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A Finite Volume Method with Staggered Grid on Time-Dependent Domains for Viscous Fiber Spinning

  • Stefan Schiessl
  • Nicole Marheineke
  • Walter Arne
  • Raimund Wegener
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

The spinning of slender viscous fibers can be described by the special Cosserat theory with one-dimensional models consisting of partial differential and algebraic equations on time-dependent spatial domains. We propose a first-order finite volume method on a staggered grid with flux approximation suitable for the underlying differential-algebraic characteristics and a proper geometric handling of the space-time domain. The numerical results confirm the theoretical convergence orders. As exemplary application a rotational spinning scenario is studied.

Notes

Acknowledgements

This work has been supported by German DFG, project 251706852, MA 4526/2-1, WE 2003/4-1.

References

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    Arne, W., Marheineke, N., Meister, A., Schiessl, S., Wegener, R.: Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets. J. Comput. Phys. 294, 20–37 (2015). doi:10.1016/j.jcp.2015.03.042Google Scholar
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    Gear, C.W.: Differential-algebraic equation index transformations. SIAM J. Sci. Stat. Comput. 9, 39–47 (1988). doi:10.1137/0909004Google Scholar
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    Schiessl, S., Marheineke, N., Wegener, R.: A moving mesh framework based on three parametrization layers for 1d PDEs. In: Progress in Industrial Mathematics at ECMI 2014. Springer, Berlin (2016)Google Scholar
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    Wegener, R., Marheineke, N., Hietel, D.: Virtual production of filaments and fleeces. In: Currents in Industrial Mathematics, pp. 103–162. Springer, Berlin/Heidelberg (2015)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Stefan Schiessl
    • 1
  • Nicole Marheineke
    • 1
  • Walter Arne
    • 2
  • Raimund Wegener
    • 2
  1. 1.FAU Erlangen-NürnbergLehrstuhl Angewandte Mathematik 1ErlangenGermany
  2. 2.Fraunhofer-Institut für Techno- und WirtschaftsmathematikKaiserslauternGermany

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