[1]黄庆宏,张 敏,许彬.从数值解浅析热传导方程的精确解[J].南京师范大学学报(工程技术版),2007,07(03):040-43.
　Huang Qinghong,Zhang Min,Xu Bin.Analyzing Exact Solutions of Heat Conduction Equations by Comparing With Numerical Solutions[J].Journal of Nanjing Normal University(Engineering and Technology),2007,07(03):040-43.
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从数值解浅析热传导方程的精确解
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南京师范大学学报（工程技术版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
07卷
期数:
2007年03期
页码:
040-43
栏目:
出版日期:
2007-09-30

文章信息/Info

Title:
Analyzing Exact Solutions of Heat Conduction Equations by Comparing With Numerical Solutions
作者:
黄庆宏1;  张 敏2;  许彬2
1. 南京师范大学动力工程学院, 江苏南京210042; 2. 南京理工大学动力工程学院, 江苏南京210094
Author(s):
Huang Qinghong1; Zhang Min2; Xu Bin2
1.School of Power Engineering,Nanjing Normal University,Nanjing 210042,China;2.College of Power Engineering,Nanjing University of Science and Technology,Nanjing 210094,China
关键词:
数值解;  精确解;  热传导方程
Keywords:
num erical so lutions;  exact so lutions;  heat conduction equation
分类号:
TK124
摘要:
用热传导方程的精确解检验数值求解过程的正确性是数值计算方法中一种重要的手段.反之,用数值解来分析精确解的完整性也是一种有意义的方法.用基元有限容积法和二阶迎风格式,在结构化网格中数值求解热传导方程,同时给出3个例子进行数值解和精确解的比较,以此来说明某些教科书中古典导热方程精确求解过程的不足,并且分析阐述两者之间的内在辨证关系和它们的互补性.
Abstract:
It is an important me thod tha t the exact so lutions of the heat conduction equations test the correctness o f the num er ica l so lutions. M eanwh ile, the sam e im po rtant is to use the nume rical so lutions ana ly zing the exact so lu tions for perfect resu lts. The hea t conduction equa tion w as so lved using based ce ll fin ite vo lum em ethod and the secondary order upw ind schem e in structured m esh. Three examp les are g iven show ing up the deficiency o f the exact solution o f the class ica l heat conduction equation in the paper. And, the inte rnal relation and the com plem entarities be tw een the exac t and the num erical so lutions are discussed

参考文献/References:

[ 1] 奥齐西克M N. 热传导[M ]. 俞昌铭, 译. 北京: 高等教育出版社, 1984: 3-4.
O zisikM N. H ea t Conduction[M ]. Yu Changm ing, T ransla ted. Be ijing: H igher Education Press, 1984: 3-4. ( in Chinese) [ 2] Kakac S, YenerY. H ea t Conduction[M ]. 3rd ed. London: Tay lor and Francis Press, 1993: 102-108.
[ 3] 南京工学院数学系. 数学物理方程和特殊函数[M ]. 北京: 高等教育出版社, 1982: 34-37.
M a them a tics Teaching and Research Group o f N an jing Eng ineer ing Co lleg e. Equations o fM athem atica l Physics and Spec ial Function[M ]. Be ijing: H igher Education Press, 1982: 34-37. ( in Ch inese)
[ 4] O zisikM N. Boundary Va lue Problem s o fH eat Conduc tion[M ]. Dover Phoen ix Ed itions. Dover Phoeo ix: Dover Press, 2002: 41-45.

相似文献/References:

[1]张钧波,黄庆宏,张敏.伽略金近似方法与数值方法的比较分析[J].南京师范大学学报(工程技术版),2010,10(03):052.
　Zhang Junbo,Huang Qinghong,Zhang Min.Comparative Analysis between Galerkin Approximating Method and Numerical Computation[J].Journal of Nanjing Normal University(Engineering and Technology),2010,10(03):052.

备注/Memo

备注/Memo:
作者简介: 黄庆宏( 1957-) , 副教授, 主要从事热能工程技术及计算机应用等方面的教学与研究. E-m ail: hu angq inghong@ n jnu. edu. cn
更新日期/Last Update: 2013-06-04