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Improved WENO finite difference method: Treating the multiple discontinuities

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  • Wu, Jian Ming
  • Huang, Cong

Abstract

The classical weighted essentially non-oscillatory method (WENO) performs well in solving hyperbolic conservation laws, but may encounter the numerical instability while treating multiple discontinuities due to the use of equal-width substencils. In order to overcome this problem, we propose an improved WENO finite difference method, namely WENO-rp2. The WENO-rp2 uses r+2 candidate substencils, which can be divided into two groups, the first group S1 consists of the classical r r-point substencils and the other group S2 consists of 2 2-point substencils. Then by introducing a TENO-like switching mechanism, S2 is used for the final WENO-rp2 reconstruction if the classical one can not handle the multiple discontinuities or is too biased, otherwise S1 is used. By doing so, the WENO-rp2 maintains the optimal (2r−1)th order of accuracy in the smooth region, avoids the non-physical oscillation near multiple discontinuities, and is more central, but does not significantly increase the computational cost and numerical dissipation.

Suggested Citation

  • Wu, Jian Ming & Huang, Cong, 2026. "Improved WENO finite difference method: Treating the multiple discontinuities," Applied Mathematics and Computation, Elsevier, vol. 512(C).
    • Handle: RePEc:eee:apmaco:v:512:y:2026:i:c:s0096300325004874
    DOI: 10.1016/j.amc.2025.129762
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    References listed on IDEAS

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    1. Feng, Hui & Huang, Cong & Wang, Rong, 2014. "An improved mapped weighted essentially non-oscillatory scheme," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 453-468.
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