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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, YesNoTurbulence modelsSteady-state rotational modelsSmall-disturbance potential equationPotential flow modelsTime-dependent Euler equationsDistributed loss modelBoundary layer approximationInviscid modelsThi
2、n shear layer approximationParabolized Navier-Stokes equationsViscous-inviscid interation modelsLarge viscous regionsThree-dimensional Reynolds averaged Navier-Stokes equationsThree-Dimensional Navier-Stokes equationsinputFluid constitutive equationClassification of various flow modelsIsentropic, ir
3、rotational flowsViscous effects negligiblePOTENTIAL EQUATIONS- SINGLE second-order non-linear differential equation- Describe conservation of mass and energy- Momentum conservation not fully satisfied in presence of shocksEULER EQUATIONS- Coupled system of five non-linear differential equations of f
4、irst order, in space and time- Describe conservation of mass, momentum and energy- Describe wave propagation (convective) phenomena NAVIER-STOKES EQUATIONS- Coupled system of five non-linear differential equations of second order, in space and time- Describe conservation of mass, momentum and energy
5、- Describe wave propagation phenomena damped by viscosityOverview of computational fluid dynamicsDeduce flow behavior:flow separation:flow rates:heat transfer:forces on bodies( skin friction, drag, lift ):efficiencies( turbine, diffuser )Solve the equations plus boundary conditionsVelocity Distribut
6、ion: Pressure : Density: Temperature: FOR EACH ELEMENT OF FLUID：Conservation of mass Continuity EquationNewtons second lawEuler Equationof motionNavier-Stokes EquationsConservation of energyEnergy EquationEquation of stateReal worldPhysicsNumerical simulationApproximation levelsDynamical approximati
7、onSpatial approximationSteadiness approximationMathematical modelDiscretization techniquesResolution of discrete system of equationsSpace discretizationMesh definitionEquationdiscretizationDefinition of numerical schemeComputational Models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 （6070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$10求解二维翼型粘性绕流若在60年代，在IBM704上工作，需要20年，费用$1000万网格点数所需CPU时间所需内存小扰动方程10万半小时1MB全位势方程10万3小时4MBEuler方程20万3昼夜32MB平均N-S方程200万3个月256MB三维机翼绕流场的数值模拟在DEC2000/500 上模拟三维机翼的绕流场（速度约为1000万次）