A computational method for multiple steady Hele-Shaw bubbles in planar domains
Nasser, Mohamed M. S. Green, Christopher C. Kalmoun, El Mostafa
Nasser, Mohamed M. S.
Green, Christopher C.
Kalmoun, El Mostafa
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2025-02-25
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Article
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Bubbles,Conformal mapping,Free boundary problem,Hele-Shaw flow,Multiply connected domain
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Citation
Nasser, Mohamed M. S., Green, Christopher C., Kalmoun, El Mostafa (2025). A computational method for multiple steady Hele-Shaw bubbles in planar domains. ETNA - Electronic Transactions on Numerical Analysis, 150-170.
Abstract
We present a unified numerical method to determine the shapes of multiple Hele-Shaw bubbles in steady motion, and in the absence of surface tension, in three planar domains: free space, the upper half-plane, and an infinite channel. Our approach is based on solving the free boundary problem for the bubble boundaries using a fast and accurate boundary integral method. The main advantage of our method is that it allows for the treatment of a very high number of bubbles. The presented method is validated by recovering some existing results for steady bubbles in channels and free space. Several numerical examples are presented, many of which feature configurations of bubbles that have not appeared in the literature before. © 2025, the Author(s)
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Kent State University
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Electronic Transactions on Numerical Analysis
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10689613