. Pritchard & S. J. Tavener

  2. Dept. de Matematicas, Universidad Autonoma, Metropolitana, Mexico

    Patricia Saavedra

  3. Department of Mathematics, The University of Houston, USA

    L. Ridgway Scott

Authors
  1. W. G. Pritchard
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  2. Patricia Saavedra
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  3. L. Ridgway Scott
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  4. S. J. Tavener
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Massachusetts Institute of Technology, Room 66-353, Cambridge, MA, 02139, USA

    Robert A. Brown

  2. Department of Engineering Science and Applied Mathematics, Northwestern University, Evanston, IL, 60208, USA

    Stephen H. Davis

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© 1994 Springer-Verlag New York, Inc.

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Pritchard, W.G., Saavedra, P., Scott, L.R., Tavener, S.J. (1994). Theoretical Issues Arising in the Modeling of Viscous Free-Surface Flows. In: Brown, R.A., Davis, S.H. (eds) Free Boundaries in Viscous Flows. The IMA Volumes in Mathematics and its Applications, vol 61. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8413-7_2

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  • DOI: https://doi.org/10.1007/978-1-4613-8413-7_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8415-1

  • Online ISBN: 978-1-4613-8413-7

  • eBook Packages: Springer Book Archive

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