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

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Progress in Industrial Mathematics at ECMI 2016 (ECMI 2016)

Part of the book series: Mathematics in Industry ((TECMI,volume 26))

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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.

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References

  1. 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.2015.03.042

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  3. 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)

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  4. Wegener, R., Marheineke, N., Hietel, D.: Virtual production of filaments and fleeces. In: Currents in Industrial Mathematics, pp. 103–162. Springer, Berlin/Heidelberg (2015)

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Acknowledgements

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

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Authors and Affiliations

  1. FAU Erlangen-Nürnberg, Lehrstuhl Angewandte Mathematik 1, Cauerstr. 11, D-91058, Erlangen, Germany

    Stefan Schiessl & Nicole Marheineke

  2. Fraunhofer-Institut für Techno- und Wirtschaftsmathematik, Fraunhofer Platz 1, D-67663, Kaiserslautern, Germany

    Walter Arne & Raimund Wegener

Authors
  1. Stefan Schiessl
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  2. Nicole Marheineke
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  3. Walter Arne
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  4. Raimund Wegener
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Corresponding author

Correspondence to Nicole Marheineke .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Peregrina Quintela

  2. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Patricia Barral

  3. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Dolores Gómez

  4. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Francisco J. Pena

  5. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Jerónimo Rodríguez

  6. Department of Applied Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain, Spain

    Pilar Salgado

  7. Department of Applied Mathematics, University of Santiago de Compostela, Lugo, Spain, Spain

    Miguel E. Vázquez-Méndez

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Schiessl, S., Marheineke, N., Arne, W., Wegener, R. (2017). A Finite Volume Method with Staggered Grid on Time-Dependent Domains for Viscous Fiber Spinning. In: Quintela, P., et al. Progress in Industrial Mathematics at ECMI 2016. ECMI 2016. Mathematics in Industry(), vol 26. Springer, Cham. https://doi.org/10.1007/978-3-319-63082-3_106

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