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International Conference on Finite Volumes for Complex Applications

FVCA 2017: Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems pp 109–117Cite as

A Splitting Scheme for Three-Phase Flow Models

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 200))

Abstract

A fractional step method that provides approximate solutions of a three-phase flow model is presented herein. The three-fluid model enables to handle smooth or discontinuous unsteady solutions. The numerical method is grounded on the use of the entropy inequality that governs smooth solutions of the set of PDEs. The evolution step relies on an explicit scheme, while implicit schemes are embedded in the relaxation step. The main properties of the scheme are given. Numerical approximations of two basic Riemann problems are eventually presented.

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Acknowledgements

The first author receives financial support by ANRT through an EDF/CIFRE grant number 2016/0611. Computational facilities were provided by EDF.

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Authors and Affiliations

  1. EDF Lab Chatou, 6, Quai Watier, 78400, Chatou, France

    Hamza Boukili & Jean-Marc Hérard

  2. I2M, Aix Marseille Université, 39 Rue Joliot Curie, 13453, Marseille, France

    Hamza Boukili & Jean-Marc Hérard

Authors
  1. Hamza Boukili
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  2. Jean-Marc Hérard
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Corresponding author

Correspondence to Jean-Marc Hérard .

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Editors and Affiliations

  1. Equipe RAPSODI, Inria Lille - Nord Europe, Villeneuve-d’Ascq, France

    Clément Cancès

  2. Commissariat à l'énergie atomique et aux énergies alternatives, Centre de Saclay, Gif-sur-Yvette, France

    Pascal Omnes

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Boukili, H., Hérard, JM. (2017). A Splitting Scheme for Three-Phase Flow Models . In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_12

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