Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6933681 | Journal of Computational Physics | 2013 | 15 Pages |
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Wenrui Hao, Jonathan D. Hauenstein, Chi-Wang Shu, Andrew J. Sommese, Zhiliang Xu, Yong-Tao Zhang,