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ALE-FEM for Two-Phase and Free Surface Flows with Surfactants

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Book cover Transport Processes at Fluidic Interfaces

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

We study two-phase and free surface flows with soluble and insoluble surfactants. A numerical analysis of the contained convection-diffusion equations is carried out. The surface equation is stabilized by Local Projection Stabilization. The benefit of Local Projection Stabilization on surfaces is shown by a numerical example. An advanced finite element method that allow for a robust and accurate numerical simulation is presented. The arbitrary Langrangian-Eulerian framework is utilized to capture the moving surface. This allows the usage of a fitted finite element mesh. A decoupling strategy is used to divide the origin problem into subproblems easier to solve. Different time discretizations are considered and the problem of spurious velocities for the spatial discretization is discussed. Numerical examples in 2d and 3d illustrate the potential of the proposed algorithm. The comparison to mathematical predicted values validates the obtained results.

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Acknowledgements

The authors wish to thank the Council of Scientific Research in India (CSIR) for financial support within the project 25(0228)/14/EMR-II and the German Research Foundation (DFG) for financial support within the Priority Programm SPP 1506 “Transport Processes at Fluidic Interfaces” with the project To143/11-2 and within the graduate program Micro-Macro-Interactions in Structured Media and Particle Systems (GK 1554).

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Authors and Affiliations

  1. Indian Institute of Science, Bangalore, 560012, India

    Sashikumaar Ganesan

  2. Fakultät für Mathematik, Otto von Guericke Universität Magdeburg, Universitätsplatz 2, 39016, Magdeburg, Germany

    Andreas Hahn, Kristin Simon & Lutz Tobiska

Authors
  1. Sashikumaar Ganesan
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  2. Andreas Hahn
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  3. Kristin Simon
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  4. Lutz Tobiska
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Corresponding author

Correspondence to Lutz Tobiska .

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Editors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt , Darmstadt, Germany

    Dieter Bothe

  2. Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Arnold Reusken

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Ganesan, S., Hahn, A., Simon, K., Tobiska, L. (2017). ALE-FEM for Two-Phase and Free Surface Flows with Surfactants. In: Bothe, D., Reusken, A. (eds) Transport Processes at Fluidic Interfaces. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-56602-3_1

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