Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Volume 19, Issue 3, Pages 827-848Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2014.19.827
Keywords
Second-order two-scale computation; integrated heat transfer problem; homogenization; error estimation; periodic porous materials
Categories
Funding
- Special Funds for National Basic Research Program of China (973 Program) [2010CB832702]
- National Natural Science Foundation of China [90916027]
- State Key Laboratory of Science and Engineering Computing
- Center for High Performance Computing of Northwestern Polytechnical University
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In this paper, a kind of second-order two-scale (SOTS) computation is developed for integrated heat transfer problem with conduction, convection and radiation in periodic porous materials, where the convection part is composed of long thin parallel pipes with periodic distribution, the conduction part occupied by solid materials and the radiation part is on the pipe's walls and the surfaces of cavities. First of all, by asymptotic expansion of the temperature field, the homogenization problem, first-order correctors and second-order correctors are obtained successively. Then, the error estimation of the second-order two-scale approximate solution is derived on some regularity hypothesis. Finally, the corresponding finite element algorithms are proposed and some numerical results are presented. The numerical tests indicate that the developed method can be successfully used for solving the integrated heat transfer problem, which can reduce the computational efforts greatly.
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