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Coupling Two Scalar Conservation Laws via Dafermos’ Self-Similar Regularization

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • A. Ambroso

    (DEN/DANS/DM2S/SFME/LETR CEA-Saclay)

  • B. Boutin

    (DEN/DANS/DM2S/SFME/LETR CEA-Saclay
    Université Pierre et Marie Curie-Paris6, UMR7598, Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique)

  • F. Coquel

    (Université Pierre et Marie Curie-Paris6, UMR7598, Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique)

  • E. Godlewski

    (Université Pierre et Marie Curie-Paris6, UMR7598, Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique)

  • P. G. LeFloch

    (Université Pierre et Marie Curie-Paris6, UMR7598, Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique)

Abstract

We are interested in the problem of coupling two scalar conservation laws with distinct flux-functions. This problem arises, for instance, in modeling fluid flows in media with discontinuous porosity and has important possible applications in the numerical computation of a singular pressure drop. This problem is also well-known to exhibit several technical difficulties due to the presence of nonconservative terms and to the resonant behavior of the system of equations. We present here a global approach consisting of two scalar problems in a half-space coupled through an algebraic jump relation. We view this problem as a 2 × 2 system of conservation laws, and introduce a viscous regularization à la Dafermos. We establish that this approximation converges as the viscosity tends to zero and we analyze the structure of the entropy solutions constructed in this way.

Suggested Citation

  • A. Ambroso & B. Boutin & F. Coquel & E. Godlewski & P. G. LeFloch, 2008. "Coupling Two Scalar Conservation Laws via Dafermos’ Self-Similar Regularization," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 209-216, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_24
    DOI: 10.1007/978-3-540-69777-0_24
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