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

Wenrui Hao, Jonathan D. Hauenstein, Chi Wang Shu, Andrew J. Sommese, Zhiliang Xu, Yong Tao Zhang

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)332-346
Number of pages15
JournalJournal of Computational Physics
Volume250
DOIs
StatePublished - Oct 1 2013

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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