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A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws

Wenrui Hao University of Notre Dame Jonathan D. Hauenstein North Carolina State University Chi-Wang Shu Brown University Andrew J. Sommese University of Notre Dame Zhiliang Xu University of Notre Dame Yong-Tao Zhang University of Notre Dame

Numerical Analysis and Scientific Computing mathscidoc:1610.25054

Journal of Computational Physics, 250, 332-346, 2013
Homotopy continuation is an efficient tool for solving polynomial systems. Its efficiency relies on utilizing adaptive stepsize and adaptive precision path tracking, and endgames. In this article, we apply homotopy continuation to solve steady state problems of hyperbolic conservation laws. A third-order accurate finite difference weighted essentially non-oscillatory (WENO) scheme with Lax-Friedrichs flux splitting is utilized to derive the difference equation. This new approach is free of the CFL condition constraint. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency and robustness of the new method.
homotopy continuation, hyperbolic conservation laws, WENO scheme, steady state problems
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@inproceedings{wenrui2013a,
  title={A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws},
  author={Wenrui Hao, Jonathan D. Hauenstein, Chi-Wang Shu, Andrew J. Sommese, Zhiliang Xu, and Yong-Tao Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012054632672915172},
  booktitle={Journal of Computational Physics},
  volume={250},
  pages={332-346},
  year={2013},
}
Wenrui Hao, Jonathan D. Hauenstein, Chi-Wang Shu, Andrew J. Sommese, Zhiliang Xu, and Yong-Tao Zhang. A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. 2013. Vol. 250. In Journal of Computational Physics. pp.332-346. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161012054632672915172.
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