An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator
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 <i>q</i> in the framework of WENO-Z plays a key role in its pe...
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/21/4449 |
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| author | Shuang Han Mingjun Li |
| author_facet | Shuang Han Mingjun Li |
| author_sort | Shuang Han |
| collection | DOAJ |
| description | 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 <i>q</i> 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 <i>q</i> = 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. |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T11:25:09Z |
| publishDate | 2023-10-01 |
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| spelling | doaj.art-36790cd86603478da5abab6b3f4ee6dc2023-11-10T15:07:55ZengMDPI AGMathematics2227-73902023-10-011121444910.3390/math11214449An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness IndicatorShuang Han0Mingjun Li1School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaSchool of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaThe 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 <i>q</i> 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 <i>q</i> = 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.https://www.mdpi.com/2227-7390/11/21/4449WENO-Z schemesmoothness indicatorpower parameterfifth-order convergencelow dissipationhigh resolution |
| spellingShingle | Shuang Han Mingjun Li An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator Mathematics WENO-Z scheme smoothness indicator power parameter fifth-order convergence low dissipation high resolution |
| title | An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator |
| title_full | An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator |
| title_fullStr | An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator |
| title_full_unstemmed | An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator |
| title_short | An Improved WENO-Z Scheme for Hyperbolic Conservation Laws with New Global Smoothness Indicator |
| title_sort | improved weno z scheme for hyperbolic conservation laws with new global smoothness indicator |
| topic | WENO-Z scheme smoothness indicator power parameter fifth-order convergence low dissipation high resolution |
| url | https://www.mdpi.com/2227-7390/11/21/4449 |
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