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Networks and Heterogeneous Media

2010, Volume 5, Issue 3: 507-524. doi: 10.3934/nhm.2010.5.507
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Theoretical and numerical aspects of the interfacial coupling: The scalar Riemann problem and an application to multiphase flows

  • 1.
    CEA-Saclay, DEN/DANS/DM2S/SFME/LETR, F-91191 Gif-sur-Yvette
  • Received: 01 January 2010 Revised: 01 April 2010

  • 35L50, 35L60, 35L65, 65M12, 65M30, 76M12, 76T10.

  • This paper is devoted to the study of the one dimensional interfacial coupling of two PDE systems at a given fixed interface, say . Each system is posed on a half-space, namely and . As an interfacial model, a coupling condition whose objective is to enforce the continuity (in a weak sense) of a prescribed variable is generally imposed at .
       We first focus on the coupling of two scalar conservation laws and state an existence result for the coupled Riemann problem. Numerical experiments are also proposed. We then consider, both from a theoretical and a numerical point of view, the coupling of two-phase flow models namely a drift-flux model and a two-fluid model. In particular, the link between both models will be addressed using asymptotic expansions.

    Citation: Christophe Chalons. Theoretical and numerical aspects of the interfacial coupling: Thescalar Riemann problem and an application to multiphase flows[J]. Networks and Heterogeneous Media, 2010, 5(3): 507-524. doi: 10.3934/nhm.2010.5.507

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  • This paper is devoted to the study of the one dimensional interfacial coupling of two PDE systems at a given fixed interface, say . Each system is posed on a half-space, namely and . As an interfacial model, a coupling condition whose objective is to enforce the continuity (in a weak sense) of a prescribed variable is generally imposed at .
       We first focus on the coupling of two scalar conservation laws and state an existence result for the coupled Riemann problem. Numerical experiments are also proposed. We then consider, both from a theoretical and a numerical point of view, the coupling of two-phase flow models namely a drift-flux model and a two-fluid model. In particular, the link between both models will be addressed using asymptotic expansions.


  • This article has been cited by:

    1. MOUHAMADOU SAMSIDY GOUDIABY, GUNILLA KREISS, A RIEMANN PROBLEM AT A JUNCTION OF OPEN CANALS, 2013, 10, 0219-8916, 431, 10.1142/S021989161350015X
    2. Jean-Marc Herard, 2012, The Coupling of Multi-phase Flow Models, 978-1-60086-933-4, 10.2514/6.2012-3357
    3. Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch, Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure, 2021, 16, 1556-181X, 283, 10.3934/nhm.2021007
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  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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