Reactive Random Walk Particle Tracking and Its Equivalence With the Advection-Diffusion-Reaction Equation

We present a reactive random walk particle-tracking approach to describe bimolecular chemical reactions and show its equivalence with the advection-diffusion-reaction equation. The method is able to efficiently simulate reactions in d-dimensional systems with homogeneous and spatially variable advection. Reactions among particles are determined by the reaction probability that is given in terms of the reaction rate coefficient, the total number of particles, and an interaction radius that describes the well-mixed support volume at which all particles have the same probability to interact. The method is meshless and free of numerical dispersion. The method is validated for the bimolecular irreversible chemical reaction A+B -> C in scenarios characterized by slow and fast chemical kinetics under diffusion and heterogeneous advection and diffusion.