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Axisymmetric free boundary problems

Published online by Cambridge University Press:  25 June 1997

MARK SUSSMAN  and
PETER SMEREKA
MARK SUSSMAN
Affiliation:
Present address: University of California Davis, Davis, CA 95616, USA. Center for Computational Sciences and Engineering, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
PETER SMEREKA
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
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Abstract

We present a number of three-dimensional axisymmetric free boundary problems for two immiscible fluids, such as air and water. A level set method is used where the interface is the zero level set of a continuous function while the two fluids are solutions of the incompressible Navier–Stokes equation. We examine the rise and distortion of an initially spherical bubble into cap bubbles and toroidal bubbles. Steady solutions for gas bubbles rising in a liquid are computed, with favourable comparisons to experimental data. We also study the inviscid limit and compare our results with a boundary integral method. The problems of an air bubble bursting at a free surface and a liquid drop hitting a free surface are also computed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 341 , 25 June 1997 , pp. 269 - 294
Copyright
© 1997 Cambridge University Press

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