北航CFD講義第1課

1、一 三維時(shí)間相關(guān)可壓縮流的navier-skokes方程： (1) (向量形式)式中， 其中, , , , , ,為了方程封閉，必須引入4個(gè)關(guān)系式(9個(gè)自變量):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計(jì)算流體力學(xué)不同發(fā)展階段所求解的四種基本方程1. 線性小擾動方程 （6070年代）式中 2. 全位勢方程 （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）年代機(jī)型cpu時(shí)間費(fèi)用70vax75020小時(shí)$1000080ibm303320分鐘$100090cray-220秒$10求解二維翼型粘性繞流若在60年代，在ibm704上工作，需要20年，費(fèi)用$1000萬網(wǎng)格點(diǎn)數(shù)所需cpu