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Semi-Implicit Multiresolution for Multiphase Flows

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • N. Andrianov

    (Institut Français du Pétrole, Département de Mathématiques Appliquées
    Currently at Schlumberger Research and Development)

  • F. Coquel

    (Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions (UMR 7598))

  • M. Postel

    (Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions (UMR 7598))

  • Q. H. Tran

    (Institut Français du Pétrole, Département de Mathématiques Appliquées)

Abstract

In the context of multiphase flows we are faced with vector PDE solutions combining waves whose speeds are several orders of magnitude apart. The wave of interest is the transport one, and is relatively slow. The other fast acoustic waves are not interesting but impose a very restrictive CFL condition if a fully explicit in time scheme is considered. We therefore use a time semi-implicit conservative scheme where the fast waves are handled with a linearized implicit formulation and the slow wave remains explicitly solved. The CFL condition, governed by the explicit wave speed is then optimal. We combine this method with a multiscale analysis of the vector solution which enables to use a time varying adaptive grid based on the relevant smoothness properties of the discrete solution. In this short paper we compare different strategies to evaluate the fluxes at cells interfaces on a non uniform grid.

Suggested Citation

  • N. Andrianov & F. Coquel & M. Postel & Q. H. Tran, 2006. "Semi-Implicit Multiresolution for Multiphase Flows," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 814-821, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_80
    DOI: 10.1007/978-3-540-34288-5_80
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