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

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

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.

Keywords: reproducing kernel particle method meshless method steady-state heat conduction problem

Received: 02 November 2009
Revised: 16 January 2010
Accepted manuscript online:

PACS:	0200
	0260
	4410

Fund: 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).

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

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