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

doi:10.1088/1674-1056/19/9/090201

中国物理B ›› 2010, Vol. 19 ›› Issue (9): 90201-090201.doi: 10.1088/1674-1056/19/9/090201

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

葛红霞¹, 程荣军²

(1)Faculty of Science, Ningbo University, Ningbo 315211, China; (2)Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

收稿日期:2009-11-02 修回日期:2010-01-16 出版日期:2010-09-15 发布日期:2010-09-15
基金资助:
Project supported by the Natural Science Foundation of Ningbo, China (Grant Nos. 2009A610014 and 2009A610154) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6090131).

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

Cheng Rong-Jun(程荣军)^a)† and Ge Hong-Xia(葛红霞)^b)

^a Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China; ^b Faculty of Science, Ningbo University, Ningbo 315211, China

Received:2009-11-02 Revised:2010-01-16 Online:2010-09-15 Published:2010-09-15
Supported by:
Project supported by the Natural Science Foundation of Ningbo, China (Grant Nos. 2009A610014 and 2009A610154) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6090131).

摘要/Abstract

摘要： 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.

Abstract: 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.

Key words: reproducing kernel particle method, meshless method, steady-state heat conduction problem

中图分类号:

0200

程荣军, 葛红霞. Meshless analysis of three-dimensional steady-state heat conduction problems[J]. 中国物理B, 2010, 19(9): 90201-090201.

Cheng Rong-Jun(程荣军) and Ge Hong-Xia(葛红霞). Meshless analysis of three-dimensional steady-state heat conduction problems[J]. Chin. Phys. B, 2010, 19(9): 90201-090201.

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

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

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