An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator
| Autor: | Shuang Han, Mingjun Li |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Mathematics, Vol 11, Iss 21, p 4449 (2023) |
| Druh dokumentu: | article |
| ISSN: | 11214449 2227-7390 |
| DOI: | 10.3390/math11214449 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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