Positivity-preserving high order finite difference WENO schemes for compressible Euler equations

Xiangxiong Zhang Brown University Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25077

Journal of Computational Physics, 231, 2245-2258, 2012
In our earlier work, we constructed uniformly high order accurate discontinuous Galerkin (DG) and finite volume schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics. In this paper, we present an extension of this framework to construct positivity-preserving high order essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) finite difference schemes for compressible Euler equations. General equations of state and source terms are also discussed. Numerical tests of the fifth order finite difference WENO scheme are reported to demonstrate the good behavior of such schemes.
positivity preserving; high order accuracy; compressible Euler equations; gas dynamics; finite difference scheme; essentially non-oscillatory scheme; weighted essentially non-oscillatory scheme
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@inproceedings{xiangxiong2012positivity-preserving,
  title={Positivity-preserving high order finite difference WENO schemes for compressible Euler equations},
  author={Xiangxiong Zhang, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012113123590964195},
  booktitle={Journal of Computational Physics},
  volume={231},
  pages={2245-2258},
  year={2012},
}
Xiangxiong Zhang, and Chi-Wang Shu. Positivity-preserving high order finite difference WENO schemes for compressible Euler equations. 2012. Vol. 231. In Journal of Computational Physics. pp.2245-2258. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012113123590964195.
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