Abstract
The methodology of cellular automata occupies one of the key positions in the discrete dynamic simulations. The adequacy of the results of solving applied problems is largely determined by the choice of the type of geometric lattice of the cellular automaton. The article presents a formalization and numerical verification of the concept of verification of the operation of a cellular automata model of the classical diffusion process for a set of basic two-dimensional geometric lattices. The approach is based on a direct comparison of the space-time solution of the diffusion equation obtained by the finite element method with the solution of a discrete analogue of this equation based on the operation of a cellular automata algorithm. The software implementation of the cell-automation was performed with the C+ using the Unity platform while the finite element solution of the evolutionary problem of mathematical physics was carried out using the Matlab tools. Cellular automaton lattices were constructed using various cell geometric primitives traditionally used in diffusion modeling applications. Obtained findings indicate that the hexagonal cellular automaton demonstrates the minimum error in the numerical implementation.
Published Version
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