{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:14:26Z","timestamp":1753881266360,"version":"3.41.2"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,5]],"date-time":"2012-04-05T00:00:00Z","timestamp":1333584000000},"content-version":"vor","delay-in-days":95,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We study the preconditioned iterative method for the unsteady Navier\u2010Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner\nwhich is derived from the Hermitian\/Skew\u2010Hermitian preconditioner to the Krylov subspace\u2010iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, Reynolds numbers, time step, and algorithm parameters. The\npreconditioner is efficient and easy to apply for the unsteady Oseen problems in rotation form.<\/jats:p>","DOI":"10.1155\/2012\/307939","type":"journal-article","created":{"date-parts":[[2012,4,5]],"date-time":"2012-04-05T21:05:56Z","timestamp":1333659956000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Alternative HSS Preconditioner for the Unsteady Incompressible Navier\u2010Stokes Equations in Rotation Form"],"prefix":"10.1155","volume":"2012","author":[{"given":"Jia","family":"Liu","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198528678.001.0001"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(199907\/08)6:5&lt;353::AID-NLA169&gt;3.0.CO;2-J"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(02)00513-3"},{"key":"e_1_2_7_4_2","doi-asserted-by":"crossref","unstructured":"OlshanskiiM. A. BatheK. J. Preconditioned iterations for the linearized Navier-Stokes system in the rotation form Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics 2003 1074\u20131077.","DOI":"10.1016\/B978-008044046-0\/50262-1"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500374881"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1761178"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100300"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:BITN.0000014548.26616.65"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479802417106"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492904000212"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-006-0679-9"},{"key":"e_1_2_7_12_2","unstructured":"LiuJ. Preconditioned Krylov subspace methods for incompressible flow problems Ph.D. thesis Emory University Ann Arbor Mich USA 2006 2709351."},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479801395458"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479803434926"},{"key":"e_1_2_7_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/0719066"},{"key":"e_1_2_7_18_2","doi-asserted-by":"publisher","DOI":"10.1137\/040606028"},{"key":"e_1_2_7_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002110000160"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/307939.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/307939.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/307939","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T07:05:32Z","timestamp":1718089532000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/307939"}},"subtitle":[],"editor":[{"given":"Kok Kwang","family":"Phoon","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/307939"],"URL":"https:\/\/doi.org\/10.1155\/2012\/307939","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-11-02","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-01-27","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"307939"}}