Computer simulation of diffusion transport processes in multilayer nanofilms

The difficulties associated with studying diffusion in multilayer films require the progress of contemporar y modeling methods and software platforms to precisely represent phenomena, taking into account transitions between adjacent layers. In addition to the indispensable role of advanced modeling techniques and software in solving the problems of studying diffusion in multilayer films, it is extremely important to admit the key contribution of sophisticated computational approaches. In this paper, the authors attempt to merge intricate mathematical models with optimal software development methodologies to address the challenge of simulating diffusion transport processes in multilayer nanofilms computationally. Based on the experimental findings and employing the suggested model, identification was conducted utilizing the theory of state control for multicomponent systems. With the help of methods of optimal control of the state of multicomponent transport systems, the analytical solution of the model and the data of experimental observations, the distributions of diffusion coefficients for the considered components of nanofilms (samples of aluminum, molybdenum, silicon) were reproduced. Numerical simulation results were compared with experimental observations. The profiles obtained from the modeling closely match the corresponding experimental profiles, especially as the duration of multilayer formation converges to the final stages of completing the protective nanofilm multilayer formation. The maximum observed deviation does not exceed 2–3%, confirming the reliability of the mathematical model and demonstrating the practical value of the results provided. A software framework is developed for the automation of the specified calculations with the possibility of extension to other subject areas with similar tasks of identifying the key factors of the process and further numerical modeling of the time-space characteristics using the obtained results.