Numerical implementation of the asymptotic theory for classical diffusion in heterogeneous media

Based on the asymptotic theory of impurity transport developed by one of the authors (P.S.K.), numerical calculations of the concentration for classical diffusion in heterogeneous media in one and two dimensions are performed. In parallel, for the same media, a direct numerical solution of the diffusion equation was carried out. The results of the two calculations are highly consistent with each other at asymptotically far distances from the impurity source. The computation time according to the asymptotic theory turned out to be two orders of magnitude less than the time required for direct calculations. Graphic abstract