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

Authors:
Wenrui Hao;Jonathan D. Hauenstein;Chi-Wang Shu;Andrew J. Sommese;Zhiliang Xu;Yong-Tao Zhang
Affiliations:
-;-;-;-;-;-
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

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.