Geodesic
Approach to numerical assessment of the adequacy of a three-dimensional cellular-automaton model of the process of matter diffusion
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 50 (2025) no. 1, pp. 111-133

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: cellular automata, verification, geometrical grid, truncated octahedron.
Mots-clés : diffusion 
@article{VKAM_2025_50_1_a6,
     author = {S. K. Sarukhanian},
     title = {Approach to numerical assessment of the adequacy of a three-dimensional cellular-automaton model of the process of matter diffusion},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {111--133},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2025_50_1_a6/}
}
TY  - JOUR
AU  - S. K. Sarukhanian
TI  - Approach to numerical assessment of the adequacy of a three-dimensional cellular-automaton model of the process of matter diffusion
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2025
SP  - 111
EP  - 133
VL  - 50
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VKAM_2025_50_1_a6/
LA  - ru
ID  - VKAM_2025_50_1_a6
ER  - 
%0 Journal Article
%A S. K. Sarukhanian
%T Approach to numerical assessment of the adequacy of a three-dimensional cellular-automaton model of the process of matter diffusion
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2025
%P 111-133
%V 50
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VKAM_2025_50_1_a6/
%G ru
%F VKAM_2025_50_1_a6
S. K. Sarukhanian. Approach to numerical assessment of the adequacy of a three-dimensional cellular-automaton model of the process of matter diffusion. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 50 (2025) no. 1, pp. 111-133. http://geodesic.mathdoc.fr/item/VKAM_2025_50_1_a6/