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

A. Ambroso (), B. Boutin (), F. Coquel (), E. Godlewski () and P. G. LeFloch ()
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A. Ambroso: DEN/DANS/DM2S/SFME/LETR CEA-Saclay
B. Boutin: DEN/DANS/DM2S/SFME/LETR CEA-Saclay
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

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 209-216 from Springer

Abstract: 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.

Keywords: Riemann Problem; Entropy Solution; Nonlinear Hyperbolic System; Thick Interface; Viscous Regularization (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_24

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