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

Shuang Han and Mingjun Li ()
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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

Mathematics, 2023, vol. 11, issue 21, 1-19

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.

Keywords: WENO-Z scheme; smoothness indicator; power parameter; fifth-order convergence; low dissipation; high resolution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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