Meshless analysis of three-dimensional steady-state heat conduction problems

• Published in: Chinese physics B Vol. 19; no. 9; pp. 36 - 41
• Main Author: 程荣军 葛红霞
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.09.2010
• Subjects: Boundary conditions; Conduction; Dirichlet problem; Finite element method; Heat conduction; Heat transfer; Mathematical analysis; Mathematical models; 偏微分方程; 工程问题; 拉普拉斯方程; 数值解; 本质边界条件; 稳态热传导问题; 网格分析
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/19/9/090201

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson＇s equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method （RKPM）. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.