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Optimal Control for Two-Phase Flows

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Trends in PDE Constrained Optimization

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 165))

Abstract

We consider an optimal control problem with respect to the two-phase Navier–Stokes equations. Different numerical schemes are presented, in particular a level-set method, as well as an approach based an Allen-Cahn phase field model. We also consider a geometrical approach to treat the interface and address the question of convergence of a numerical scheme.

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Acknowledgements

The authors acknowledge the support by the German Research Association (DFG) under grant SPP-1253, BR-3391/4-1 and PR-548/8-1.

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Authors and Affiliations

  1. Mathematical Seminar, Christian-Albrechts-University of Kiel, Ludewig-Meyn-Str. 4, 24098, Kiel, Germany

    Malte Braack & Benjamin Tews

  2. Mathematical Institute, Tübingen University, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Markus Klein & Andreas Prohl

Authors
  1. Malte Braack
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  2. Markus Klein
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  3. Andreas Prohl
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  4. Benjamin Tews
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Corresponding author

Correspondence to Malte Braack .

Editor information

Editors and Affiliations

  1. Department Mathematik, Universität Erlangen-Nürnberg, Erlangen, Germany

    Günter Leugering

  2. Institut für Dynamik komplexer technisch, Max-Planck-Institut, Magdeburg, Germany

    Peter Benner

  3. Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Dortmund, Germany

    Sebastian Engell

  4. Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany

    Andreas Griewank

  5. Mathematisches Institut, Universität Basel, Basel, Switzerland

    Helmut Harbrecht

  6. Fachbereich Mathematik Optimierung und Approximation, Universität Hamburg, Hamburg, Germany

    Michael Hinze

  7. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

    Rolf Rannacher

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

    Stefan Ulbrich

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Braack, M., Klein, M., Prohl, A., Tews, B. (2014). Optimal Control for Two-Phase Flows. In: Leugering, G., et al. Trends in PDE Constrained Optimization. International Series of Numerical Mathematics, vol 165. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-05083-6_22

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