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Improved weighted essentially non-oscillatory schemes with modified stencil approximation

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Abstract

In this article, a new modified stencil approximation for weighted essentially non-oscillatory (WENO) schemes is proposed to reduce numerical dissipation of classical weighted essentially non-oscillatory (WENO-JS) schemes. Since the addition of high-order terms \(p^k(x)\) improves the accuracy of approximation polynomials of candidate stencils, the approximate accuracy of numerical fluxes of candidate stencils in classical WENO scheme is improved. In addition, the corresponding candidate fluxes are calculated, which can make the resulting scheme (called WENO-MS) achieve optimal convergence order in smooth regions including first-order critical points. A series of numerical examples are presented to demonstrate the performance of the new scheme. The numerical results show that the proposed WENO-MS schemes provide a comparable or higher resolution of fine smooth structures compared with the WENO-JS and WENO-Z schemes.

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Acknowledgements

This work is supported by Key scientific research projects of Henan Province colleges and universities (22B110020).

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Authors and Affiliations

  1. School of Mathematical and Statistics, Zhengzhou Normal University, Henan, 450044, People’s Republic of China

    Yahui Wang

  2. ICMSEC and LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Yahui Wang

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Yahui Wang

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Correspondence to Yahui Wang.

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Communicated by Abdellah Hadjadj.

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Wang, Y. Improved weighted essentially non-oscillatory schemes with modified stencil approximation. Comp. Appl. Math. 42, 82 (2023). https://doi.org/10.1007/s40314-022-02075-y

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  • DOI: https://doi.org/10.1007/s40314-022-02075-y

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