Three Indication Variables and Their Performance for the Troubled-Cell Indicator Using K-Means Clustering

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.