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Operator Splitting Algorithms for Free Surface Flows: Application to Extrusion Processes

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Book cover Splitting Methods in Communication, Imaging, Science, and Engineering

Part of the book series: Scientific Computation ((SCIENTCOMP))

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Abstract

We investigate the benefits of operator splitting methods in the context of computational fluid dynamics. In particular, we exploit their capacity at handling free surface flows and a large variety of physical phenomena in a flexible way. A mathematical and computational framework is presented for the numerical simulation of free surface flows, where the operator splitting strategy allows to separate inertial effects from the other effects. The method of characteristics on a fine structured grid is put forward to accurately approximate the inertial effects while continuous piecewise polynomial finite element associated with a coarser subdivision made of simplices is advocated for the other effects. In addition, the splitting strategy also allows modularity, and in a straightforward manner rheological model change for the fluid. We will emphasize this flexibility by treating Newtonian flows, visco-elastic flows, multi-phase, and multi-density immiscible incompressible Newtonian flows. The numerical framework is thoroughly presented; the test case of the filling of a cylindrical tube with potential die swell in an extrusion process is taken as the main illustration of the advantages of operator splitting.

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Notes

  1. 1.

    The case of non-vanishing Dirichlet boundary conditions reads similarly upon defining a lifting of the boundary conditions.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA

    Andrea Bonito

  2. Haute Ecole de Gestion de Genève, University of Applied Sciences Western Switzerland (HES-SO), Rue de la Tambourine 17, 1227, Carouge, Switzerland

    Alexandre Caboussat

  3. MATHICSE, Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Marco Picasso

Authors
  1. Andrea Bonito
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  2. Alexandre Caboussat
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  3. Marco Picasso
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Correspondence to Andrea Bonito .

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Editors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, Texas, USA

    Roland Glowinski

  2. Department of Mathematics, UCLA, Los Angeles, California, USA

    Stanley J. Osher

  3. Department of Mathematics, UCLA, Los Angeles, California, USA

    Wotao Yin

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Bonito, A., Caboussat, A., Picasso, M. (2016). Operator Splitting Algorithms for Free Surface Flows: Application to Extrusion Processes. In: Glowinski, R., Osher, S., Yin, W. (eds) Splitting Methods in Communication, Imaging, Science, and Engineering. Scientific Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-41589-5_21

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