Vestnik КRAUNC. Fiz.-Mat. Nauki. 2025. vol. 50. no. 1. P. 111 – 133. ISSN 2079-6641

MATHEMATICAL MODELING
https://doi.org/10.26117/2079-6641-2025-50-1-111-133
Research Article
Full text in Russian
MSC 92.06

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Approach to Numerical Assessment of the Adequacy of a Three-Dimensional Cellular-Automaton Model of the Process of Matter Diffusion

S. K. Sarukhanian^{\ast}

Amur State University, 675027, Blagoveshchensk, Ignatyevskoye Shosse, 21, Russia

Abstract. This paper explores the use of a discrete-dynamic approach, employing three-dimensional cellular automata, to model evolutionary diffusion. The main focus is on verifying the accuracy of modeling classical diffusion using different geometric lattices. We present a numerical technique for assessing the suitability of a cellular automaton algorithm for a test problem: modeling substance diffusion using various threedimensional lattices. Our approach compares the spatiotemporal solution from the finite element method with a discrete cellular automaton solution, identifying the optimal cell geometry that minimizes numerical error. The cellular automaton model is implemented with C# using the Unity platform. Computational experiments investigate the efficiency of the algorithm with different lattices. Error calculations and visualizations indicate that truncated octahedral cellular automata provide the lowest error, making them suitable for discrete-dynamic diffusion modeling. These findings can aid in optimizing cellular automaton model algorithms.

Key words: cellular automata, diffusion, verification, geometrical grid, truncated octahedron.

Received: 12.02.2025; Revised: 18.02.2025; Accepted: 25.02.2025; First online: 22.03.2025

For citation. Sarukhanian S. K. Approach to numerical assessment of the adequacy of a three-dimensional cellularautomaton model of the process of matter diffusion. Vestnik KRAUNC. Fiz.-mat. nauki. 2025, 50: 1, 111-133. EDN: BHWDOA. https://doi.org/10.26117/2079-6641-2025-50-1-111-133.

Funding. The study was conducted without the support of foundations.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. The author participated in the writing of the article and is fully responsible for the submission of the final version of the article for publication.

^{\ast}Correspondence: E-mail: saruhanyans@gmail.com

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Sarukhanian S. K., 2025

© Institute of Cosmophysical Research and Radio Wave Propagation, 2025 (original layout, design, compilation)

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Information about the author

Sarukhanian Samvel – PhD student, assistant, Mathematical Analysis and Modeling Department, Amur State University, Blagoveshchensk, Russia, ORCID 0000-0002-4537-6453.

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