The lattice Monte Carlo method for solving phenomenological mass and thermal diffusion problems

In this overview, we introduce the recently developed Lattice Monte Carlo method for addressing and solving phenomenologically-based mass and thermal diffusion problems especially for composite and porous materials. With examples, we describe the application of this numerical method to calculate effective mass diffusivities and concentration profiles. Next, we describe the application of this method to the calculation of effective thermal conductivities/thermal diffusivities and temperature profiles.