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Large Time Step Positivity-Preserving Method for Multiphase Flows

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • F. Coquel

    (Université Pierre et Marie Curie, CNRS et Laboratoire Jacques Louis Lions)

  • Q. -L. Nguyen

    (Institut Français du Pétrole, Département Mathématiques Appliquées)

  • M. Postel

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

  • Q. -H. Tran

    (Institut Français du Pétrole, Département Mathématiques Appliquées)

Abstract

Using a relaxation strategy in a Lagrangian–Eulerian formulation, we propose a scheme in local conservation form for approximating weak solutions of complex compressible flows involving wave speeds of different orders of magnitude. Explicit time integration is performed on slow transport waves for the sake of accuracy while fast acoustic waves are dealt with implicitly to enable large time stepping. A CFL condition based on the slow waves is derived ensuring positivity properties on the density and the mass fraction. Numerical benchmarks validate the method.

Suggested Citation

  • F. Coquel & Q. -L. Nguyen & M. Postel & Q. -H. Tran, 2008. "Large Time Step Positivity-Preserving Method for Multiphase Flows," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 849-856, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_88
    DOI: 10.1007/978-3-540-75712-2_88
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