北航计算流体力学第1课

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-dependentEulerequationsDistributedlossmodelBoundarylayerapproximationInviscidmodelsThinshearlayerapproximationParabolizedNavier-StokesequationsViscous-inviscidinterationmodelsLargeviscousregionsThree-dimensionalReynoldsaveragedNavier-StokesequationsThree-DimensionalNavier-StokesequationsinputFluidconstitutiveequationYesNoTurbulencemodelsSteady-staterotationalmodelsSmall-disturbancepotentialequationPotentialflowmodelsTime-dependentEulerequationsDistributedlossmodelBoundarylayerapproximationInviscidmodelsThinshearlayerapproximationParabolizedNavier-StokesequationsViscous-inviscidinterationmodelsLargeviscousregionsThree-dimensionalReynoldsaveragedNavier-StokesequationsThree-DimensionalNavier-StokesequationsinputFluidconstitutiveequationClassificationofvariousflowmodelsIsentropic,irrotationalflowsViscouseffectsnegligiblePOTENTIALEQUATIONSSINGLEsecond-ordernon-lineardifferentialequationDescribeconservationofmassandenergyMomentumconservationnotfullysatisfiedinpresenceofshocksClassificationofvariousflowmodelsIsentropic,irrotationalflowsViscouseffectsnegligiblePOTENTIALEQUATIONSSINGLEsecond-ordernon-lineardifferentialequationDescribeconservationofmassandenergyMomentumconservationnotfullysatisfiedinpresenceofshocksEULEREQUATIONSCoupledsystemoffivenon-lineardifferentialequationsoffirstorder,inspaceandtimeDescribeconservationofmass,momentumandenergyDescribewavepropagation(convective)phenomenaNAVIER-STOKESEQUATIONSCoupledsystemoffivenon-lineardifferentialequationsofsecondorder,inspaceandtimeDescribeconservationofmass,momentumandenergyDescribewavepropagationphenomenadampedbyviscosityOverviewofcomputationalfluiddynamicsDeduceflowbehavior : flowseparation : flowrates : heattransfer : forcesonbodies (skinfriction,drag,lift) : efficienciesOverviewofcomputationalfluiddynamicsDeduceflowbehavior : flowseparation : flowrates : heattransfer : forcesonbodies (skinfriction,drag,lift) : efficiencies (turbine,diffuser)SolvetheequationsplusboundaryconditionsVelocityDistribution : Pressure `` :Density `` : Temperature `` : FOREACHELEMENTOFFLUID： Conservationofmass ContinuityEquation Newton’ssecondlaw EulerEquation ofmotion Navier-StokesEquations Conservationofenergy EnergyEquation Equationofstate RealworldRealworldPhysicsNumericalsimulationApproximationlevelsDynamicalapproximationSpatialapproximationSteadinessapproximationMathematicalmodelDiscretizationtechniquesResolutionofdiscretesystemofequationsSpacediscretizationMeshdefinitionEquationdiscretizationDefinitionofnumericalmethodmmschemeComputationalModels计算流体力学不同发展阶段所求解的几种基本方程线性小扰动方程（60~70年代）式中全位势方程（70年代中~80年代初）Euler方程（80年代）4.平均N-S方程（90年代）5．大涡模拟6．直接求解N-S方程年代机型CPU时间费用70VAX75020小时$1000080IBM303320分钟$10