数值传热考试复习题(完成)

《数值传热考试复习题(完成)》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、1.TaylorseriesandFiniteDifferenceAccuracy(lecture3)Answer：Errorisasignofitsaccuracy2.Forward,CentralandBackwarddifferences(lecture3)a)truncationerrorsAnswer：showedintheproblem1,erroristhetruncationerror3.Finitedifferencemodelsfor1stand2ndderivatives(l

2、ecture3)4.Basisfunctionsforderivingfinitedifferenceequations(lecture3)1.Writeenergybalanceforvarioustypesofelements(lecture3)Answer:Boundary:walltemperature:Heatflux:**ConjugateHeatTransfer1.Whataresingleanddoubleprecision?(lecture3new)Answer:Real-4by

3、tes(32bits)~7digitsDouble-8bytes~15digitsMinimum/MaximumReal:1x10-38<

4、x

5、<3x1038Double:2x10-308<

6、x

7、<2x103082.Methodsfornon-rectangularareas(lecture6)Answer:7.1Fitgeometrytogrid(easy)优点：(1)曲线边界用梯形网格逼近，可以在直角坐标系中实现复杂问题的数值计算。(2)网格构造简单，可以适用于任何形状物体。缺点：计算边界是带

8、有90o角尖峰的锯齿状粗糙表面。7.2Modifyfinitedifferenceequations:(1)ForTwall=constant,nottoodifficult,(2)Forqwall=constant,verydifficult(3)Verydifficultforfluids7.3CoordinateTransformationMethods(P435)适体坐标系——各坐标轴与所计算区域的边界一一相符合的坐标系。优点：通过计算方法构造适体坐标系，可以实现对复杂的物理空间进行求解，

9、把物理空间上的不规则区域变换成计算空间上的规则区域进行求解，精度高。缺点：建立适体坐标系和物理坐标系的对应关系困难。1.Transientmethods–describethemethods–advantagesanddisadvantagesAnswer：(1)Explicit显式(forward):Useresultsfromprevioustimestep.a)Noiterationsb)Eachtimestepisveryfastc)Requiresmanytimestepsd)Accur

10、ate(forsmalltimesteps)e)Notstable(2)Implicit隐式(backward):Useresultsfromnexttimestep.a)Solvesimultaneously同时的b)Iterate迭代c)Eachtimestepisslower,butfewertimestepsd)Complexe)UnconditionallyStable无条件稳定,butlessaccurate不精确thanCrank-Nicolson(3)Crank-Nicolson(

11、central):Centraldifferencea)Solvesimultaneouslyb)Iteratec)Eachtimestepisslower,butfewertimestepsd)Complexe)Moreaccuratethanimplicitf)UnconditionallyStable1.Solvea1Denergyequationproblem(conductionwith3-4points)Answer:(1)稳态Homework1Dconduction.(2)瞬态：如果

12、让计算的话，就用显示的方法吧，两个小时估计没有时间来迭代啊~~2.Central/upwindproblem(advectionproblems)–WhatiswrongwiththeFirstOrderUpwindScheme?–WhatiswrongwiththePowerLawscheme(乘方格式)?Answer：(1)虽然可以获得物理上可接受的解，但当Peclet数较大时，假扩散较严重。为避免此问题，常需要加密计算网格。(2)主要适用于无源项的对流扩散问题，对有非常数源项