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.
It is an important method that the exact solutions of the heat conduction equations test the correctness of the numerical solutions. Meanwhile, the same important is to use the numerical solutions analyzing the exact solutions for perfect results. The heat conduction equation was solved using based cell finite volume method and the secondary order upwind scheme in structured mesh. Three examples are given showing up the deficiency of the exact solution of the classical heat conduction equation in the paper. And, the internal relation and the complementarities between the exact and the numerical solutions are discussed.
出处
《南京师范大学学报（工程技术版）》
CAS
2007年第3期40-43,共4页
Journal of Nanjing Normal University(Engineering and Technology Edition)
关键词
数值解
精确解
热传导方程
numerical solutions, exact solutions, heat conduction equation
