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An Improved Third-Order WENO-Z Scheme

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Abstract

In this paper, we develop an improved third-order WENO-Z scheme. Firstly, a new reference smoothness indicator is derived by slightly modifying that of WENO-N3 scheme proposed by Wu and Zhang (Int. J. Numer. Meth. Fl. 78:162–187, 2015). Then a new term is added to the weights of the developed scheme to further slightly increase the weight of less-smooth stencil. Some numerical experiments are provided to demonstrate that the improved scheme is stable and significantly outperforms the conventional third-order WENO scheme of Jiang and Shu, while providing essentially non-oscillatory solutions near strong discontinuities.

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Acknowledgements

The authors acknowledge the support of National Defense Fundamental Research Project (B1420133057), National Natural Science Foundation of China (51409202 and 11502180) and the Fundamental Research Funds for the Central Universities (2016-YB-016).

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Authors and Affiliations

  1. Key Laboratory of High Performance Ship Technology, Wuhan University of Technology, Wuhan, 430063, China

    Weizheng Xu & Weiguo Wu

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  1. Weizheng Xu
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  2. Weiguo Wu
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Correspondence to Weizheng Xu.

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Xu, W., Wu, W. An Improved Third-Order WENO-Z Scheme. J Sci Comput 75, 1808–1841 (2018). https://doi.org/10.1007/s10915-017-0587-4

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  • DOI: https://doi.org/10.1007/s10915-017-0587-4

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