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Numerical Capture of Shock Solutions of Nonconservative Hyperbolic Systems via Kinetic Functions

  • Christophe Chalons
  • Frédéric Coquel
Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)

Abstract

This paper reviews recent contributions to the numerical approximation of solutions of nonconservative hyperbolic systems with singular viscous perturbations. Various PDE models for complex compressible materials enter the proposed framework. Due to lack of a conservative form in the limit systems, associated weak solutions are known to heavily depend on the underlying viscous regularization. This small scales sensitiveness drives the classical approximate Riemann solvers to grossly fail in the capture of shock solutions. Here, small scales sensitiveness is encoded thanks to the notion of kinetic functions so as to consider a set of generalized jump conditions. To enforce for validity these jump conditions at the discrete level, we describe a systematic and effective correction procedure. Numerical experiments assess the relevance of the proposed method.

Keywords

Weak Solution Hyperbolic System Travel Wave Solution Riemann Problem Singular Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Christophe Chalons
    • 1
  • Frédéric Coquel
    • 2
  1. 1.Université Paris 7 & Laboratoire JLL, U.M.R. 7598Paris Cedex 05France
  2. 2.Centre National de la Recherche Scientifique & Laboratoire JLL, U.M.R. 7598Paris Cedex 05France

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