JS-type and Z-type weights for fourth-order central-upwind weighted essentially non-oscillatory schemes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910847346933760 |
|---|---|
| author | Gu, Jiaxi Chen, Xinjuan Park, Kwanghyuk Jung, Jae-Hun |
| author_facet | Gu, Jiaxi Chen, Xinjuan Park, Kwanghyuk Jung, Jae-Hun |
| contents | The central-upwind weighted essentially non-oscillatory (WENO) scheme introduces the downwind substencil to reconstruct the numerical flux, where the smoothness indicator for the downwind substencil is of critical importance in maintaining high order in smooth regions and preserving the essentially nonoscillatory behavior in shock capturing. In this study, we design the smoothness indicator for the downwind substencil by simply summing up all local smoothness indicators and taking the average, which includes the regularity information of the whole stencil. Accordingly the JS-type and Z-type nonlinear weights, based on simple local smoothness indicators, are developed for the fourth-order central-upwind WENO scheme. The accuracy, robustness, and high-resolution properties of our proposed schemes are demonstrated in a variety of one- and two-dimensional problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19221 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | JS-type and Z-type weights for fourth-order central-upwind weighted essentially non-oscillatory schemes Gu, Jiaxi Chen, Xinjuan Park, Kwanghyuk Jung, Jae-Hun Numerical Analysis The central-upwind weighted essentially non-oscillatory (WENO) scheme introduces the downwind substencil to reconstruct the numerical flux, where the smoothness indicator for the downwind substencil is of critical importance in maintaining high order in smooth regions and preserving the essentially nonoscillatory behavior in shock capturing. In this study, we design the smoothness indicator for the downwind substencil by simply summing up all local smoothness indicators and taking the average, which includes the regularity information of the whole stencil. Accordingly the JS-type and Z-type nonlinear weights, based on simple local smoothness indicators, are developed for the fourth-order central-upwind WENO scheme. The accuracy, robustness, and high-resolution properties of our proposed schemes are demonstrated in a variety of one- and two-dimensional problems. |
| title | JS-type and Z-type weights for fourth-order central-upwind weighted essentially non-oscillatory schemes |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2502.19221 |