Author(s): Yu-Qing Lin, Qiu-Wen Chen, Arthur Mynett, Cheng Chen, Lei Tang, Gang Li
Linked Author(s): Yuqing Lin
Keywords: Unstructured cellular automata, partial differential equations, characteristic parameter, analogies
Abstract: Cellular Automata (CA) is a non-linear dynamical system which discrete in time and space. Cellular automata constitute many simple components, each of them starts from an initial state and all the cells update their states synchronously every discrete steps according to the simple local rule. Compared to partial differential equations (PDE), Cellular automata are rule-based methods with the advantages of homogeneity, local interactions, discrete states and parallelism, so that they are often considered as an alternative approach in modelling nonlinear systems with large degrees of freedom. Moreover, Unstructured cellular automaton (UCA) has been proposed based on the unstructured meshes with advantages which are missing in CA. UCA allows varying sizes of elements, permits accurate representation of boundaries and it avoids mapping results from unstructured grid into structured grid during cellular automata process. Compared with classical CA, UCA contains unequal cells, the object cell and its neighbors differ from each other. The aim of this article is to show the analogies between discrete solutions of PDEs and equivalent approaches derived from CA and UCA. Finite difference methods have been used to deduce transition rules for CA-modelling from PDE-based approaches. Specific types of partial differential equations (diffusion equation, wave equation) have been reviewed as a reference for evaluating the equivalent performance of CA simulations. Since UCA can have varying neighbourhood properties in contrast with classical CA, Finite Volume Method has been used to deduce transition rules for UCA-modelling and the influence of cell size in UCA has been analyzed in this paper. A characteristic parameter �min distance of UCA� has been put forward and tested by several numerical experiments on different types of meshes (rough meshes, locally refined meshes, globally refined meshes) in order to demonstrate the usefulness of this parameter
Year: 2017