For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front, giving a direct estimate on the service life of the material. In this paper, we propose a random walk algorithm able to lead to good numerical approximations of both the concentration profile and the location of the sharp front. Essentially, the proposed scheme decouples the target evolution system in two steps: (i) the ordinary differential equation corresponding to the evaluation of the speed of the moving boundary is solved via an explicit Euler method, and (ii) the associated diffusion problem is solved by a random walk method. To verify the correctness of our random walk algorithm we compare the resulting approximations to results based on a finite element approach with a controlled convergence rate. Our numerical experiments recover well penetration depth measurements of an experimental setup targeting dense rubbers.

翻译：针对橡胶技术中出现的特定材料科学场景，具有动力学边界条件的一维移动边界问题能够揭示扩散剂渗透前沿的长时间行为，从而直接估算材料的使用寿命。本文提出了一种随机游走算法，可对浓度分布与尖锐前沿位置均给出良好的数值近似。该方案本质上通过两步解耦目标演化系统：(i) 通过显式欧拉方法求解对应移动边界速度评估的常微分方程，(ii) 通过随机游走方法求解关联的扩散问题。为验证随机游走算法的正确性，我们将所得近似结果与基于有限元方法且具有可控收敛率的计算结果进行对比。实验数值结果与针对致密橡胶实验装置所测量的渗透深度数据吻合良好。