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A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws

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Abstract

In this paper, we develop a new sixth-order WENO scheme by adopting a convex combination of a sixth-order global reconstruction and four low-order local reconstructions. Unlike the classical WENO schemes, the associated linear weights of the new scheme can be any positive numbers with the only requirement that their sum equals one. Further, a very simple smoothness indicator for the global stencil is proposed. The new scheme can achieve sixth-order accuracy in smooth regions. Numerical tests in some one- and two-dimensional benchmark problems show that the new scheme has a little bit higher resolution compared with the recently developed sixth-order WENO-Z6 scheme, and it is more efficient than the classical fifth-order WENO-JS5 scheme and the recently developed sixth-order WENO6-S scheme.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (91641107, 91852116, 12071470) and Fundamental Research of Civil Aircraft (MJ-F-2012-04) of Ministry of Industrialization and Information of China. The computations were partly done on the high-performance computers of State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences.

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Authors and Affiliations

  1. State Key Laboratory of Scientific and Engineering Computing (LSEC) and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Kunlei Zhao & Li Yuan

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China

    Kunlei Zhao & Li Yuan

  3. School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Yulong Du

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  1. Kunlei Zhao
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  2. Yulong Du
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  3. Li Yuan
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Correspondence to Li Yuan.

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Zhao, K., Du, Y. & Yuan, L. A New Sixth-Order WENO Scheme for Solving Hyperbolic Conservation Laws. Commun. Appl. Math. Comput. 5, 3–30 (2023). https://doi.org/10.1007/s42967-020-00112-3

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  • DOI: https://doi.org/10.1007/s42967-020-00112-3

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