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

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...

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Published inChinese physics B Vol. 19; no. 9; pp. 36 - 41
Main Author 程荣军 葛红霞
Format Journal Article
LanguageEnglish
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
Online AccessGet full text
ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/19/9/090201

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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.
AbstractList 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.
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.
Author 程荣军 葛红霞
AuthorAffiliation Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China Faculty of Science, Ningbo University, Ningbo 315211, China
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reproducing kernel particle method, meshless method, steady-state heat conduction problem
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SubjectTerms 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
Title Meshless analysis of three-dimensional steady-state heat conduction problems
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