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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.05489 |
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| _version_ | 1866909339956019200 |
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| author | Zhang, Hong Zhao, Yue Ji, Xing Xu, Kun |
| author_facet | Zhang, Hong Zhao, Yue Ji, Xing Xu, Kun |
| contents | This paper introduces an effcient class of adaptive stencil extension reconstruction methods based on a discontinuity feedback factor, addressing the challenges of weak robustness and high computational cost in high-order schemes, particularly those of 7th-order or above. Two key innovations are presented: The accuracy order adaptively increases from the lowest level based on local stencil smoothness, contrasting with conventional methods like Weighted Essentially Non-Oscillatory (WENO) and Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL)limiters, which typically reduce order from the highest level. The Discontinuity Feedback Factor (DF) serves a dual purpose: detecting sub-cell discontinuity strength and explicitly incorporating into the reconstruction process as a local smoothness measure. This approach eliminates the need for computationally expensive smoothness indicators often required in very high-order schemes, such as 9th-order schemes, and can be easily generalized to arbitrary high-order schemes. Rigorous test cases, including a Mach 20000 jet, demonstrate the exceptional robustness of this approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05489 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Adaptive Reconstruction Method for Arbitrary High-Order Accuracy Using Discontinuity Feedback Zhang, Hong Zhao, Yue Ji, Xing Xu, Kun Numerical Analysis This paper introduces an effcient class of adaptive stencil extension reconstruction methods based on a discontinuity feedback factor, addressing the challenges of weak robustness and high computational cost in high-order schemes, particularly those of 7th-order or above. Two key innovations are presented: The accuracy order adaptively increases from the lowest level based on local stencil smoothness, contrasting with conventional methods like Weighted Essentially Non-Oscillatory (WENO) and Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL)limiters, which typically reduce order from the highest level. The Discontinuity Feedback Factor (DF) serves a dual purpose: detecting sub-cell discontinuity strength and explicitly incorporating into the reconstruction process as a local smoothness measure. This approach eliminates the need for computationally expensive smoothness indicators often required in very high-order schemes, such as 9th-order schemes, and can be easily generalized to arbitrary high-order schemes. Rigorous test cases, including a Mach 20000 jet, demonstrate the exceptional robustness of this approach. |
| title | An Adaptive Reconstruction Method for Arbitrary High-Order Accuracy Using Discontinuity Feedback |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.05489 |