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A note on WENO-Z scheme

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  • Hu, Fuxing

Abstract

In this paper we recover a latent advantage of WENO-Z schemes. Taking the fifth-order WENO-Z scheme for instance, we realize that the scheme can be regarded as a nonlinear combination of a five-cell stencil and three three-cell stencils. The five-cell stencil is allotted a global higher-order indicator of smoothness than three-cell stencils. Then the five-cell stencil dominates the nonlinear combination and ensures the optimal accuracy in the smooth regions even at extremal points. In non-smooth regions, the three-cell stencils dominate the combination and compress the nonphysical oscillations. As the adaptive order WENO schemes which release the requirement of linear optimal weights, we will show that there is no requirement of linear optimal weights for the WENO-Z schemes as well, and even it is unnecessary to require the sum of linear optimal weights to be one.

Suggested Citation

  • Hu, Fuxing, 2021. "A note on WENO-Z scheme," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    • Handle: RePEc:eee:apmaco:v:396:y:2021:i:c:s0096300320308390
    DOI: 10.1016/j.amc.2020.125886
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    Cited by:

    1. Tang, Shujiang & Feng, Yujie & Li, Mingjun, 2022. "Novel weighted essentially non-oscillatory schemes with adaptive weights," Applied Mathematics and Computation, Elsevier, vol. 420(C).

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