Solving Complex Thermal and Mass Transport Problems with the Lattice Monte Carlo Method

The Lattice Monte Carlo (LMC) method recently developed by the authors is an unusually powerful and flexible method in which a given phenomenological thermal or mass transport problem is mapped onto a fine-grained lattice which is then analyzed with discrete random walk methods. We provide an overview of the LMC method. For mass diffusion we highlight the addressing of diffusion with reversible reaction. For thermal transport we highlight a calculation of the effective thermal conductivity of sintered hollow sphere structures making use of CT scans of actual material as well as the determination of temperature profiles in phase-change composites.