ThispageintentionallyleftblankCOMPUTATIONALMETHODSFORMULTIPHASEFLOWPredictingthebehaviorofmultiphaseflowsisaproblemofimmenseim-portanceforbothindustrialandnaturalprocesses.Thankstohigh-speedcomputersandadvancedalgorithms,itisstartingtobepossibletosimulatesuchflowsnumerically.Researchersandstudentsalikeneedtohaveaone-stopaccountofthearea,andthisbookisthat:it’sacomprehensiveandself-containedgraduate-levelintroductiontothecomputationalmodelingofmultiphaseflows.Eachchapteriswrittenbyarecognizedexpertinthefieldandcontainsextensivereferencestocurrentresearch.Thebooksisorga-nizedsothatthechaptersarefairlyindependent,toenableittobeusedforarangeofadvancedcourses.Inthefirstpart,avarietyofdifferentnumer-icalmethodsfordirectnumericalsimulationsaredescribedandillustratedwithsuitableexamples.Thesecondpartisdevotedtothenumericaltreat-mentofhigher-level,averaged-equationsmodels.Nootherbookoffersthesimultaneouscoverageofsomanytopicsrelatedtomultiphaseflow.Itwillbewelcomedbyresearchersandgraduatestudentsinengineering,physics,andappliedmathematics.COMPUTATIONALMETHODSFORMULTIPHASEFLOWEditedbyANDREAPROSPERETTIANDGR´ETARTRYGGVASONCAMBRIDGEUNIVERSITYPRESSCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,CambridgeCB28RU,UKFirstpublishedinprintformatISBN-13978-0-521-84764-3ISBN-13978-0-511-29454-9©CambridgeUniversityPress20072006Informationonthistitle:(EBL)eBook(EBL)hardbackContentsPrefacepageviiAcknowledgmentsx1Introduction:Acomputationalapproachtomultiphaseflow1A.ProsperettiandG.Tryggvason2DirectnumericalsimulationsoffiniteReynoldsnumberflows19G.TryggvasonandS.Balachandar3Immersedboundarymethodsforfluidinterfaces37G.Tryggvason,M.SussmanandM.Y.Hussaini4Structuredgridmethodsforsolidparticles78S.Balachandar5Finiteelementmethodsforparticulateflows113H.Hu6LatticeBoltzmannmodelsformultiphaseflows157S.Chen,X.HeandL.-S.Luo7BoundaryintegralmethodsforStokesflows193J.Blawzdziewicz8Averagedequationsformultiphaseflow237A.Prosperetti9Point-particlemethodsfordisperseflows282K.Squires10Segregatedmethodsfortwo-fluidmodels320A.Prosperetti,S.Sundaresan,S.PannalaandD.Z.Zhang11Coupledmethodsformultifluidmodels386A.ProsperettiReferences436Index466vPrefaceComputationhasmadetheorymorerelevantThisisagraduate-leveltextbookintendedtoserveasanintroductiontocomputationalapproacheswhichhaveprovenusefulforproblemsarisinginthebroadareaofmultiphaseflow.Eachchaptercontainsreferencestothecurrentliteratureandtorecentdevelopmentsoneachspecifictopic,buttheprimarypurposeofthisworkistoprovideasolidbasisonwhichtobuildbothapplicationsandresearch.Forthisreason,whilethereaderisexpectedtohavehadsomeexposuretograduate-levelfluidmechanicsandnumericalmethods,noextensiveknowledgeofthesesubjectsisassumed.Thetreat-mentofeachtopicstartsatarelativelyelementarylevelandisdevelopedsoastoenablethereadertounderstandthecurrentliterature.Alargenumberoftopicsfallunderthegenericlabelof“computationalmul-tiphaseflow,”rangingfromfullyresolvedsimulationsbasedonfirstprin-ciplestoapproachesemployingsomesortofcoarse-grainingandaveragedequations.Thebookisideallydividedintotwopartsreflectingthisdistinc-tion.Thefirstpart(Chapters2–5)dealswithmethodsforthesolutionoftheNavier–Stokesequationsbyfinitedifferenceandfiniteelementmethods,whilethesecondpart(Chapters9–11)dealswithvariousreduceddescrip-tions,frompoint-particlemodelstotwo-fluidformulationsandaveragedequations.Thetwopartsareseparatedbythreemorespecializedchap-tersonthelatticeBoltzmannmethod(Chapter6),theboundaryintegralmethodforStokesflow(Chapter7),andonaveragingandtheformulationofaveragedequation(Chapter8).Thisisamulti-authorvolume,butwehavemadeanefforttounifythenotationandtoincludecross-referencingamongthedifferentchapters.Hope-fullythisfeatureavoidstheneedforasequentialreadingofthechapters,pos-siblyasidefromsomeintroductorymaterialmostlypresentedinChapter1.Theobjectiveofthisworkistodescribecomputationalmethods,ratherviiviiiPrefacethanthephysicsofmultiphaseflow.Withthisaspectinmind,theprimarycriterionintheselectionofspecificexampleshasbeentheirusefulnesstoillustratethecapabilitiesofanalgorithmratherthanthecharacteristicsofparticularflows.TheoriginalideaforthisbookwasconceivedwhenwechairedtheStudyGrouponComputationalPhysicsinconnectionwiththeWorkshoponSci-entificIssuesinMultiphaseFlow.Theworkshop,chairedbyProf.T.J.Hanratty,wassponsoredbytheU.S.DepartmentofEnergyandheldonthecampusoftheUniversityofIllinoisatUrbana-ChampaignonMay7–92002;a