{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:37:11Z","timestamp":1787704631778,"version":"build-2784847793"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"The use of approximate projection methods for modeling low Mach number flows avoids many of the numerical complications associated with exact projection methods, but introduces additional design choices in developing a robust algorithm. In this paper we first explore these design choices in the setting of inviscid incompressible flow using several computational examples. We then develop a framework for analyzing the behavior of the different design variations and use that analysis to explain the features observed in the computations. As part of this work we introduce a new variation of the approximate projection algorithm that combines the advantages of several of the previous versions.<\/jats:p>","DOI":"10.1137\/s1064827599357024","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1139-1159","source":"Crossref","is-referenced-by-count":89,"title":["Approximate Projection Methods: Part I. Inviscid Analysis"],"prefix":"10.1137","volume":"22","author":[{"given":"Ann S.","family":"Almgren","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John B.","family":"Bell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"William Y.","family":"Crutchfield","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.5890"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827593244213"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"J. B. Bell, P. Colella, and H. M. Glaz,\n A second\u2010order projection method for the incompressible Navier\u2013Stokes equations\n , in the AIAA 8th Computational Fluid Dynamics Conference, Honolulu, 1987, pp. 789\u2013794.","DOI":"10.2514\/6.1987-1176"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"J. B. Bell, P. Colella, and L. H. Howell,\n An efficient second\u2010order projection method for viscous incompressible flow\n , in the AIAA 10th Computational Fluid Dynamics Conference, Honolulu, 1991, pp. 360\u2013367.","DOI":"10.2514\/6.1991-1560"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1968-0242392-2"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0906009"},{"key":"R7","unstructured":"M. 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