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High-resolution WENO schemes using local variation-based smoothness indicator

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Abstract

A novel smoothness indicator is proposed herein for WENO schemes based on the point-wise local variation in the candidate stencils. The proposed indicator is further used to define non-linear weights for a WENO scheme. The main feature of the resulting schemes is that they give a higher resolution of the solution compared to other state of art WENO schemes, e.g., WENO-JS, WENO-Z and very recent WENO-L. Moreover, these resulting WENO schemes maintain high-order accuracy and retains the non-oscillatory approximation property. The computational cost of the new scheme is comparable to WENO-Z and WENO-JS schemes. Computational results of selected benchmark test problems illustrate the higher resolution, accuracy and non-oscillatory property of the new schemes.

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Authors and Affiliations

  1. Research Institute, Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India

    Prashant Kumar Pandey & Ritesh Kumar Dubey

  2. School of Aerospace Engineering, Engineering Campus, Universiti Sains Malaysia, Gelugor, Malaysia

    Farzad Ismail

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  1. Prashant Kumar Pandey
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  2. Farzad Ismail
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  3. Ritesh Kumar Dubey
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Correspondence to Ritesh Kumar Dubey.

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Communicated by Abdellah Hadjadj.

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Prashant Kumar Pandey and Ritesh Kumar Dubey acknowledge support from SERB India through project file number MTR/2017/000187.

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Pandey, P.K., Ismail, F. & Dubey, R.K. High-resolution WENO schemes using local variation-based smoothness indicator. Comp. Appl. Math. 41, 208 (2022). https://doi.org/10.1007/s40314-022-01916-0

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  • DOI: https://doi.org/10.1007/s40314-022-01916-0

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