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Computing finite-time singularities in interfacial flows

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Modern Methods in Scientific Computing and Applications

Part of the book series: NATO Science Series ((NAII,volume 75))

Abstract

Finite-time singularities occurring in mathematical models of free-surface flows indicate that important qualitative changes are taking place; for problems in solid and fluid mechanics this includes topological transitions—blow-up and pinch-off. For many problems, the dynamics leading to the formation of such singularities are described by self-similar solutions of the governing nonlinear partial differential equations. We present an analytical and numerical study of these similarity solutions and discuss their stability.

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  1. Department of Mathematics, Duke University, Durham, NC, 27708-0320, USA

    Thomas P. Witelski

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  1. Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec, Canada

    Anne Bourlioux  & Gert Sabidussi  & 

  2. Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada

    Martin J. Gander

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Witelski, T.P. (2002). Computing finite-time singularities in interfacial flows. In: Bourlioux, A., Gander, M.J., Sabidussi, G. (eds) Modern Methods in Scientific Computing and Applications. NATO Science Series, vol 75. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0510-4_12

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