相变传热与流体流动数值分析作业3

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1、相变传热与流体流动数值分析作业3学院（系）：能源与动力学院专业：能源与动力工程学生姓名：王佳琪学号：21110060指导教师：宋永臣教授完成日期：2012.3.6大连理工大学DalianUniversityofTechnologyTheFiniteVolumeMethodforConvection-DiffusionProblemsSubject:ApropertyΦistransportedbymeansofconvectionanddiffusionthroughtheone-dimensionaldomainsketchedi

2、nFigure1.ThegoverningdddΦequationisρuΦ=(Γ);boundaryconditionsareΦ0=1atdxdxdxx=0andΦL=0atx=L.UsingfiveequallyspacedcellsforconvectionanddiffusioncalculatethedistributionofΦafunctionofxforcase:(i)Case1:u=0.1m/s;(ii)Case2:u=2.5m/s;(iii)Case3:u=2.5m/swith20gridnodes;Thefol

3、lowingdataapply:LengthL=1.0m,ρ=1.0kg/m3,Γ=0.1kg/m/s.Φ=1Φ=0X=0x=1Solution:(I)Thecentraldifferencingscheme://王佳琪-作业-中心差分.cpp:定义控制台应用程序的入口点。//#include#include#include#include#include#include#include#include<

4、sstream>#include#defineN5usingnamespacestd;inti;doubleaw[N],b[N],ae[N],f[N],x[N];/*-------追赶法求解数组-------*/voidtdma(){doublel[N],u[N],y[N];for(i=1;i

5、;x[N-1]=y[N-1]/u[N-1];for(i=N-2;i>=0;i--)x[i]=(y[i]-ae[i]*x[i+1])/u[i];}voidmain(){voidOutput();/*---------定义变量及边界条件---------*/doubleF,D,u,ρ,Γ,x,L,φA,φB,Sp[N];u=0.1;ρ=1;Γ=0.1;L=1;φA=1;φB=0;x=L/N;F=ρ*u;D=Γ/x;/*---------网格离散---------*/for(i=0;i

6、[i]=-(D-F/2);Sp[i]=-(2*D+F);f[i]=(2*D+F)*φA;}elseif(i==N-1){ae[i]=0;aw[i]=-(D+F/2);Sp[i]=-(2*D-F);f[i]=(2*D-F)*φB;}else{aw[i]=-(D+F/2);ae[i]=-(D-F/2);Sp[i]=0;f[i]=0;}b[i]=-aw[i]-ae[i]-Sp[i];}tdma();Output();}voidOutput(){/*---------后处理文件生成---------*/ostringstreamname;n

7、ame.str("");name<<"central_.plt";ofstreamout(name.str().c_str());out<<"Title=central"<

8、0.1m/s;N=5;（ii）Case2:u=2.5m/s;N=5;（iii）case3:u=2.5m/s;N=20;Discussion:Fromthefigure,wecanseetheagreementswiththeanaly