MATLAB Implementation of a Singular Boundary Method for Transient Heat Conduction

LI Yudong; WANG Fajie; CHEN Wen

doi:10.21656/1000-0887.390225

Volume 40 Issue 3

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2019 > 40(3): 259-268

LI Yudong, WANG Fajie, CHEN Wen. MATLAB Implementation of a Singular Boundary Method for Transient Heat Conduction[J]. Applied Mathematics and Mechanics, 2019, 40(3): 259-268. doi: 10.21656/1000-0887.390225

Citation:

PDF( 2907 KB)

MATLAB Implementation of a Singular Boundary Method for Transient Heat Conduction

doi: 10.21656/1000-0887.390225

¹College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R.China;²National Engineering Research Center for Intelligent Electrical Vehicle Power System(Qingdao University), Qingdao, Shandong 266071, P.R.China;³School of Electromechanic Engineering, Qingdao University, Qingdao, Shandong 266071, P.R.China

Funds: The National Natural Science Foundation of China（11802151;11572111;11372097）

Received Date: 2018-08-27
Rev Recd Date: 2018-09-16
Publish Date: 2019-03-01

Abstract

Abstract

The singular boundary method (SBM) based on the timedependent fundamental solutions to dynamic problems is a meshless boundary collocation technique with the merits of easy implementation and mathematical simplicity. This method effectively avoids the singularity of source points through introduction of the origin intensity factor. The SBM was implemented to simulate the transient heat conduction problem via the MATLAB programming, and the MATLAB toolbox was created to provide a simple and efficient tool for the numerical analysis of transient heat conduction problems and actual operating problems. In numerical experiments, 2D and 3D problems were investigated in regular geometrical regions. The method was applied to the solution of the temperature field in the low temperature transient state. The results indicate that the MATLAB toolbox for the SBM with the inverse interpolation technique and the empirical formula is simple, accurate and efficient.
- singular boundary method,
- inverse interpolation technique,
- empirical formula,
- transient heat conduction,
- MATLAB

FullText(HTML)

References(14)

References

[1]	赵金军, 彭海峰, 原志超. 三维变系数热传导问题边界元分析中几乎奇异积分计算[J]. 计算力学学报, 2015,32(1): 7-13.(ZHAO Jinjun, PENG Haifeng, YUAN Zhichao. Evaluation of nearly singular integrals in boundary element analysis of 3D heat conduction problem with variable coefficients[J]. Chinese Journal of Computational Mechanics,2015,32(1): 7-13.(in Chinese))
[2]	高效伟, 曾文浩, 崔苗. 等参管单元及其在热传导问题边界元法中的应用[J]. 计算力学学报, 2016,33(3): 328-334.(GAO Xiaowei, ZENG Wenhao, CUI Miao. Isoparametric tube elements and their application in heat conduction BEM analysis[J]. Chinese Journal of Computational Mechanics,2016,33(3): 328-334.(in Chinese))
[3]	李庆华, 陈莘莘. 基于无网格自然邻接点Petrov-Galerkin法求解带源参数瞬态热传导问题[J]. 动力学与控制学报, 2014,12(2): 178-182.(LI Qinghua, CHEN Shenshen. Analysis of transient heat conduction problems with a source parameter based on meshless natural neighbour Petrov-Galerkin method[J]. Journal of Dynamics and Control,2014,12(2): 178-182.(in Chinese))
[4]	陈豪龙, 周焕林, 余波. 瞬态热传导问题的精细积分-双重互易边界元法[J]. 应用力学学报, 2017,34(5): 835-841.(CHEN Haolong, ZHOU Huanlin, YU Bo. Precise integration DRBEM for solving transient heat conduction problems[J]. Chinese Journal of Applied Mechanics,2017,34(5): 835-841.(in Chinese))
[5]	YANG K, GAO X W. Radial integration BEM for transient heat conduction problems[J]. Engineering Analysis With Boundary Elements, 2010,34(6): 557-563.
[6]	YU B, ZHOU H L, CHEN H L. Precise time-domain expanding dual reciprocity boundary element method for solving transient heat conduction problems[J]. International Journal of Heat and Mass Transfer,2015,91: 110-118.
[7]	陈文. 奇异边界法:一个新的、简单、无网格、边界配点数值方法[J]. 固体力学学报, 2009,30(6): 592-599.(CHEN Wen. Singular boundary method: a novel, simple, meshfree, boundary collocation numerical method[J]. Chinese Journal of Solid Mechanics,2009,30(6): 592-599.(in Chinese))
[8]	BREBBIA C A, TELLES J C F, WROBEL L C. Boundary Element Techniques: Theory and Applications in Engineering[M]. Springer Science & Business Media, 2012.
[9]	姚厚朴, 校金友, 文立华. 高阶边界元奇异积分的一种通用高效计算方法[J]. 计算力学学报, 2015,32(1): 1-6, 13.(YAO H, XIAO Jinyou, WEN Lihua. An efficient method for numerically evaluating singular integrals in high order boundary element method[J]. Chinese Journal of Computational Mechanics,2015,32(1): 1-6, 13.(in Chinese))
[10]	CUI M, XU B B, FENG W Z. A radial integration boundary element method for solving transient heat conduction problems with heat sources and variable thermal conductivity[J]. Numerical Heat Transfer Fundamentals,2018,73(1): 1-18.
[11]	QU W, CHEN W, ZHENG C. Diagonal form fast multipole singular boundary method applied to the solution of high-frequency acoustic radiation and scattering[J]. International Journal for Numerical Methods in Engineering,2017,111(9): 803-815.
[12]	GU Y, CHEN W, ZHANG C Z. Singular boundary method for solving plane strain elastostatic problems[J]. International Journal of Solids & Structure,2011,48(18): 2549-2556.
[13]	WANG F J, CHEN W. Singular boundary method for transient convection-diffusion problems with time-dependent fundamental solution[J]. International Journal of Heat and Mass Transfer,2017,114: 1126-1134.
[14]	WANG F J, CHEN W. Accurate empirical formulas for the evaluation of origin intensity factor in singular boundary method using time-dependent diffusion fundamental solution[J].International Journal of Heat and Mass Transfer,2016,103: 360-369.