{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T08:52:40Z","timestamp":1789721560759,"version":"4.0.1"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"NUPTSF","award":["NY220040"],"award-info":[{"award-number":["NY220040"]}]},{"DOI":"10.13039\/100012905","name":"Department of Science and Technology of Shandong Province","doi-asserted-by":"publisher","award":["2019KJ1002"],"award-info":[{"award-number":["2019KJ1002"]}],"id":[{"id":"10.13039\/100012905","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11871443"],"award-info":[{"award-number":["11871443"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20191375"],"award-info":[{"award-number":["BK20191375"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>An accurate troubled-cell indicator (TCI) is always desired by the discontinuous Galerkin methods for solving nonlinear hyperbolic conservation laws. In this paper, we will design a new TCI using K-means clustering. The values of a troubled-cell indication variable are in general of different magnitudes between smooth and discontinuous regions, so the values from a local region are grouped into clusters by a K-means clustering algorithm so that each cluster consists of either the troubled cells or the untroubled cells. A classification criterion is also proposed to discriminate what kind of cells that each cluster contains. The main advantage of the new TCI is its great potential of extensibility. It works for structured meshes and is expected to work for unstructured meshes and irregular meshes, using various indication variables. Also, it is free of problem-dependent parameters. Extensive numerical tests in both one and two dimensions show that the new TCI can detect the troubled cells accurately using the KXRCF indication variable, and it is in general better than the original KXRCF TCI.<\/jats:p>","DOI":"10.1137\/20m1344081","type":"journal-article","created":{"date-parts":[[2021,8,26]],"date-time":"2021-08-26T11:30:06Z","timestamp":1629977406000},"page":"A3009-A3031","source":"Crossref","is-referenced-by-count":11,"title":["A New Troubled-Cell Indicator for Discontinuous Galerkin Methods Using K-Means Clustering"],"prefix":"10.1137","volume":"43","author":[{"given":"Hongqiang","family":"Zhu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiyun","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhen","family":"Gao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,8,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(94)90029-9"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6718"},{"key":"atypb3","first-page":"545","volume":"54","author":"Cockburn B.","year":"1990","journal-title":"Math. 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