About cellular-automatic models of convection-diffusion processes of substances

Abstract

The work is devoted to cellular-automaton modeling of the substance diffusion and convection. Used approaches allow us to represent a complex process by a relatively simple transition functions and can serve as a supplement to the traditional models used to study the impurity transfer. We constructed models of the single-component substance migration in terms of cellular automatons for plane and spatial cases, which can be used in solving the environmental problems. Two dimensional CA with Margolus neighbourhood (TM diffusion), extended in three-dimensional space, is used as the basis for cellular-automaton model of impurity propagation in atmosphere. The classical model of the TM diffusion is supplemented by the elements that implement pollution transference by the wind and the obstacle avoidance of scattering impurities. The wording of the rules of movement and collision ensures that the laws of conservation of mass and momentum are valid. We also created windows-based application that implements described CA-algorithms. Pulse and continual sources of impurity emission can be considered in the application, and it is possible to demonstrate results as the projection on one of the planes at the set distance from the source. In addition, we implemented the transition from Boolean values to the continuous distribution functions of the impurity concentration, which is done by averaging the values of the states of the cells using the user-defined proximity.