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Construction of an Improved Third-Order WENO Scheme with a New Smoothness Indicator

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Abstract

The aim of this study is to present an improved third-order weighted essentially non-oscillatory (WENO) scheme for solving hyperbolic conservation laws. We first present a novel smoothness indicator by using discrete differential operator which annihilates exponential polynomials. The new smoothness indicator can vanish to zero in smooth regions with higher rates than the classical methods such that it can distinguish the smooth region and discontinuity more efficiently. The proposed scheme achieves the maximal approximation order without loss of accuracy at critical points. A detailed analysis is provided to verify the third-order accuracy. The proposed scheme attains better resolution in smooth regions, while reducing numerical dissipation significantly near singularities. The advantages are more pronounced in two-dimensional model problems. Some numerical experiments are provided to illustrate the performance of the proposed WENO scheme.

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Acknowledgements

J. Yoon was supported by the National Research Foundation (NRF) of Korea under Grant NRF-2015R1A5A1009350 and Grant NRF-2019R1F1A1060804 and Y. Ha has been supported by the Grant NRF-2017R1D1A1B03034912.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, Seoul, South Korea

    Youngsoo Ha

  2. Department of Computer Engineering, Konkuk University Glocal Campus, Chungju, South Korea

    Chang Ho Kim

  3. Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, USA

    Hyoseon Yang

  4. Department of Mathematics, Ewha Womans University, Seoul, South Korea

    Jungho Yoon

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  1. Youngsoo Ha
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  2. Chang Ho Kim
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  3. Hyoseon Yang
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  4. Jungho Yoon
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Correspondence to Jungho Yoon.

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Ha, Y., Kim, C.H., Yang, H. et al. Construction of an Improved Third-Order WENO Scheme with a New Smoothness Indicator. J Sci Comput 82, 63 (2020). https://doi.org/10.1007/s10915-020-01164-6

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  • DOI: https://doi.org/10.1007/s10915-020-01164-6

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