Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates

doi:10.1016/j.cam.2016.04.007

	Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates
	Ma, Qiang 1,2; Cui, Junzhi3 ; Li, Zhihui 1,2; Wang, Ziqiang 4
	2016-11-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	306 页码:87-115
摘要	A new second-order two-scale (SOTS) asymptotic analysis method is presented for the heat conduction problems concerning composite materials with periodic configuration under the coordinate transformation. The heat conduction problems are solved on the transformed regular domain with quasi-periodic structure in the general curvilinear coordinate system. By the asymptotic expansion, the cell problems, effective material coefficients and homogenized heat conduction problems are obtained successively. The main characteristic of the approximate model is that each cell problem defined on the microscopic cell domain is associated with the macroscopic coordinate. The error estimation of the asymptotic analysis method is established on some regularity hypothesis. Some common coordinate transformations are discussed and the reduced SOTS solutions are presented. Especially by considering the general one-dimensional problem, the explicit expressions of the SOTS solutions are derived and stronger error estimation is presented. Finally, the corresponding finite element algorithms are presented and numerical results are analyzed. The numerical errors presented agree well with the theoretical prediction, which demonstrate the effectiveness of the second-order asymptotic analysis method. By the coordinate transformation, the asymptotic analysis method can be extended to more general domain with periodic microscopic structures. (C) 2016 Published by Elsevier B.V.
关键词	Asymptotic analysis Heat conduction equation Quasi-periodic problem Coordinate transformation Finite element computation Error estimation
DOI	10.1016/j.cam.2016.04.007
语种	英语
资助项目	National Key Basic Research and Development Program[2014CB744100] ; National Natural Science Foundation of China[11325212] ; National Natural Science Foundation of China[11501140] ; National Natural Science Foundation of China[11426074] ; National Natural Science Foundation of China[91530319] ; China Post-doctoral Science Foundation[2014M562616]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000378459500006
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23027
专题	计算数学与科学工程计算研究所
通讯作者	Li, Zhihui
作者单位	1.China Aerodynam Res & Dev Ctr, Hyperveloc Aerodynam Inst, Mianyang 621000, Peoples R China 2.BUAA, Natl Lab Computat Fluid Dynam, Beijing 100191, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 4.Guizhou Minzu Univ, Coll Sci, Guiyang 550025, Peoples R China
推荐引用方式 GB/T 7714	Ma, Qiang,Cui, Junzhi,Li, Zhihui,et al. Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2016,306:87-115.
APA	Ma, Qiang,Cui, Junzhi,Li, Zhihui,&Wang, Ziqiang.(2016).Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,306,87-115.
MLA	Ma, Qiang,et al."Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 306(2016):87-115.