@Article{CiCP-24-204,
author = {Zhiqiang Yang, Yi Sun, Junzhi Cui and Xiao Li},
title = {A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {1},
pages = {204--233},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0103},
url = {http://global-sci.org/intro/article_detail/cicp/10934.html}
}