一类周期多孔固体材料热传导性能计算的孔洞填充方法

对于一类周期多孔固体材料,提出了一种孔洞填充方法,用一种极低热导率的材料填充孔洞,将原本几何复杂的单相多孔区域的热传导边值问题转化为几何简单的多相无孔区域上的问题,借助于延拓定理给出了填充前后材料的热传导问题解和均匀化热导率的误差估计,对结果的分析表明可以用填充后材料热传导问题的双尺度解近似原孔洞问题的解,在最后的数值算例中,讨论了具有对称和非对称单胞构造的周期多孔固体的热传导边值问题,分别比较了多孔固体材料填充前后的均匀化热导率、温度和温度梯度解,结果表明孔洞填充方法的确可行。

THE HOLE-FILLING METHOD OF HEAT-CONDUCTION PERFORMANCES FOR A KIND OF PERIODIC PERFORATED MATERIALS

In this paper, a hole-filling method for a kind of periodic perforated materials is developed by which all holes are filled by an almost degenerated phase and heat-conduction problem for a single-phase perforated domain with complex geometry are converted into a multi-phase problem in a non-perforated domain with simple geometry. And then by the classical extension theory the error estimate for solutions of heat-conduction problems and homogenized heat conductivities are given, and the result indicates that the two-scale solu- tion for heat-conduction problem of the multi-phase domain can be used to approximate the solution of original problem in the perforated domain. Finally, in the numerical examples the heat-conduction problems for periodic perforated domains consisting of cells with symmetric and non-symetric construction are investigated. The homogenized heat conductivities, temperature and temperature gradient between heat-condution problems for perforated domain and multi-phase problems are compared, which shows a good agreement and verifies the feasiblility of the hole-filling method.