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The relevance of the model and the robustness of the numerical strategy are illustrated by several numerical simulations in a one-dimensional framework. In particular, the method seems well suited to the numerical study of the hydraulics of underground rivers and coastal caves, such as the Cosquer Cave, and to the simulation of marine energy converters, such as the oscillating water column.<\/jats:p>","DOI":"10.1137\/22m1514908","type":"journal-article","created":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T10:22:36Z","timestamp":1701080556000},"page":"B828-B852","source":"Crossref","is-referenced-by-count":6,"title":["Congested Shallow Water Model: Trapped Air Pockets Modeling"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7040-8384","authenticated-orcid":true,"given":"Martin","family":"Parisot","sequence":"first","affiliation":[{"name":"INRIA, University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, 33405 Talence cedex, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,11,27]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/06067167X"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2010036"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.220313.111013a"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.01.020"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/18M1174180"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1051\/proc\/202107005"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109486"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.01.020"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2012036"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2006.10.086"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)HY.1943-7900.0000680"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7930(00)00031-1"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1115\/1.2955990"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.3406\/bspf.1992.10536"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(02)02366-X"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.04.025"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1121\/1.388844"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.rser.2009.11.003"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s00161-016-0531-0"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2018032"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.5802\/smai-jcm.67"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/j.rser.2013.04.012"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.250910.131011a"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2014021"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2004024"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s40818-017-0029-5"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1063\/1.3053183"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1039\/b700766c"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1002\/fld.4766"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/15M1021817"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1561\/2200000073"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1121\/1.396145"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s007910050055"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109723"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6810"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1002\/fld.417"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1514908","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:20:39Z","timestamp":1787332839000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1514908"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,27]]},"references-count":36,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12,31]]}},"alternative-id":["10.1137\/22M1514908"],"URL":"https:\/\/doi.org\/10.1137\/22m1514908","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,11,27]]}}}