Astudyofanumericalsolutionofthesteady twodimensionsNavier–Stokesequations inaconstrictedchannelproblem byacompactfourthordermethod P.F.A.Mancera 1 Departamento de Bioestat  ıstica, Instituto de Bioci^ encias, cp 510, Rubi ~ ao Jr., UNESP, Botucatu 18618-000, Brazil Abstract Wepresentanumericalsolutionforthesteady2DNavier–Stokesequationsusinga fourth order compact-type method. The geometry of the problem is a constricted symmetricchannel,wheretheboundarycanbevaried,viaaparameter,fromasmooth constrictiontoonepossessingaverysharpbutsmoothcornerallowingustoanalysethe behaviouroftheerrorswhenthesolutionissmoothornearsingular.Thesetofnon- linear equations is solved by the Newton method. Results have been obtained for Reynoldsnumberupto500.Estimatesoftheerrorsincurredhaveshownthattheresults areaccurateandbetterthanthoseofthecorrespondingsecondordermethod. Ó 2002ElsevierInc.Allrightsreserved. Keywords: Steady 2D Navier–Stokes equations; High order methods; Compact methods; Streamfunctionvorticityformulation;Incompressibleflow;Laminarflow 1. Introduction Weconsideracompactfourthordernumericalmethodtosolvethesteady 2DNavier–Stokesequationsinthestreamfunctionvorticityformulationwhere thevelocitiesaresolvedbyanotherfourthorderformulae.Usuallyfluidflow E-mail address: pmancera@ibb.unesp.br (P.F.A.Mancera). 1 Contractsponsors:CNPq(Processno.450829/01-4(NV))andFAPESP(Processes01/03922-9 and01/09681-3). 0096-3003/$-seefrontmatter Ó 2002ElsevierInc.Allrightsreserved. doi:10.1016/S0096-3003(02)00630-6 AppliedMathematicsandComputation146(2003)771–790 www.elsevier.com/locate/amc