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Viscous Interfacial Motion: Analysis and Computation

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New Frontiers of Multidisciplinary Research in STEAM-H (Science, Technology, Engineering, Agriculture, Mathematics, and Health)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 90))

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Abstract

We consider the interfacial flows between two viscous incompressible fluids. After formulating the mathematical framework, we first present analytical solutions to the linearized problem, and discuss some results from linear asymptotic analysis. We then describe a numerical method for computing the nonlinear motion which ensures a high accuracy on and near the moving interface. Simulation results on viscous Stokes waves are presented to demonstrate the advantages of this method. In addition, as an example of nonlinear asymptotic study, we conduct a perturbation series analysis for Stokes waves with small viscosity, the results of which provide an analytical justification to the numerical observation.

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Acknowledgements

The author is grateful to Drs. B. Toni and Z. Xie for an invited visit at Virginia State University. The author would also like to thank the anonymous reviewers for helpful comments. This work was partially supported by the National Science Foundation under Grant Numbers 1216936 and 1245769, and the Simons Foundation under Grant Number 208716.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA

    Jin Wang

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  1. Jin Wang
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Correspondence to Jin Wang .

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Editors and Affiliations

  1. Dept of Mathematics & Computer Sciences, Virginia State University, Petersburg, Virginia, USA

    Bourama Toni

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Wang, J. (2014). Viscous Interfacial Motion: Analysis and Computation. In: Toni, B. (eds) New Frontiers of Multidisciplinary Research in STEAM-H (Science, Technology, Engineering, Agriculture, Mathematics, and Health). Springer Proceedings in Mathematics & Statistics, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-07755-0_16

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