Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

Juan Cheng Institute of Applied Physics and Computational Mathematics, Beijing 100088, China Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1610.25039

Journal of Computational Physics, 272, 245-265, 2014
In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, based on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.
Lagrangian scheme; symmetry-preserving; conservative; second order; multi-material compressible flow; cylindrical coordinates
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@inproceedings{juan2014second,
  title={Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates},
  author={Juan Cheng, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012042315148816157},
  booktitle={Journal of Computational Physics},
  volume={272},
  pages={245-265},
  year={2014},
}
Juan Cheng, and Chi-Wang Shu. Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates. 2014. Vol. 272. In Journal of Computational Physics. pp.245-265. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012042315148816157.
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