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Volume 15, Issue 2
Three Indication Variables and Their Performance for the Troubled-Cell Indicator Using K-Means Clustering

Zhihuan Wang, Zhen Gao, Haiyun Wang, Qiang Zhang & Hongqiang Zhu

DOI: 10.4208/aamm.OA-2021-0234

Adv. Appl. Math. Mech., 15 (2023), pp. 522-544.

Published online: 2022-12

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  • Abstract

In Zhu, Wang and Gao (SIAM J. Sci. Comput., 43 (2021), pp. A3009–A3031), we proposed a new framework of troubled-cell indicator (TCI) using K-means clustering and the numerical results demonstrate that it can detect the troubled cells accurately using the KXRCF indication variable. The main advantage of this TCI framework is its great potential of extensibility. In this follow-up work, we introduce three more indication variables, i.e., the TVB, Fu-Shu and cell-boundary jump indication variables, and show their good performance by numerical tests to demonstrate that the TCI framework offers great flexibility in the choice of indication variables. We also compare the three indication variables with the KXRCF one, and the numerical results favor the KXRCF and the cell-boundary jump indication variables.

  • Keywords

Troubled-cell indicator, indication variable, discontinuous Galerkin method, shock detection, K-means clustering.

  • AMS Subject Headings

65M60, 35L60, 35L65, 35L67

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-522, author = {Wang , ZhihuanGao , ZhenWang , HaiyunZhang , Qiang and Zhu , Hongqiang}, title = {Three Indication Variables and Their Performance for the Troubled-Cell Indicator Using K-Means Clustering}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {2}, pages = {522--544}, abstract = {

In Zhu, Wang and Gao (SIAM J. Sci. Comput., 43 (2021), pp. A3009–A3031), we proposed a new framework of troubled-cell indicator (TCI) using K-means clustering and the numerical results demonstrate that it can detect the troubled cells accurately using the KXRCF indication variable. The main advantage of this TCI framework is its great potential of extensibility. In this follow-up work, we introduce three more indication variables, i.e., the TVB, Fu-Shu and cell-boundary jump indication variables, and show their good performance by numerical tests to demonstrate that the TCI framework offers great flexibility in the choice of indication variables. We also compare the three indication variables with the KXRCF one, and the numerical results favor the KXRCF and the cell-boundary jump indication variables.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0234}, url = {http://global-sci.org/intro/article_detail/aamm/21279.html} }
TY - JOUR T1 - Three Indication Variables and Their Performance for the Troubled-Cell Indicator Using K-Means Clustering AU - Wang , Zhihuan AU - Gao , Zhen AU - Wang , Haiyun AU - Zhang , Qiang AU - Zhu , Hongqiang JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 522 EP - 544 PY - 2022 DA - 2022/12 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0234 UR - https://global-sci.org/intro/article_detail/aamm/21279.html KW - Troubled-cell indicator, indication variable, discontinuous Galerkin method, shock detection, K-means clustering. AB -

In Zhu, Wang and Gao (SIAM J. Sci. Comput., 43 (2021), pp. A3009–A3031), we proposed a new framework of troubled-cell indicator (TCI) using K-means clustering and the numerical results demonstrate that it can detect the troubled cells accurately using the KXRCF indication variable. The main advantage of this TCI framework is its great potential of extensibility. In this follow-up work, we introduce three more indication variables, i.e., the TVB, Fu-Shu and cell-boundary jump indication variables, and show their good performance by numerical tests to demonstrate that the TCI framework offers great flexibility in the choice of indication variables. We also compare the three indication variables with the KXRCF one, and the numerical results favor the KXRCF and the cell-boundary jump indication variables.

Zhihuan Wang, Zhen Gao, Haiyun Wang, Qiang Zhang & Hongqiang Zhu. (2022). Three Indication Variables and Their Performance for the Troubled-Cell Indicator Using K-Means Clustering. Advances in Applied Mathematics and Mechanics. 15 (2). 522-544. doi:10.4208/aamm.OA-2021-0234
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