A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws
A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws
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DOI：
10.1016/j.jcp.2013.05.008
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发表时间：
2013-10
期刊：
影响因子：
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通讯作者：
Wenrui Hao;J. Hauenstein;Chi-Wang Shu;A. Sommese;Zhiliang Xu;Yong-Tao Zhang
中科院分区：
文献类型：
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作者：
Wenrui Hao;J. Hauenstein;Chi-Wang Shu;A. Sommese;Zhiliang Xu;Yong-Tao Zhang
同伦延拓是求解多项式系统的有效工具。其效率依赖于利用自适应步长和自适应精确路径跟踪以及残局。在本文中，我们应用同伦延拓来解决双曲守恒定律的稳态问题。利用具有 Lax-Friedrichs 通量分裂的三阶精确有限差分加权本质上非振荡 (WENO) 方案来推导差分方程。这种新方法不受 CFL 条件限制。一维和二维标量和系统测试问题的大量数值例子证明了新方法的效率和鲁棒性。
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.