Volume 24, Issue 1
A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

Zhiqiang Yang, Yi Sun, Junzhi Cui & Xiao Li

Commun. Comput. Phys., 24 (2018), pp. 204-233.

Published online: 2018-03

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  • 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.

  • Keywords

Multiscale asymptotic analysis, radiation boundary condition, quasi-periodic structures, nonlinear heat transfer problems.

  • AMS Subject Headings

35B27, 34E13, 74Q05, 83C30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-204, author = {}, 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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0103}, url = {http://global-sci.org/intro/article_detail/cicp/10934.html} }
TY - JOUR T1 - A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures JO - Communications in Computational Physics VL - 1 SP - 204 EP - 233 PY - 2018 DA - 2018/03 SN - 24 DO - http://doi.org/10.4208/cicp.OA-2017-0103 UR - https://global-sci.org/intro/article_detail/cicp/10934.html KW - Multiscale asymptotic analysis, radiation boundary condition, quasi-periodic structures, nonlinear heat transfer problems. AB -

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.

Zhiqiang Yang, Yi Sun, Junzhi Cui & Xiao Li. (2020). A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures. Communications in Computational Physics. 24 (1). 204-233. doi:10.4208/cicp.OA-2017-0103
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