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Convergence of second-order schemes for isentropic gas dynamics

Gui-Qiang Chen The University of Chicago Jian-Guo Liu Courant Institute of Mathematical Sciences, New York

Numerical Analysis and Scientific Computing mathscidoc:1702.25073

Mathematics of Computation, 6, (204), 607-627, 1993.10
Convergence of a second-order shock-capturing scheme for the system of isentropic gas dynamics with $ {L^\infty }$ initial data is established by analyzing the entropy dissipation measures. This scheme is modified from the classical MUSCL scheme to treat the vacuum problem in gas fluids and to capture local entropy near shock waves. Convergence of this scheme for the piston problem is also discussed.
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@inproceedings{gui-qiang1993convergence,
  title={Convergence of second-order schemes for isentropic gas dynamics},
  author={Gui-Qiang Chen, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209143712549210415},
  booktitle={Mathematics of Computation},
  volume={6},
  number={204},
  pages={607-627},
  year={1993},
}
Gui-Qiang Chen, and Jian-Guo Liu. Convergence of second-order schemes for isentropic gas dynamics. 1993. Vol. 6. In Mathematics of Computation. pp.607-627. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209143712549210415.
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