一维对流扩散问题求解

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1、Subjects：Apropertyistransportedbymeansofconvectionanddiffusionthroughtheone-dimensionaldomain.Thegoverningequationis;boundaryconditionsareatx=0andatx=L.Usingfiveequallyspacedcellsandthecentraldifferencingschemeforconvectionanddiffusioncalculatethedistributionofasafunctionofxfor(i)Case1:u=

2、0.1m/s,(ii)Case2:Case1:u=2.5m/s,andcomparetheresultswiththeanalyticalsolution.(iii)Case3:recalculatethesolutionforu=2.5m/swith20gridnodesandcomparetheresultswiththeanalyticalsolution,thefollowingdateapply:lengthL=1.0m,.31Solution:Programminglanguage:Filename:二维稳态导热模拟.cppCompilesoftware:Mi

3、crosoftVisualC++6.0Code:#include#include#includeusingnamespacestd;#defineGn15//网格节点数.#defineGn220//网格节点数.#defineP1//流体密度，单位：kg/m/m/m.#defineProA1//A端传递特性.#defineProB0//B端传递特性.//////FDD///////追赶法过程voidTDMA1(doublea[],doubleb[],doublec[],doublef[],double*p){//矩阵形式//b0c0

4、00//=f0//a0b1c10//=f1//...............//00...b(N-1)c(N-2)//=f(N-1)doubled[Gn1-1],u[Gn1],ll[Gn1-1],y[Gn1],X[Gn1];inti;for(i=0;i<=Gn1-2;i++){d[i]=c[i];}u[0]=b[0];for(i=1;i<=Gn1-1;i++){ll[i-1]=a[i-1]/u[i-1];u[i]=b[i]-ll[i-1]*c[i-1];}y[0]=f[0];for(i=1;i<=Gn1-1;i++){y[i]=f[i]-ll[i-1]*y[i-1];}X[Gn1-1]

5、=y[Gn1-1]/u[Gn1-1];31for(i=Gn1-2;i>=0;i--){X[i]=(y[i]-c[i]*X[i+1])/u[i];}for(i=0;i<=Gn1-1;i++)*(p+i)=X[i];}voidTDMA2(doublea[],doubleb[],doublec[],doublef[],double*p){doubled[Gn2-1],u[Gn2],ll[Gn2-1],y[Gn2],X[Gn2];inti;for(i=0;i<=Gn2-2;i++){d[i]=c[i];}u[0]=b[0];for(i=1;i<=Gn2-1;i++){ll[i-1]=a[i-1

6、]/u[i-1];u[i]=b[i]-ll[i-1]*c[i-1];}y[0]=f[0];for(i=1;i<=Gn2-1;i++){y[i]=f[i]-ll[i-1]*y[i-1];}X[Gn2-1]=y[Gn2-1]/u[Gn2-1];for(i=Gn2-2;i>=0;i--){X[i]=(y[i]-c[i]*X[i+1])/u[i];}for(i=0;i<=Gn2-1;i++)*(p+i)=X[i];}voidmain(){doubleu,L=1,T=0.1,min_x,F,D,aW,aE,m,n;doublea[Gn2],b[Gn2],c[Gn2],f[Gn2],X[Gn2];

7、intserial_number1,serial_number2,i;printf("Therearefourmethodstosolvethesecases:");printf("1.Thecentraldifferencingscheme.");printf("2.Theupwinddifferencingscheme.");printf("3.Thehybriddifferencingscheme.");printf("4