Random walk to describe diffusion phenomena in three-dimensional discontinuous media: Step-balance and fictitious-velocity corrections.

In this paper, we show that diffusion phenomena in three-dimensional discontinuous media can be described as a random walk by two simple interface-correction methods, namely step-balance and fictitious-velocity corrections, which are completely different in a physical picture but equivalent in that the continuity of the random walk at interfaces is considered. In both corrections, asymmetric interface permeability of a random walker, which comes from ensuring the continuity, causes apparent confinement of the walker in higher-diffusivity layers for benchmark tests on heat diffusion in two-phase multilayered systems. Effective thermal conductivities (walker diffusivities) computed from the trajectories are in excellent agreement with the series and parallel conduction formulas, indicating the equivalence of the two corrections and the importance of ensuring the continuity of a random walk at interfaces.