A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures
Year: 2018
Communications in Computational Physics, Vol. 24 (2018), Iss. 1 : pp. 204–233
Abstract
This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures. In these porous materials, they have periodic configurations and associated coefficients are dependent on the macro-location. Also, radiation effect at microscale has an important influence on the macroscopic temperature fields, which is our particular interest in this study. The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first. Then, the second-order multiscale formulas for solving temperature fields of the nonlinear problems are constructed, and associated explicit convergence rates are obtained on some regularity hypothesis. Finally, the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail. Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy. They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely, and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0103
Communications in Computational Physics, Vol. 24 (2018), Iss. 1 : pp. 204–233
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Multiscale asymptotic analysis radiation boundary condition quasi-periodic structures nonlinear heat transfer problems.