Three Indication Variables and Their Performance for the Troubled-Cell Indicator Using K-Means Clustering
Year: 2023
Author: Zhihuan Wang, Zhen Gao, Haiyun Wang, Qiang Zhang, Hongqiang Zhu
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0234
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 2 : pp. 522–544
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Troubled-cell indicator indication variable discontinuous Galerkin method shock detection K-means clustering.