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Numerical Study of Free Interface Problems Using Boundary Integral Methods

Hou, Thomas Yizhao (1998) Numerical Study of Free Interface Problems Using Boundary Integral Methods. Documenta Mathematica, Extra (Volume). pp. 601-610. ISSN 1431-0635.

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Numerical study of fluid interfaces is a difficult task due to the presence of high frequency numerical instabilities. Small perturbations even at the round-off error level may experience rapid growth. This makes it very difficult to distinguish the numerical instability from the physical one. Here, we perform a careful numerical stability analysis for both the spatial and time discretization. We found that there is a compatibility condition between the numerical discretizations of the singular integral operators and of the Lagrangian derivative operator. Violation of this compatibility condition will lead to numerical instability. We completely eliminate the numerical instability by enforcing this discrete compatibility condition. The resulting scheme is shown to be stable and convergent in both two and three dimensions. The improved method enables us to perform a careful numerical study of the stabilizing effect of surface tension for fluid interfaces. Several interesting phenomena have been observed. Numerical results will be presented.

Item Type:Article
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Subject Keywords:Free boundary, numerical stability, surface tension, topological singularity
Issue or Number:Volume
Record Number:CaltechAUTHORS:HOUdmicm98
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:760
Deposited By: Archive Administrator
Deposited On:28 Sep 2005
Last Modified:02 Oct 2019 22:36

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