Branching processes and neutron transport equations represent two interconnected yet distinct areas that lie at the interface of probability theory, statistical physics and applied mathematics.

In this paper, the numerical approximation of a nonlinear diffusion equation arising in contaminant transport is studied. The equation is characterized by advection, diffusion, and adsorption.

$\bullet$ Nonlinear partial differential equations and their qualitative analysis. $\bullet$ Interacting particle systems. $\bullet$ Limiting procedures. $\bullet$ A. Scheel, A. Stevens, and C.