Positivity-preserving method for high-order conservative schemes solving compressible Euler equations

Xiangyu Y. Hu Technische Universitat Munchen Nikolaus A. Adams Technische Universitat Munchen Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25059

Journal of Computational Physics, 242, 169-180, 2013
In this work a simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed. The method detects critical numerical fluxes which may lead to negative density and pressure, and then imposes a simple flux limiter combining the high-order numerical flux with the first-order Lax-Friedrichs flux to satisfy a sufficient condition for preserving positivity. Though an extra time-step size condition is required to maintain the formal order of accuracy, it is less restrictive than those in previous works. A number of numerical examples suggest that this method, when applied on an essentially non-oscillatory scheme, can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.
numerical method, compressible flow, high-order conservative scheme, positivity-preserving
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@inproceedings{xiangyu2013positivity-preserving,
  title={Positivity-preserving method for high-order conservative schemes solving compressible Euler equations},
  author={Xiangyu Y. Hu, Nikolaus A. Adams, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012061532630522177},
  booktitle={Journal of Computational Physics},
  volume={242},
  pages={169-180},
  year={2013},
}
Xiangyu Y. Hu, Nikolaus A. Adams, and Chi-Wang Shu. Positivity-preserving method for high-order conservative schemes solving compressible Euler equations. 2013. Vol. 242. In Journal of Computational Physics. pp.169-180. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012061532630522177.
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