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A Time Semi-Implicit Relaxation Scheme for Two-Phase Flows in Pipelines

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Michaël Baudin

    (Institut Français du Pétrole)

  • Frédéric Coquel

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

  • Quang-Huy Tran

    (Institut Français du Pétrole)

Abstract

Summary The aim of this paper is to present a relaxation scheme designed to approximate the solutions of the system of conservation laws which arises in the modeling of two-phase flows in oil and gas pipelines. The main idea is to relax only the highly non-linear closure laws, thanks to a Lagrangian change of coordinates. By construction, all the fields of the nonlinear hyperbolic relaxation system are linearly degenerated. In addition to the simplicity of the evaluation of the flux function, the relaxation coefficients can be easily devised so as to guaranty the positivity of the mass fractions. We propose to use an integration in time which is explicit with respect to the small eigenvalues and linearly implicit with respect to the large eigenvalues. In the first part, we construct a second-order explicit relaxation scheme based on a Godunov method. In the second part, we present the semi-implicit relaxation scheme. A “stiff” numerical simulation of an industrial case is shown.

Suggested Citation

  • Michaël Baudin & Frédéric Coquel & Quang-Huy Tran, 2004. "A Time Semi-Implicit Relaxation Scheme for Two-Phase Flows in Pipelines," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 102-111, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_7
    DOI: 10.1007/978-3-642-18775-9_7
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