Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation Laws
This paper studies the energy stability property of the correction procedure via reconstruction (CPR) method with staggered flux points based on second-order subcell limiting. The CPR method with staggered flux points uses the Gauss point as the solution point, dividing flux points based on Gauss we...
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| Format: | Article |
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MDPI AG
2023-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/5/729 |
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| author | Ran Liu Zhen-Guo Yan Huajun Zhu Feiran Jia Xinlong Feng |
| author_facet | Ran Liu Zhen-Guo Yan Huajun Zhu Feiran Jia Xinlong Feng |
| author_sort | Ran Liu |
| collection | DOAJ |
| description | This paper studies the energy stability property of the correction procedure via reconstruction (CPR) method with staggered flux points based on second-order subcell limiting. The CPR method with staggered flux points uses the Gauss point as the solution point, dividing flux points based on Gauss weights, with the flux points being one more point than the solution points. For subcell limiting, a shock indicator is used to detect troubled cells where discontinuities may exist. Troubled cells are calculated by the second-order subcell compact nonuniform nonlinear weighted (CNNW2) scheme, which has the same solution points as the CPR method. The smooth cells are calculated by the CPR method. The linear energy stability of the linear CNNW2 scheme is proven theoretically. Through various numerical experiments, we demonstrate that the CNNW2 scheme and CPR method based on subcell linear CNNW2 limiting are energy-stable and that the CPR method based on subcell nonlinear CNNW2 limiting is nonlinearly stable. |
| first_indexed | 2024-03-11T03:45:20Z |
| format | Article |
| id | doaj.art-05d2e1dd22024f868d583dab27fd38e5 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T03:45:20Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-05d2e1dd22024f868d583dab27fd38e52023-11-18T01:15:33ZengMDPI AGEntropy1099-43002023-04-0125572910.3390/e25050729Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation LawsRan Liu0Zhen-Guo Yan1Huajun Zhu2Feiran Jia3Xinlong Feng4School of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, ChinaState Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, ChinaState Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, ChinaState Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, ChinaSchool of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, ChinaThis paper studies the energy stability property of the correction procedure via reconstruction (CPR) method with staggered flux points based on second-order subcell limiting. The CPR method with staggered flux points uses the Gauss point as the solution point, dividing flux points based on Gauss weights, with the flux points being one more point than the solution points. For subcell limiting, a shock indicator is used to detect troubled cells where discontinuities may exist. Troubled cells are calculated by the second-order subcell compact nonuniform nonlinear weighted (CNNW2) scheme, which has the same solution points as the CPR method. The smooth cells are calculated by the CPR method. The linear energy stability of the linear CNNW2 scheme is proven theoretically. Through various numerical experiments, we demonstrate that the CNNW2 scheme and CPR method based on subcell linear CNNW2 limiting are energy-stable and that the CPR method based on subcell nonlinear CNNW2 limiting is nonlinearly stable.https://www.mdpi.com/1099-4300/25/5/729conservation lawscorrection procedure via reconstruction (CPR)second-order compact nonuniform nonlinear weighted (CNNW2) schemeenergy stability |
| spellingShingle | Ran Liu Zhen-Guo Yan Huajun Zhu Feiran Jia Xinlong Feng Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation Laws Entropy conservation laws correction procedure via reconstruction (CPR) second-order compact nonuniform nonlinear weighted (CNNW2) scheme energy stability |
| title | Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation Laws |
| title_full | Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation Laws |
| title_fullStr | Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation Laws |
| title_full_unstemmed | Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation Laws |
| title_short | Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation Laws |
| title_sort | energy stability property of the cpr method based on subcell second order cnnw limiting in solving conservation laws |
| topic | conservation laws correction procedure via reconstruction (CPR) second-order compact nonuniform nonlinear weighted (CNNW2) scheme energy stability |
| url | https://www.mdpi.com/1099-4300/25/5/729 |
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