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An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator

Author

Listed:
  • Shuang Han

    (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China)

  • Mingjun Li

    (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
    Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China)

Abstract

The fifth-order WENO-Z scheme proposed by Borges et al., using a linear combination of low-order smoothness indicators, is designed to provide a low numerical dissipation to solve hyperbolic conservation laws, while the power q in the framework of WENO-Z plays a key role in its performance. In this paper, a novel global smoothness indicator with fifth-order accuracy, which is based on several lower-order smoothness indicators on two-point sub-stencils, is presented, and a new lower-dissipation WENO-Z scheme (WENO-NZ) is developed. The spectral properties of the WENO-NZ scheme are studied through the ADR method and show that this new scheme can exhibit better spectral results than WENO-Z no matter what the power value is. Accuracy tests confirm that the accuracy of WENO-Z with q = 1 would degrade to the fourth order at first-order critical points, while WENO-NZ can recover the optimal fifth-order convergence. Furthermore, numerical experiments with one- and two-dimensional benchmark problems demonstrate that the proposed WENO-NZ scheme can efficiently decrease the numerical dissipation and has a higher resolution compared to the WENO-Z scheme.

Suggested Citation

  • Shuang Han & Mingjun Li, 2023. "An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator," Mathematics, MDPI, vol. 11(21), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4449-:d:1268588
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