Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The interface coupling of the gas dynamics equations


Authors: Christophe Chalons, Pierre-Arnaud Raviart and Nicolas Seguin
Journal: Quart. Appl. Math. 66 (2008), 659-705
MSC (2000): Primary 76N15, 35F25, 35L65
DOI: https://doi.org/10.1090/S0033-569X-08-01087-X
Published electronically: October 1, 2008
MathSciNet review: 2465140
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Abstract: We investigate the one-dimensional coupling of two systems of gas dynamics at a fixed interface. The coupling constraints consist in requiring the continuity of a system of nonconservative variables at the interface. Since we are dealing with hyperbolic systems, weak coupling conditions are proposed. The existence and the uniqueness of the solutions of the coupled Riemann problem are investigated. Several examples of solutions satisfying the weak coupling conditions are contructed, either continuous or discontinuous with respect to the nonconservative variables at the interface.


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Additional Information

Christophe Chalons
Affiliation: UMR 7598 Laboratoire Jacques-Louis Lions, Université Paris 7-Denis Diderot, Boîte courrier 187, 75252 Paris Cedex 05, France
Email: chalons@math.jussieu.fr

Pierre-Arnaud Raviart
Affiliation: UMR 7598 Laboratoire Jacques-Louis Lions, CNRS & Université Pierre et Marie Curie-Paris 6, Boîte courrier 187, 75252 Paris Cedex 05, France
Email: pa@raviart.com

Nicolas Seguin
Affiliation: UMR 7598 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie-Paris 6, Boîte courrier 187, 75252 Paris Cedex 05, France
Email: seguin@ann.jussieu.fr

DOI: https://doi.org/10.1090/S0033-569X-08-01087-X
Received by editor(s): March 16, 2007
Published electronically: October 1, 2008
Article copyright: © Copyright 2008 Brown University


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