WENO scheme with subcell resolution for computing nonconservative Euler equations with applications to one-dimensional compressible two-medium flows

Tao Xiong University of Science and Technology of China Chi-Wang Shu Brown University Mengping Zhang University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1610.25073

Journal of Scientific Computing, 53, 222-247, 2012
High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems. Recently, it has been observed that this approach may have some computational issues and shortcomings. In this paper, a modification to the high order path-conservative scheme in is proposed to improve its computational performance and to overcome some of the shortcomings. This modification is based on the high order finite volume WENO scheme with subcell resolution and it uses an exact Riemann solver to catch the right paths at the discontinuities. An application to one-dimensional compressible two-medium flows of nonconservative or primitive Euler equations is carried out to show the effectiveness of this new approach.
path-conservative schemes; high order finite volume WENO scheme; subcell resolution; nonconservative hyperbolic systems; primitive Euler equations; two-medium flows; exact Riemann solver
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@inproceedings{tao2012weno,
  title={WENO scheme with subcell resolution for computing nonconservative Euler equations with applications to one-dimensional compressible two-medium flows},
  author={Tao Xiong, Chi-Wang Shu, and Mengping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012110956914992191},
  booktitle={Journal of Scientific Computing},
  volume={53},
  pages={222-247},
  year={2012},
}
Tao Xiong, Chi-Wang Shu, and Mengping Zhang. WENO scheme with subcell resolution for computing nonconservative Euler equations with applications to one-dimensional compressible two-medium flows. 2012. Vol. 53. In Journal of Scientific Computing. pp.222-247. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012110956914992191.
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