Grid anisotropy reduction for simulation of growth processes with cellular automaton

Abstract

Growth processes simulated on a regular cellular automaton grid with simple capture rules are considerably influenced by the structure of the grid. Some of the growth directions are favored over others leading to highly anisotropic or, at least, orientation-dependent growth pattern. A new method is proposed for significant reduction of artificial grid anisotropy in 2D and 3D cellular automata with continuous state variable. The method employs additional diffusion process controlling the growth rate and allows for isotropic or anisotropic growth where the anisotropy is decoupled from the grid structure. Verification of the method is provided in the case of isotropic circular growth, isotropic growth of various shapes in uniform and spatially varying fields, and anisotropic growth with respect to orientation and symmetry of the pattern. Finally, the reduction of grid anisotropy is demonstrated in 2D simulation of dendritic grain growth in pure metal. The shape of the grain is shown to be virtually independent of the orientation. An example growth of a grain with six-fold symmetry is also included.