  We propose a novel density based numerical method for uncertainty propagation
under certain partial differential equation dynamics. The main idea is to
translate them into objects that we call cellular probabilistic automata and to
evolve the latter. The translation is achieved by state discretization as in
set oriented numerics and the use of the locality concept from cellular
automata theory. We develop the method at the example of initial value
uncertainties under deterministic dynamics and prove a consistency result. As
an application we discuss arsenate transportation and adsorption in drinking
water pipes and compare our results to Monte Carlo computations.
