中文摘要：

放射性气体的屏蔽是辐射防护领域的一个热点,而研究放射性气体在不同介质中的扩散行为是这项研究工作的关键。放射性气体在介质中扩散行为的数学解析计算过程较为复杂。本文首先阐述了放射性气体在介质中的扩散模型,然后将低浓度侧边界外推,再先后讨论了显式与隐式有限差分法的计算方法,最后通过数值计算实验和模拟应用试验考察,讨论了它们的误差与在现实应用的可行性与精度。在进一步的研究之后,可以应用数值法代替传统的解析法模拟计算相关的放射性气体在介质中扩散的扩散行为,从而提高计算效率。

英文摘要：

Radioactive gas diffusion behavior in the medium of mathematics analytic calculation process is complicated. Firstly, the diffusion model of the radioactive gas within the medium is expounded. Secondly,with the extrapolated boundary in the low - concentration side, the solution of explicit finite difference and implicit finite difference are discussed in the paper. Finally, their error, feasibility and precision in the practical application are investigated by numerical numeration and simulation experiment. After further study, the numerical method can be used to replace of the traditional analysis method to calculate the model of the radioactive gas diffusing within the medium. Thus the computational efficiency is improved in practice.