Modern Numerical Methods for Fluid Flow

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1、ModernNumericalMethodsforFluidFlowPhillipColellaDepartmentofMechanicalEngineeringUniversityofCalifornia,BerkeleyandElbridgeGerryPuckettDepartmentofMathematicsUniversityofCalifornia,DavisPleasefeelfreetomakecopiesofthisdraftforyourstudentsandcolleagues.Yourarealsowelcometouseitasc

2、oursematerial.Wewouldappreciateanycomments,suggestionsanderratathatyoumayhave.Theseshouldbesenttothesecondauthorategp@math.ucdavis.eduCopyright1998byPhillipColellaandElbridgeGerryPuckett.Allrightsreserved.ModernNumericalMethodsforFluidFlowP.ColellaandE.G.PuckettI.CompressibleFlow

3、1.Finitedifferencemethodsforlinearscalarproblems.........................................................................11.1Consistency,stability,andconvergence...............................................................................21.2TheVonNeumannstabilityanalysis......

4、..............................................................................51.3Somesimplefinitedifferenceschemes................................................................................91.3.1UpwindDifferencing..............................................................

5、...............................91.3.2DownwindDifferencing......................................................................................101.3.3CenteredDifferencing.........................................................................................111.3.4TheTwo-StepLax

6、-WendroffScheme................................................................121.4Upwindschemesandthegeometricinterpretationoffinitedifferences............................151.5Fourieranalysisandaccuracy.............................................................................

7、...............201.5.1Amplitudeerror...................................................................................................221.5.2Phaseerrors.........................................................................................................231.6Themodifiedequatio

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