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1、一．三维时间相关可压缩流的Navier-Skokes方程：(1)(向量形式)式中，其中,,,,,,为了方程封闭，必须引入4个关系式(9个自变量):1,3,2,4,YesNoTurbulencemodelsSteady-staterotationalmodelsSmall-disturbancepotentialequationPotentialflowmodelsTime-dependentEulerequationsDistributedlossmodelBoundarylayerapproxim
2、ationInviscidmodelsThinshearlayerapproximationParabolizedNavier-StokesequationsViscous-inviscidinterationmodelsLargeviscousregionsThree-dimensionalReynoldsaveragedNavier-StokesequationsThree-DimensionalNavier-StokesequationsinputFluidconstitutiveequati
3、onClassificationofvariousflowmodelsIsentropic,irrotationalflowsViscouseffectsnegligiblePOTENTIALEQUATIONS-SINGLEsecond-ordernon-lineardifferentialequation-Describeconservationofmassandenergy-MomentumconservationnotfullysatisfiedinpresenceofshocksEULERE
4、QUATIONS-Coupledsystemoffivenon-lineardifferentialequationsoffirstorder,inspaceandtime-Describeconservationofmass,momentumandenergy-Describewavepropagation(convective)phenomenaNAVIER-STOKESEQUATIONS-Coupledsystemoffivenon-lineardifferentialequationsofs
5、econdorder,inspaceandtime-Describeconservationofmass,momentumandenergy-DescribewavepropagationphenomenadampedbyviscosityOverviewofcomputationalfluiddynamicsDeduceflowbehavior:flowseparation:flowrates:heattransfer:forcesonbodies(skinfriction,drag,lift):
6、efficiencies(turbine,diffuser)SolvetheequationsplusboundaryconditionsVelocityDistribution:Pressure``:Density``:Temperature``:FOREACHELEMENTOFFLUID：ConservationofmassContinuityEquationNewton’ssecondlawEulerEquationofmotionNavier-StokesEquationsConservat
7、ionofenergyEnergyEquationEquationofstateRealworldPhysicsNumericalsimulationApproximationlevelsDynamicalapproximationSpatialapproximationSteadinessapproximationMathematicalmodelDiscretizationtechniquesResolutionofdiscretesystemofequationsSpacediscretiza
8、tionMeshdefinitionEquationdiscretizationDefinitionofnumericalschemeComputationalModels计算流体力学不同发展阶段所求解的四种基本方程1.线性小扰动方程（60~70年代）式中2.全位势方程（70年代中~80年代初）3.Euler方程（80年代）4.平均N-S方程（90年代）年代机型CPU时间费用70VAX75020小时$1000080IBM303320分钟$100090Cray-220秒
