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 Second-order asymptotic algorithm for heat conduction problems of periodic composite materials in curvilinear coordinates Ma, Qiang1,2; Cui, Junzhi3; Li, Zhihui1,2; Wang, Ziqiang4 2016-11-01 Source Publication JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS ISSN 0377-0427 Volume 306Pages:87-115 Abstract 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. Keyword Asymptotic analysis Heat conduction equation Quasi-periodic problem Coordinate transformation Finite element computation Error estimation DOI 10.1016/j.cam.2016.04.007 Language 英语 Funding Project 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 Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000378459500006 Publisher ELSEVIER SCIENCE BV Citation statistics Cited Times:9[WOS]   [WOS Record]     [Related Records in WOS] Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/23027 Collection 计算数学与科学工程计算研究所 Affiliation 1.China Aerodynam Res & Dev Ctr, Hyperveloc Aerodynam Inst, Mianyang 621000, Peoples R China2.BUAA, Natl Lab Computat Fluid Dynam, Beijing 100191, Peoples R China3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China4.Guizhou Minzu Univ, Coll Sci, Guiyang 550025, Peoples R China Recommended CitationGB/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.
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