Modeling the migration of pollutants using three-dimensional cellular automata

Abstract

The paper proposes a modification of the CA-model of diffusion with the vicinity of Margolus. Its spatial implementation and the addition of factors affecting the propagation of matter (wind and gravity) brings the model closer to the simulated process. 

The automata simulating diffusion operates in a two-stroke synchronous mode. The model also introduces the possibility of bypassing the obstacles (uneven terrain, elements of construction, etc.). To simulate the convection process, a third cycle was introduced into the CA operation algorithm, which is responsible for the movement of particles under the influence of the wind, taking into account their possible collision. CA-diffusion in space with various kinds of obstacles was implemented. When modeling the interaction between a substance and an obstacle, each block in the basic substitution is associated with a binary type parameter, as a result of which all blocks are subdivided into two types: internal and boundary. As a result, the introduced parameter determines the necessity to rotate the block under consideration when performing basic substitution. In this case, the boundary of the modeling area can be specified in the form of planes (plates) and parallelepipeds. Obstacles are specified by a separate boolean three-dimensional array. The use of such obstacles, simulating walls and buildings, allows us to simulate the diffusion of contaminants, for example, in urban environments. With a given probability, particles can settle on vertical and horizontal surfaces.

An additional parameter was also introduced into the CA, which makes it possible to simulate the movement of a pollutant under the influence of gravity. To take into account the degradation of the impurity, one more phase was added to the cellular automata model, at which each cell with a particle can turn into a cell of the environment with a certain given probability.

For the convenience of interpretation and analysis of the proposed model results, the possibility of transition from Boolean values obtained with the help of the CA to continuous functions describing the field of impurity concentration by means of averaging over a given radius is provided.