東南大學(xué)傳熱學(xué)二維穩(wěn)態(tài)差分接點計算論文

1、；.二維穩(wěn)態(tài)計算實驗報告 王# 能源與環(huán)境學(xué)院 03012#一、題目要求二、各節(jié)點離散化代數(shù)方程取研究節(jié)點為t(i,j)，其上部節(jié)點溫度用T表示，下部節(jié)點溫度用B表示，左側(cè)節(jié)點溫度用L表示，右側(cè)節(jié)點溫度用R表示。該題目各節(jié)點離散化代數(shù)方程可分為四個區(qū)域：區(qū)域一：t(i,j)=區(qū)域二：t(i,j)=ti-1,j+ti,j-1+ti+1,j+ti,j+14區(qū)域三：t(i,j)=區(qū)域四：t(i,j)=三、源程序Jacobi迭代計算代碼（C#）：for (int n = 0; n 6; n+) mg0m, n = newButton();mg0m, n.Text = mgm, n.Text.ToStr

2、ing (); for (int m = 1; m 4; m+) int n = 1;double t = Convert.ToDouble(mg0m - 1, n.Text.ToString();double b = Convert.ToDouble(mg0m + 1, n.Text.ToString();double l = Convert.ToDouble(mg0m, n - 1.Text.ToString();double r = Convert.ToDouble(mg0m, n + 1.Text.ToString();double center = (200 + t + 2*r +

3、b) / 24;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int m = 1; m 4; m+) for (int n = 2; n 5; n+) double t = Convert.ToDouble(mg0m - 1,n.Text.ToString();double b = Convert.ToDouble(mg0m + 1, n.Text.ToString();double l = Convert.ToDouble(mg0m, n - 1.Text.ToString();double r

4、 = Convert.ToDouble(mg0m, n + 1.Text.ToString();double center = (l + t + r + b) / 4;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int m = 4; m 5; m+) int n = 1;double t = Convert.ToDouble(mg0m - 1, n.Text.ToString();double l = Convert.ToDouble(mg0m, n - 1.Text.ToString();do

5、uble r = Convert.ToDouble(mg0m, n + 1.Text.ToString();double center = (100 + t + r) / 12;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int n = 2; n 5; n+) int m = 4;double t = Convert.ToDouble(mg0m - 1, n.Text.ToString();double l = Convert.ToDouble(mg0m, n - 1.Text.ToString

6、();double r = Convert.ToDouble(mg0m, n + 1.Text.ToString();double center = (2*t + r + l) / 4;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; j = Convert.ToDouble(mg1, 1.Text.ToString();for (int m = 0; m 6; m+) for (int n = 0; n 6; n+) mg0m, n = newButton();mg0m, n.Text = mgm, n.Te

7、xt.ToString(); 高斯（Gauss）-賽德爾（Seidel）迭代計算代碼（C#）：for (int m = 1; m 4; m+) int n = 1;double t = Convert.ToDouble(mgm - 1, n.Text.ToString();double b = Convert.ToDouble(mgm + 1, n.Text.ToString();double l = Convert.ToDouble(mgm, n - 1.Text.ToString();double r = Convert.ToDouble(mgm, n + 1.Text.ToString(

8、);double center = (200 + t + 2*r + b) / 24;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int m = 1; m 4; m+) for (int n = 2; n 5; n+) double t = Convert.ToDouble(mgm - 1, n.Text.ToString();double b = Convert.ToDouble(mgm + 1, n.Text.ToString();double l = Convert.ToDouble(mg

9、m, n - 1.Text.ToString();double r = Convert.ToDouble(mgm, n + 1.Text.ToString();double center = (l + t + r + b) / 4;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int m = 4; m 5; m+) int n = 1;double t = Convert.ToDouble(mgm - 1, n.Text.ToString();double l = Convert.ToDouble

10、(mgm, n - 1.Text.ToString();double r = Convert.ToDouble(mgm, n + 1.Text.ToString();double center = (100 + t + r) / 12;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; for (int n = 2; n 5; n+) int m = 4;double t = Convert.ToDouble(mgm - 1, n.Text.ToString();double l = Convert.ToDoub

11、le(mgm, n - 1.Text.ToString();double r = Convert.ToDouble(mgm, n + 1.Text.ToString();double center = (2 * t + r + l) / 4;mgm, n.Text =center.ToString();mgm, n.BackColor = Color.LightBlue; 四、不同初值時的收斂快慢將從0100的不同初值代入，均已絕對誤差小于等于0.001為收斂條件。以迭代次數(shù)為縱坐標(biāo)，初值為橫坐標(biāo)作圖。1.采用Jacobi迭代計算時的最佳初值可看到當(dāng)初值=77時，最小迭代次數(shù)為7次。2.高斯（

12、Gauss）-賽德爾（Seidel）迭代計算時的最佳初值可看到當(dāng)初值=88時，最小迭代次數(shù)為7次。五、上下邊界的熱流量上邊界熱流量：=解得，=358.99W。下邊界熱流量：下邊界絕熱 =0。六、計算結(jié)果的等溫圖七、計算小結(jié)本次實驗的目的是研究二維穩(wěn)態(tài)導(dǎo)熱問題計算效率的影響因素，運用MATLAB，C#等計算工具，從迭代方法，初值設(shè)置等方面研究計算效率。得出以下結(jié)論：1.迭代計算方法G-S迭代計算方法優(yōu)于Jacobi迭代計算方法。因為G-S迭代方法在每次計算中都用到周圍節(jié)點的最新計算值，該值比初值更接近于穩(wěn)態(tài)值，所以一定程度上減少了計算步驟。2.初值設(shè)置通過將不同初值代入并比較運算次數(shù)，結(jié)合圖線我們可以找到迭代計算的最佳初值，在該初值下迭代計算最少的次數(shù)便可達到收斂條件。G-S迭代法與Jacobi的最佳初值不同。研究最佳初值的設(shè)置可以幫助我們在工程中提高實際傳熱問題的計算效率。3.穩(wěn)態(tài)溫度等值線由穩(wěn)態(tài)溫度等值線我們可以