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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINFLUIDS,VOL.6,659-670(1986)LAGRANGIANFINITEELEMENTMETHODFORTHEANALYSISOFTWO-DIMENSIONALSLOSHINGPROBLEMSBALASUBRAMANIAMRAMASWAMY,MUTSUTOKAWAHARAANDTSUKASANAKAYAMADepartmentofCivilEngineering,ChuoUniversity,13-27,Kasuga1-Chome,Bu
2、nkyo-ku,Tokyo112,JapanSUMMARYAnewversionofanumericalalgorithmfortheLagrangiantreatmentofincompressiblefluidflowswithfreesurfacesisdeveloped.ThenovelfeaturesofthepresentmethodaretheadoptionsoftheLagrangianfiniteelementmethodandthevelocitycorrectiontechnique.Theuseofth
3、evelocitycorrectionapproachmakesthecomputationalschemeextremelysimpleinalgorithmicstructure.Hence,thepresentmethodisparticularlyattractiveforlarge-scaleproblems.Thetechniquesdiscussedhereareappliedtosometwo-dimensionalsloshingproblems,whichmayindicatetheversatilityan
4、deffectivenessofthepresentmethod.INTRODUCTIONThispaperdealsindetailwithanewfiniteelementtechniqueforthenumericalsolutionoffluidflowproblemsinvolvingfreesurfaces,andwiththenumericalanalysisoftwo-dimensionalsloshingproblems.Theanalysisofsloshingphenomenaisaveryimportan
5、tproblemofengineeringsignificance,asexemplifiedbyoiloscillationsinlargestoragetanksandwateroscillationsinreservoirsduetoearthquakes.ManytheoreticalandnumericalanalysesofsloshingproblemshavebeencarriedoutbymanyMostofthem,however,arebasedonthepotentialflowtheories,andc
6、annotbeappliedtooiloscillationswithstrongviscouseffects.Toovercomethisdifficultythepresentpaperdealswithtransientmotionsofincompressibleviscousfluidincontainers.Thenumericalanalysisofviscousfluidflowproblemsinvolvingfreesurfacesisverycomplicated.Therearetworeasonsfor
7、this.First,thepositionofthefreesurfacevarieswithtimeinamannernotknownapriori,andthisfactpreventstheanalysisfrombeingcompletelystraightforward.Hence,theremustbesomemeansoftrackingthepositionofthefreesurface.Secondly,theaccuratefreesurfaceboundaryconditionmustbeimposed
8、.InsolvingsuchdifficultproblemsthefiniteelementmethodcombinedwiththeLagrangiandescriptioncanbeappliedeffectively.Twobasicviewpoints
