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1、ThisispageiPrinter:OpaquethisComputationalTurbulentIncompressibleFlowAppliedMathematics:Body&SoulVol4JohanHoffmanandClaesJohnson31stAugust2006iiPrefaceAppliedMathematics:Body&Soulisamathematicseducationreformprogramincludingaseriesofbooks,togetherwithassociatededucationa
2、lmaterialandopensourcesoftwarefreelyavailablefromtheprojectwebpageatwww.bodysoulmath.org.Body&Soulre
ectstherevolutionarynewpossibilitiesofmathematicalmodelingopenedbythemoderncomputerintheformofComputationalCalculus(CC),whichisnowchangingtheparadigmofmathematicalmod-eli
3、nginscienceandtechnologywithnewmethods,questionsandanswers,asamodernformoftheclassicalcalculusofLeibnizandNewton.TheBody&SoulseriesofbookspresentsCCinasynthesisofcompu-tationalmathematics(Body)andanalyticalmathematics(Soul)includingapplications.Volumes1-3[36]giveamodernv
4、ersionofcalculusandlinearalgebraincludingcomputationstartingatabasicundergraduatelevel,andsubsequentvolumesonagraduatelevelcoverdi erentareasofapplicationswithfocusoncomputationalmethods:Volume4:ComputationalTurbulentIncompressibleFlow.Volume5:ComputationalThermodynami
5、cs.Volume6:ComputationalDynamicalSystems.ThepresentbookisVolume4,withVolumes5and6toappearin2007andfurthervolumesonsolidmechanicsandelectro-magneticsbeingplanned.AgentleintroductiontotheBody&Soulseriesisgivenin[63].TheoverallgoaloftheBody&SoulprojectmaybeformulatedastheA
6、utomationofComputationalMathematicalModeling(ACMM)involvingthekeystepsofautomationof(i)discretization,(ii)optimizationand(iii)modeling.TheobjectiveofACMMistoopenformassiveuseofCCinscience,engineering,medicine,andotherareasofapplication.ACMMisrealizedintheFEniCSproject(ww
7、w.fenics.org),whichmaybeseentorepresentthetopsoftwarepartofBody&Soul.Theautomationofdiscretization(i)involvesautomatictranslationofagivendi erentialequationinstandardmathematicalnotationintoadis-cretesystemofequations,whichcanbeautomaticallysolvedusingnumer-icallinearalg
8、ebratoproduceanapproximatesolutionofthedi erentialequation.Thetranslationisperformedusingadaptivestabil
