Application of cellular automata to diffusion equations compared with classical numerical methods / Adam Zaborski // W: Deterioration and failure of structural materials : chair of strength of materials ... więcej

Application of cellular automata to diffusion equations compared with classical numerical methods / Adam Zaborski // W: Deterioration and failure of structural materials : chair of strength of materials studies / ed. by Janusz German ; tł. Robin Gill ; Politechnika Krakowska im. Tadeusza Kościuszki. – Kraków : Wydaw. PK, 2014. – (Monografia / Politechnika Krakowska im. Tadeusza Kościuszki. Inżynieria Lądowa). – S. 137-154 : rys. – Bibliogr. 8 poz., Streszcz., Summ. – Tyt. streszcz.: Zastosowanie automatów komórkowych do równań dyfuzji w odniesieniu do klasycznej metody implicite naprzemiennych kierunków. – Seria gł.: Monografia / Politechnika Krakowska im. Tadeusza Kościuszki, ISSN 0860-097X ; 469

In this paper two methods for calculating diffusion equations are presented and compared. The methods are applied to a description of propagation of environmental action inside the material. The classical ... więcej

In this paper two methods for calculating diffusion equations are presented and compared. The methods are applied to a description of propagation of environmental action inside the material. The classical Alternating Directions Implicit method with the Crank-Nicholson scheme (the Peaceman-Rachford scheme) was generalized to the case of variant diffusion coefficients. Similar formulae for Cellular Automata with Neumann and Moore neighbourhoods were obtained. These formulae were generalized into the case of cross-effects for coupled flows. The tests and numerical examples show that the cellular automata method is an efficient method for calculating diffusional transport processes.