Understanding the transport of diffusants into rubber plays an important role in forecasting the material's durability. In this regard, we study different models, conduct numerical analysis, and present simulation results that predict the evolution of the penetration front of diffusants.

We start with a moving-boundary approach to model this phenomenon, employing a numerical scheme to approximate the diffusant profile and the position of the moving boundary capturing the penetration front. Our numerical scheme utilizes the Galerkin finite element method for space discretization and the backward Euler method for time discretization. We analyze both semi-discrete and fully discrete approximations of the weak solution to the model equations, proving error estimates and demonstrating good agreement between numerical and theoretical convergence rates. Numerically approximated penetration front of the diffusant recovers well the experimental data.  

As an alternative approach to finite element approximation, we introduce a random walk algorithm that employs a finite number of particles to approximate both the diffusant profile and the location of the penetration front. The transport of diffusants is due to unbiased randomness, while the evolution of the penetration front is based on biased randomness. Simulation results obtained via the random walk approach are comparable with the one based on the finite element method.

In a multi-dimensional scenario, we consider a strongly coupled elliptic-parabolic two-scale system with nonlinear dispersion that describes particle transport in porous media. We construct two numerical schemes approximating the weak solution to the two-scale model equations. We present simulation results obtained with both schemes and compare them based on computational time and approximation errors in suitable norms. By introducing a precomputing strategy, the computational time for both schemes is significantly improved.

Understanding the transport of diffusants into rubber plays an important role in forecasting the material's durability. In this regard, we study different models, conduct numerical analysis, and present simulation results that predict the evolution of diffusant penetration fronts. We employ a moving-boundary approach to model this phenomenon, utilizing a numerical scheme based on the Galerkin finite element method combined with the backward time discretization, to approximate the diffusant profile and the position of the penetration front. Both semi-discrete and fully discrete approximations are analyzed, demonstrating good agreement between numerical and theoretical convergence rates. Numerically approximated diffusants penetration front recovers well the experimental data. We introduce a random walk algorithm as an alternative tool to the finite element method, showing comparable results to the finite element approximation. In a multi-dimensional scenario, we consider a strongly coupled elliptic-parabolic two-scale system with nonlinear dispersion, describing the particle transport in a porous medium. We present two numerical schemes and compare them based on computational time and approximation errors. A precomputing strategy significantly improves computational efficiency.