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High-order Techniques for Calculating Surface Tension Forces

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Free Boundary Problems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 154))

Abstract

In this paper we develop further the “height fraction” technique for computing curvature directly from volume fractions. In particular we, (1) develop a systematic approach for calculating curvature from volume fractions which is accurate to any order, and (2) we test the second-order “height fraction” technique on the following two-phase problems: (1) the break-up of a cylindrical column of liquid due to Rayleigh-capillary instability, (2) surface tension induced droplet oscillations and (3) the steady motion of gas bubbles rising in liquid.

Work supported in part by NSF grant number 0242524 (U.S. Japan Cooperative Science). Work supported in part by JSPS.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    M. Sussman

  2. Department of Applied Chemistry, Muroran Institute of Technology, 27-1, Mizumotocho, Muroran-shi, Hokkaido, 050-8585, Japan

    M. Ohta

Authors
  1. M. Sussman
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  2. M. Ohta
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Editor information

Editors and Affiliations

  1. Departamento de Matemática Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal

    Isabel Narra Figueiredo

  2. Universidade de Lisboa / CMAF, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    José Francisco Rodrigues

  3. Departamento de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Lisa Santos

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Sussman, M., Ohta, M. (2006). High-order Techniques for Calculating Surface Tension Forces. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_41

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