Three Indication Variables and Their Performance for the Troubled-Cell Indicator Using K-Means Clustering (Advances in Applied Mathematics and Mechanics, 2022)
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 threemore indication variables, i.e., the TVB, Fu-Shu and cell-boundary jump indicationvariables, and show their good performance by numerical tests to demonstrate thatthe TCI framework offers great flexibility in the choice of indication variables. We alsocompare the three indication variables with the KXRCF one, and the numerical resultsfavor the KXRCF and the cell-boundary jump indication variables.