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1、COMMUNICATIONSINNUMERICALMETHODSINENGINEERINGCommun.Numer.Meth.Engng2003;00:1–14Preparedusingcnmauth.cls[Version:2000/03/22v1.0]Onthecalculationofnormalsinfree-surfaceflowproblemsM.A.Walkley1,,P.H.Gaskell2,P.K.Jimack1,M.A.Kelmanson3,J.L.Summers2andM.C.T.Wilson21SchoolofComputing,UniversityofLe
2、eds,Leeds,LS29JT,UK2SchoolofMechanicalEngineering,UniversityofLeeds,Leeds,LS29JT,UK3DepartmentofAppliedMathematics,UniversityofLeeds,Leeds,LS29JT,UKSUMMARYTheuseofboundary-conformingfinite-elementmethodsisconsideredforthesolutionofsurface-tension-dominatedfree-surfaceflowproblemsinthreedimension
3、s.Thisclassofmethodisbasedupontheuseofamovingmeshwhosevelocityisdrivenbythemotionofthefreesurface,whichisinturndeterminedviaakinematicboundaryconditionforthenormalvelocity.Thesignificanceofthemethodusedtocomputethenormaldirectionatthefinite-elementnodepointsforaC0piecewise-polynomialfreesurfacei
4、sinvestigated.Inparticular,itisdemonstratedthattheconceptofmass-consistentnormalsonanisoparametricquadratictetrahedralmeshisflawed.Inthiscaseanalternative,purelygeometric,normalisshowntoleadtoafarmorerobustnumericalalgorithm.Copyrightc2003JohnWiley&Sons,Ltd.KEYWORDS:Finiteelementmethod;Freesur
5、faceflow;Surfacetension;Normals1.INTRODUCTIONFree-surfaceflowproblemsareofgreatimportanceinthemodellingofawiderangeofphysicalphenomena,fromphase-changeproblems[1,2]throughtocoatingflows[3,4],sintering[5,6]ortheCorrespondenceto:M.A.Walkley,SchoolofComputing,UniversityofLeeds,Leeds,LS29JT,UK.Email
6、:markw@comp.leeds.ac.ukContract/grantsponsor:EPSRC;contract/grantnumber:GR/R25453/01Copyrightc2003JohnWiley&Sons,Ltd.2M.A.WALKLEYETAL.spreadingofviscousfluids[7,8].Intwodimensions,computationalfluiddynamics(CFD)techniquesforsolvingtime-dependentfree-surfaceproblemsarebecomingwellestablished[6,9
7、,10]and,inthreedimensions,therehasbeenasignificantamountofimportantrecentresearch[2,11,12,13].Oneofthemostpopularclassesofmethodsinbothtwoandthreedimensionsisbasedupontheuseofboundary-conformingmoving/adaptingmeshes,asinthearbitraryLagra
