Time-Implicit Approximation of the Multipressure Gas Dynamics Equations in Several Space Dimensions

@article{Chalons2010TimeImplicitAO,
  title={Time-Implicit Approximation of the Multipressure Gas Dynamics Equations in Several Space Dimensions},
  author={Christophe Chalons and Fr{\'e}d{\'e}ric Coquel and Claude Marmignon},
  journal={SIAM J. Numer. Anal.},
  year={2010},
  volume={48},
  pages={1678-1706}
}
The present work is devoted to the numerical approximation of the solutions of the inviscid limit of multipressure Navier-Stokes equations in several space dimensions. The nonconservation form of the Euler-like limit model makes the shock solutions sensitive with respect to the underlying small scales and then challenges their numerical approximation. In particular, classical algorithms fail in producing good numerical results. Here we are mainly concerned with (large time stepping) implicit… 
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