A Two-Step High-Order Compact Corrected WENO Scheme
In this study, we introduce a novel 2-step compact scheme-based high-order correction method for computational fluid dynamics (CFD). Unlike traditional single-formula-based schemes, our proposed approach refines flux function values by leveraging results from high-order compact schemes on the same s...
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MDPI AG
2025-06-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/18/6/364 |
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| author | Yong Yang Caixia Chen Shiming Yuan Yonghua Yan |
| author_facet | Yong Yang Caixia Chen Shiming Yuan Yonghua Yan |
| author_sort | Yong Yang |
| collection | DOAJ |
| description | In this study, we introduce a novel 2-step compact scheme-based high-order correction method for computational fluid dynamics (CFD). Unlike traditional single-formula-based schemes, our proposed approach refines flux function values by leveraging results from high-order compact schemes on the same stencils, provided a certain smoothness condition is met. By applying this method, we achieve a more stable and efficient compact corrected Weighted Essentially Non-Oscillatory (WENO) scheme. The results demonstrate significant improvements across all enhanced schemes, particularly in capturing shock waves sharply and maintaining stability in complex scenarios, such as two interacting blast waves, as validated through 1D benchmark tests. In addition, error analysis is also provided for the two different correction configurations based on WENO. |
| format | Article |
| id | doaj-art-9ce57b6395d94bf1a0cde4e82ffb75d4 |
| institution | Kabale University |
| issn | 1999-4893 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj-art-9ce57b6395d94bf1a0cde4e82ffb75d42025-08-20T03:24:29ZengMDPI AGAlgorithms1999-48932025-06-0118636410.3390/a18060364A Two-Step High-Order Compact Corrected WENO SchemeYong Yang0Caixia Chen1Shiming Yuan2Yonghua Yan3Department of Mathematics, West Texas A&M University, Canyon, TX 79016, USADepartment of Mathematics and Statistical Sciences, Jackson State University, Jackson, MS 39217, USADepartment of Mathematics and Statistical Sciences, Jackson State University, Jackson, MS 39217, USADepartment of Mathematics and Statistical Sciences, Jackson State University, Jackson, MS 39217, USAIn this study, we introduce a novel 2-step compact scheme-based high-order correction method for computational fluid dynamics (CFD). Unlike traditional single-formula-based schemes, our proposed approach refines flux function values by leveraging results from high-order compact schemes on the same stencils, provided a certain smoothness condition is met. By applying this method, we achieve a more stable and efficient compact corrected Weighted Essentially Non-Oscillatory (WENO) scheme. The results demonstrate significant improvements across all enhanced schemes, particularly in capturing shock waves sharply and maintaining stability in complex scenarios, such as two interacting blast waves, as validated through 1D benchmark tests. In addition, error analysis is also provided for the two different correction configurations based on WENO.https://www.mdpi.com/1999-4893/18/6/364numerical schemeCFDWENOMWCS |
| spellingShingle | Yong Yang Caixia Chen Shiming Yuan Yonghua Yan A Two-Step High-Order Compact Corrected WENO Scheme Algorithms numerical scheme CFD WENO MWCS |
| title | A Two-Step High-Order Compact Corrected WENO Scheme |
| title_full | A Two-Step High-Order Compact Corrected WENO Scheme |
| title_fullStr | A Two-Step High-Order Compact Corrected WENO Scheme |
| title_full_unstemmed | A Two-Step High-Order Compact Corrected WENO Scheme |
| title_short | A Two-Step High-Order Compact Corrected WENO Scheme |
| title_sort | two step high order compact corrected weno scheme |
| topic | numerical scheme CFD WENO MWCS |
| url | https://www.mdpi.com/1999-4893/18/6/364 |
| work_keys_str_mv | AT yongyang atwostephighordercompactcorrectedwenoscheme AT caixiachen atwostephighordercompactcorrectedwenoscheme AT shimingyuan atwostephighordercompactcorrectedwenoscheme AT yonghuayan atwostephighordercompactcorrectedwenoscheme AT yongyang twostephighordercompactcorrectedwenoscheme AT caixiachen twostephighordercompactcorrectedwenoscheme AT shimingyuan twostephighordercompactcorrectedwenoscheme AT yonghuayan twostephighordercompactcorrectedwenoscheme |