Abstract
In Zhu et al. (SIAM J Sci Comput 43: A3009–A3031, 2021), we proposed a new framework of troubled-cell indicator (TCI) using K-means clustering for the discontinuous Galerkin (DG) methods. However, there are two user-tunable parameters in the framework that depend on the polynomial degree of the solution space, the indication variable and even the test problem, which circumscribe the application of the framework. To overcome this drawback, we introduce two simple techniques in this paper: one is to modify the indication variables and the other is to apply a statistical normalization to the modified values. Coupled with four different indication variables, the modified framework is tested via the classical benchmark problems and produces close results under the same setting of the parameters. The discontinuities are overall well captured and the solutions are free of spurious oscillations. The numerical results demonstrate the effectiveness and flexibility of the modified framework and the success in unifying the parameters. Existing TCIs/limiters for the DG methods can be easily implemented into this framework.
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Enquiries about data availability should be directed to the authors.
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The custom codes generated during the current study are available from the corresponding author on reasonable request.
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Funding
The research of Z. Gao is partially supported by the National Key Research and Development Program of China (2021YFF0704002) and Shandong Provincial Qingchuang Science and Technology Project (2019KJI002). The four authors, Z. Wang, Z. Gao, H. Wang and H. Zhu, want to acknowledge the funding support by NSFC Grant 11871443. The research of Q. Zhang is partially supported by NSFC Grant 12071214. The research of Z. Wang and H. Zhu is also partially sponsored by Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant No. KYCX20_0787.
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Zhu, H., Wang, Z., Wang, H. et al. Troubled-Cell Indication Using K-means Clustering with Unified Parameters. J Sci Comput 93, 21 (2022). https://doi.org/10.1007/s10915-022-01987-5
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DOI: https://doi.org/10.1007/s10915-022-01987-5
Keywords
- Troubled-cell indicator
- Indication variable
- Discontinuous Galerkin method
- Shock detection
- K-means clustering