Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting
The discontinuous Galerkin spectral element method (DGSEM) is a compact and high-order method applicable to complex meshes. However, the aliasing errors in simulating under-resolved vortex flows and non-physical oscillations in simulating shock waves may lead to instability of the DGSEM. In this pap...
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| Format: | Article |
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MDPI AG
2023-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/6/911 |
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| author | Yang Liu Huajun Zhu Zhen-Guo Yan Feiran Jia Xinlong Feng |
| author_facet | Yang Liu Huajun Zhu Zhen-Guo Yan Feiran Jia Xinlong Feng |
| author_sort | Yang Liu |
| collection | DOAJ |
| description | The discontinuous Galerkin spectral element method (DGSEM) is a compact and high-order method applicable to complex meshes. However, the aliasing errors in simulating under-resolved vortex flows and non-physical oscillations in simulating shock waves may lead to instability of the DGSEM. In this paper, an entropy-stable DGSEM (ESDGSEM) based on subcell limiting is proposed to improve the non-linear stability of the method. First, we discuss the stability and resolution of the entropy-stable DGSEM based on different solution points. Second, a provably entropy-stable DGSEM based on subcell limiting is established on Legendre–Gauss (LG) solution points. Numerical experiments demonstrate that the ESDGSEM-LG scheme is superior in non-linear stability and resolution, and ESDGSEM-LG with subcell limiting is robust in shock-capturing. |
| first_indexed | 2024-03-11T02:29:42Z |
| format | Article |
| id | doaj.art-679f169475244f6bb74bd9874828e7fd |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T02:29:42Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-679f169475244f6bb74bd9874828e7fd2023-11-18T10:18:08ZengMDPI AGEntropy1099-43002023-06-0125691110.3390/e25060911Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell LimitingYang Liu0Huajun Zhu1Zhen-Guo Yan2Feiran 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, ChinaThe discontinuous Galerkin spectral element method (DGSEM) is a compact and high-order method applicable to complex meshes. However, the aliasing errors in simulating under-resolved vortex flows and non-physical oscillations in simulating shock waves may lead to instability of the DGSEM. In this paper, an entropy-stable DGSEM (ESDGSEM) based on subcell limiting is proposed to improve the non-linear stability of the method. First, we discuss the stability and resolution of the entropy-stable DGSEM based on different solution points. Second, a provably entropy-stable DGSEM based on subcell limiting is established on Legendre–Gauss (LG) solution points. Numerical experiments demonstrate that the ESDGSEM-LG scheme is superior in non-linear stability and resolution, and ESDGSEM-LG with subcell limiting is robust in shock-capturing.https://www.mdpi.com/1099-4300/25/6/911high-order methodsGauss solution pointsentropy-stablesubcell limitingshock capturing |
| spellingShingle | Yang Liu Huajun Zhu Zhen-Guo Yan Feiran Jia Xinlong Feng Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting Entropy high-order methods Gauss solution points entropy-stable subcell limiting shock capturing |
| title | Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting |
| title_full | Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting |
| title_fullStr | Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting |
| title_full_unstemmed | Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting |
| title_short | Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting |
| title_sort | entropy stable dgsem schemes of gauss points based on subcell limiting |
| topic | high-order methods Gauss solution points entropy-stable subcell limiting shock capturing |
| url | https://www.mdpi.com/1099-4300/25/6/911 |
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