A minimum entropy principle of high order schemes for gas dynamics equations

Xiangxiong Zhang Brown University Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25078

Numerische Mathematik, 121, 545-563, 2012
The entropy solutions of the compressible Euler equations satisfy a minimum principle for the specific entropy. First order schemes such as Godunov-type and Lax-Friedrichs schemes and the second order kinetic schemes also satisfy a discrete minimum entropy principle. In this paper, we show an extension of the positivity-preserving high order schemes for the compressible Euler equations, to enforce the minimum entropy principle for high order finite volume and discontinuous Galerkin (DG) schemes.
compressible Euler equations; discontinuous Galerkin method; high order accuracy; gas dynamics; finite volume scheme; essentially non-oscillatory scheme; weighted essentially non-oscillatory scheme; minimum entropy principle
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@inproceedings{xiangxiong2012a,
  title={A minimum entropy principle of high order schemes for gas dynamics equations},
  author={Xiangxiong Zhang, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012113456467075196},
  booktitle={Numerische Mathematik},
  volume={121},
  pages={545-563},
  year={2012},
}
Xiangxiong Zhang, and Chi-Wang Shu. A minimum entropy principle of high order schemes for gas dynamics equations. 2012. Vol. 121. In Numerische Mathematik. pp.545-563. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012113456467075196.
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