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1、JournalofComputationalPhysics154,468–496(1999)ArticleIDjcph.1999.6323,availableonlineathttp://www.idealibrary.comonModelingMeltConvectioninPhase-FieldSimulationsofSolidificationC.Beckermann,¤H.-J.Diepers,yI.Steinbach,yA.Karma,zandX.Tong¤¤DepartmentofMechanicalE
2、ngineering,UniversityofIowa,IowaCity,Iowa52242-1527;yACCESSe.V.,Intzestraße5,52072Aachen,Germany;zDepartmentofPhysics,NortheasternUniversity,Boston,Massachusetts02115E-mail:becker@icaen.uiowa.eduReceivedNovember24,1998;revisedApril22,1999Anoveldiffuseinterface
3、modelispresentedforthedirectnumericalsimulationofmicrostructureevolutioninsolidificationprocessesinvolvingconvectionintheliquidphase.Thesolidificationfrontistreatedasamovinginterfaceinthediffuseapproximationasknownfromphase-fieldtheories.Theno-slipconditionbetwee
4、nthemeltandthesolidisrealizedviaadragresistivityinthediffuseinterfaceregion.Themodelisshowntoaccuratelyreproducetheusualsharpinterfaceconditionsinthelimitofathindiffuseinterfaceregion.Afirsttestofthemodelisprovidedforflowthroughregulararraysofcylinderswithastati
5、onaryinterface.Then,twoexamplesarepresentedthatinvolvesolid/liquidphase-change:(i)coarseningofamushofabinaryalloy,whereboththeinterfacecurvatureandtheflowpermeabilityevolvewithtime,and(ii)dendriticgrowthinthepresenceofmeltconvectionwithparticularemphasisontheop
6、eratingpointofthetip.°c1999AcademicPressKeyWords:phase-fieldmethod;convection;dendriticgrowth;coarsening.1.INTRODUCTIONTheformationofmorphologicalfeaturesinsolidificationofpurematerialsandalloyshasbeeninvestigatedovermanyyearsandtheliteratureaboundsinreferenceso
7、nsubjectsasdiverseasstabilityofaplanarsolid/liquidinterface[1],dendriticgrowth[2],andcoarseningofasolid/liquidmixture[3,4].Theselectionofsolidificationpatternsiscontrolledbytheinterplayofthermal,solutal,capillary,andkineticlengthortimescales[5].Comparablylittle
8、isknownabouttheinfluenceofnaturalorforcedconvectiononmicrostructuredevelopment.Meltconvectionaddsnewlengthandtimescalestotheproblemandresultsinmorphologiesthatarepotentiallymuchdiff