{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:36:29Z","timestamp":1787322989210,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100014086","name":"Fondation Sciences Math\u00e9matiques de Paris","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100014086","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-18-CE40-0027-01"],"award-info":[{"award-number":["ANR-18-CE40-0027-01"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-15-CE40-0010"],"award-info":[{"award-number":["ANR-15-CE40-0010"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary differential equations. Such a method is well justified in the full plane, thanks to the explicit representation formulas of Biot and Savart. In an exterior domain, we also replace the impermeable boundary by a collection of point vortices generating the circulation around the obstacle. The density of these point vortices is chosen in order that the flow remains tangent at midpoints between adjacent vortices and that the total vorticity around the obstacle is conserved. In this work, we provide a rigorous justification of this method for any smooth exterior domain, one of the main mathematical difficulties being that the Biot--Savart kernel defines a singular integral operator when restricted to a curve (here, the boundary of the domain). We also introduce an alternative method---the fluid charge method---which, as we argue, is better conditioned and therefore leads to significant numerical improvements.<\/jats:p>","DOI":"10.1137\/19m1291947","type":"journal-article","created":{"date-parts":[[2020,8,20]],"date-time":"2020-08-20T12:37:33Z","timestamp":1597927053000},"page":"3881-3961","source":"Crossref","is-referenced-by-count":5,"title":["The Vortex Method for Two-Dimensional Ideal Flows in Exterior Domains"],"prefix":"10.1137","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4190-5100","authenticated-orcid":true,"given":"Diogo","family":"Ars\u00e9nio","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9683-6173","authenticated-orcid":true,"given":"Emmanuel","family":"Dormy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2488-4117","authenticated-orcid":true,"given":"Christophe","family":"Lacave","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,8,20]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.5802\/jedp.108"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-16830-7"},{"key":"atypb3","volume-title":"Method of Discrete Vortices","author":"Belotserkovsky S. M.","year":"1993"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1215\/ijm\/1248355344"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0089771"},{"key":"atypb6","volume-title":"Theory of Ordinary Differential Equations","author":"Coddington E. A.","year":"1955"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.2307\/2007065"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511526442"},{"key":"atypb9","volume-title":"Methods of Mathematical Physics: Partial Differential Equations Vol II","author":"Courant R.","year":"1989"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02545747"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1977.26.26007"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-2898-1_12"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-015-0889-3"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61798-0"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01760-5"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160430305"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09432-8"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1978.11994567"},{"key":"atypb20","volume-title":"Numerical Computation of Internal and External Flows","author":"Hirsch C.","year":"1988"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1081\/PDE-120019386"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-86748-4"},{"key":"atypb23","first-page":"63","volume":"30","author":"Kikuchi K.","year":"1983","journal-title":"J. Fac. Sci. Univ. Tokyo Sect. IA Math."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2014.63.5402"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-00-01271-0"},{"key":"atypb26","volume-title":"Vorticity and Incompressible Flow","author":"Majda A. J.","year":"2002"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-88958-4.50007-0"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4284-0"},{"key":"atypb29","volume-title":"Singular Integral Equations: Boundary Problems of Functions Theory and Their Applications to Mathematical Physics","author":"Muskhelishvili N. I.","year":"1972"},{"key":"atypb30","volume-title":"Methods of Modern Mathematical Physics","volume":"1","author":"Reed M.","year":"1980","edition":"2"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199609)49:9<911::AID-CPA2>3.0.CO;2-A"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03915-1"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(84)90066-1"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.2307\/1968745"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61859-8"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1291947","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:36:19Z","timestamp":1787319379000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1291947"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/19M1291947"],"URL":"https:\/\/doi.org\/10.1137\/19m1291947","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}