Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates

Dan Ling Juan Cheng Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1804.25018

Computers and Fluids, 157, 112-130, 2017
For a Lagrangian scheme solving the compressible Euler equations in cylindrical coordinates, two important issues are whether the scheme can maintain spherical symmetry (symmetry-preserving) and whether the scheme can maintain positivity of density and internal energy (positivity-preserving). While there were previous results in the literature either for symmetry-preserving in the cylindrical coordinates or for positivity-preserving in cartesian coordinates, the design of a Lagrangian scheme in cylindrical coordinates, which is high order in one-dimension and second order in two-dimensions, and can maintain both spherical symmetry-preservation and positivity-preservation simultaneously, is challenging. In this paper we design such a Lagrangian scheme and provide numerical results to demonstrate its good behavior.
Lagrangian method; cylindrical coordinates; symmetry-preserving; positivity-preserving; compressible flows
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@inproceedings{dan2017positivity-preserving,
  title={Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates},
  author={Dan Ling, Juan Cheng, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416103300507902053},
  booktitle={Computers and Fluids},
  volume={157},
  pages={112-130},
  year={2017},
}
Dan Ling, Juan Cheng, and Chi-Wang Shu. Positivity-preserving and symmetry-preserving Lagrangian schemes for compressible Euler equations in cylindrical coordinates. 2017. Vol. 157. In Computers and Fluids. pp.112-130. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416103300507902053.
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