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

doi:10.1016/j.jcp.2013.05.008

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 journal › Article › peer-review

42 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 language	English (US)
Pages (from-to)	332-346
Number of pages	15
Journal	Journal of Computational Physics
Volume	250
DOIs	https://doi.org/10.1016/j.jcp.2013.05.008
State	Published - Oct 1 2013

All Science Journal Classification (ASJC) codes

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

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10.1016/j.jcp.2013.05.008

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

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.",

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AU - Hao, Wenrui

AU - Hauenstein, Jonathan D.

AU - Shu, Chi Wang

AU - Sommese, Andrew J.

AU - Xu, Zhiliang

AU - Zhang, Yong Tao

PY - 2013/10/1

Y1 - 2013/10/1

N2 - 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.

AB - 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.

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

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

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