A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures (Communications in Computational Physics, 2018)
This paper develops a second-order multiscale asymptotic analysis and numericalalgorithms for predicting heat transfer performance of porous materials withquasi-periodic structures. In these porous materials, they have periodic configurationsand associated coefficients are dependent on the macro-location. Also, radiation effectat microscale has an important influence on the macroscopic temperature fields,which is our particular interest in this study. The characteristic of the coupled multiscalemodel between macroscopic scale and microscopic scale owing to quasi-periodicstructures is given at first. Then, the second-order multiscale formulas for solving temperaturefields of the nonlinear problems are constructed, and associated explicit convergencerates are obtained on some regularity hypothesis. Finally, the correspondingfinite element algorithms based on multiscale methods are brought forward and somenumerical 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 thermalbehavior precisely, and the local and global oscillations of the temperature fields aredependent on the microscopic and macroscopic part of the coefficients respectively.