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 Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second-order two-scale method Ma, Qiang1,2; Li, Zhihui1,2; Yang, Zihao3; Cui, Junzhi4 2017-09-30 Source Publication MATHEMATICAL METHODS IN THE APPLIED SCIENCES ISSN 0170-4214 Volume 40Issue:14Pages:5109-5130 Abstract A novel second-order two-scale (SOTS) analysis method is developed for predicting the transient heat conduction performance of porous materials with periodic configurations in curvilinear coordinates. Under proper coordinate transformations, some non-periodic porous structures in Cartesian coordinates can be transformed into periodic structures in general curvilinear coordinates, which is our particular interest in this study. The SOTS asymptotic expansion formulas for computing the temperature field of transient heat conduction problem in curvilinear coordinates are constructed, some coordinate transformations are discussed, and the related SOTS formulas are given. The feature of this asymptoticmodel is that each of the cell functions defined in the periodic cell domain is associated with themacroscopic coordinates and the homogenized material coefficients varies continuously in the macroscopic domain behaving like the functional gradient material. Finally, the corresponding SOTS finite element algorithms are brought forward, and some numerical examples are given in detail. The numerical results demonstrate that the SOTSmethod proposed in this paper is valid to predict transient heat conduction performance of porous materials with periodicity in curvilinear coordinates. By proper coordinate transformations, the SOTS asymptotic analysis method can be extended to more general non-periodic porous structures in Cartesian coordinates. Copyright (C) 2017 John Wiley & Sons, Ltd. Keyword SOTS asymptotic analysis transient heat conduction porous materials curvilinear coordinates coordinate transformation DOI 10.1002/mma.4374 Language 英语 Funding Project National Key Basic Research and Development Program[2014CB744100] ; National Natural Science Foundation of China[11501449] ; National Natural Science Foundation of China[11325212] ; National Natural Science Foundation of China[91530319] ; China Postdoctoral Science Foundation[2014M562616] ; China Postdoctoral Science Foundation[2016T91019] ; State Key Laboratory of Science and Engineering Computing WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000409046200009 Publisher WILEY Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/26461 Collection 计算数学与科学工程计算研究所 Corresponding Author Li, Zhihui 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.Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China4.Chinese Acad Sci, LSEC, ICMSEC, Acad Math & Syst Sci, Beijing 100190, Peoples R China Recommended CitationGB/T 7714 Ma, Qiang,Li, Zhihui,Yang, Zihao,et al. Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second-order two-scale method[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES,2017,40(14):5109-5130. APA Ma, Qiang,Li, Zhihui,Yang, Zihao,&Cui, Junzhi.(2017).Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second-order two-scale method.MATHEMATICAL METHODS IN THE APPLIED SCIENCES,40(14),5109-5130. MLA Ma, Qiang,et al."Asymptotic computation for transient heat conduction performance of periodic porous materials in curvilinear coordinates by the second-order two-scale method".MATHEMATICAL METHODS IN THE APPLIED SCIENCES 40.14(2017):5109-5130.
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