{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:28:18Z","timestamp":1787336898097,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>A discrete velocity model with spatial and velocity discretization based on a lattice Boltzmann method is considered in the low Mach number limit. A uniform numerical scheme for this model is investigated. In the limit, the scheme reduces to a finite difference scheme for the incompressible Navier--Stokes equation, which is a projection method with a second order spatial discretization on a regular grid. The discretization is analyzed and the method is compared to Chorin's original spatial discretization. Numerical results supporting the analytical statements are presented.<\/jats:p>","DOI":"10.1137\/s1064827599357188","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1-19","source":"Crossref","is-referenced-by-count":55,"title":["Discretizations for the Incompressible Navier--Stokes Equations Based on the Lattice Boltzmann Method"],"prefix":"10.1137","volume":"22","author":[{"given":"Michael","family":"Junk","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Axel","family":"Klar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.5595"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01026608"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0370-1573(92)90090-M"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994268090"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.55.R21"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.45.R5339"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Shiyi Chen, Gary Doolen, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., Vol. 30, Annual Reviews, Palo Alto, CA, 1998, 329\u201336498m:76118","DOI":"10.1146\/annurev.fluid.30.1.329"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1968-0242392-2"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160420810"},{"key":"R10","unstructured":"D. d\u2019Humi\u00e8res,\n                      Generalized Lattice\u2010Boltzmann Equations\n                      , in AIAA Rarefied Gas Dynamics: Theory and Applications, Progress in Astronautics and Aeoronautics 159, Academic Press, New York, 1992, pp. 450\u2013458."},{"key":"R11","first-page":"649","volume":"1","author":"Frisch Uriel","year":"1987","journal-title":"Complex Systems"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i1998-00296-0"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.55.R6333"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1023\/B:JOSS.0000015179.12689.e4"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.6811"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1995.1103"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1063\/1.869426"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0149"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997315962"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160480303"},{"key":"R21","unstructured":"M. Junk,\n                      A Finite Difference Interpretation of the Lattice Boltzmann method\n                      , Universit\u00e4t Kaiserslautern, Kaiserslautern, Germany, 1999, preprint."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6228"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996305558"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997321765"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6147"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90229-5"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.5984"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/1030045"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/17\/6\/001"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7930(94)00037-Y"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.65"},{"key":"R32","doi-asserted-by":"crossref","unstructured":"Y. Sone,\n                      Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers\n                      , in Advances in Kinetic Theory and Continuum Mechanics, Proceedings of a Symposium Held in Honour of Henri Cabannes, R. Gatignol and Soubbaramayer, eds., Springer\u2010Verlag, Paris, 1990, pp. 19\u201331.","DOI":"10.1007\/978-3-642-50235-4_3"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0016"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994274749"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142995289986"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599357188","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:35:44Z","timestamp":1787333744000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599357188"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827599357188"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599357188","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}