On the iota-delta function: a link between cellular automata and partial differential equations for modeling advection–dispersion from a constant source

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• 作者：Luan Carlos de S. M. Ozelim ; André Luís B. Cavalcante…
• 关键词：Cellular automata ; Advection–dispersion iota delta function ; Advection ; Diffusion
• 刊名：The Journal of Supercomputing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：73
• 期：2
• 页码：700-712
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Programming Languages, Compilers, Interpreters; Processor Architectures; Computer Science, general;
• 出版者：Springer US
• ISSN：1573-0484
• 卷排序：73

文摘

Describing complex phenomena by means of cellular automata (CAs) has shown to be a very effective approach in pure and applied sciences. Most of the applications, however, rely on multidimensional CAs. For example, lattice gas CAs and lattice Boltzmann methods are widely used to simulate fluid flow and both share features with two-dimensional CAs. One-dimensional CAs, on the other hand, seem to have been neglected for modeling physical phenomena. In the present paper, we demonstrate that some one-dimensional CAs are equivalent to a stable linear finite difference scheme used to solve advection–diffusion partial differential equations (PDEs) by relying on the so-called iota-delta representation. Consequently, this work shows an important link between continuous and discrete models in general, and PDEs and CAs more in particular.