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Computing Through Singularities in Potential Flow with Applications to Electrohydrodynamic Problems

  • Maria Garzon
  • James A. Sethian
  • Len J. Gray
  • August Johansson
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

Many interesting fluid interface problems, such as wave propagation and breaking, droplet and bubble break-up, electro-jetting, rain drops, etc. can be modeled using the assumption of potential flow. The main challenge, both theoretically and computationally, is due to the presence of singularities in the mathematical models. In all the above mentioned problems, an interface needs to be advanced by a velocity determined by the solution of a surface partial differential equation posed on this moving boundary. By using a level set framework, the two surface equations of the Lagrangian formulation can be implicitly embedded in PDEs posed on one higher dimension fixed domain. The advantage of this approach is that it seamlessly allows breakup or merging of the fluid domain and therefore provide a robust algorithm to compute through these singular events. Numerical results of a solitary wave breaking, the Rayleigh-Taylor instability of a fluid column, droplets and bubbles breaking-up and the electrical droplet distortion and subsequent jet emission can be obtained using this levelset/extended potential model.

Notes

Acknowledgements

This work was supported by the U.S. Department of Energy, under contract Number DE-AC02-05CH11231, the Spanish Ministry of Science and Innovation, Project Number MTM2013-43671-P. The third author was also supported by the Research Council of Norway through a Centers of Excellence grant to the Center for Biomedical Computing at Simula Research Laboratory, Project Number 179578, as well as through the FRIPRO program at Simula Research Laboratory, project number 251237.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Maria Garzon
    • 1
  • James A. Sethian
    • 2
  • Len J. Gray
    • 3
  • August Johansson
    • 4
  1. 1.Department of MathematicsUniversidad de OviedoOviedoSpain
  2. 2.University of CaliforniaBerkeleyUSA
  3. 3.Bergen Software Services InternationalBergenNorway
  4. 4.Simula Research LaboratoryFornebuNorway

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