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

@article{Hao2013AHM,
  title={A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws},
  author={Wenrui Hao and Jonathan D. Hauenstein and Chi-Wang Shu and Andrew J. Sommese and Zhiliang Xu and Yong-Tao Zhang},
  journal={J. Comput. Physics},
  year={2013},
  volume={250},
  pages={332-346}
}
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. The algorithm is based on discretization of the hyperbolic PDEs by a third order finite difference weighted essentially non-oscillatory (WENO) scheme with Lax-Friedrichs flux splitting. This new approach is… CONTINUE READING