An adaptive cellular automata approach with the use of radial basis functions for the simulation of elastic wave propagation

Abstract

A physics-based adaptive approach constructed on cellular automata is proposed for the analysis of two-dimensional (2D) elastodynamic initial boundary value problems. Although any 2D cell may be used in this approach, because of easy construction of arbitrary geometry, triangular plane cells are used as primary reference. The analysis of the problem includes two principal parts. In the first part, after discretization of the problem domain, a physics-based configuration considering the conservation of mass and the balance of momentum is developed as reference for cellular automata used in the next step. In the second part, radial basis functions (RBFs) are employed for an adaptive solution. For this purpose, after analysing the problem based on an arbitrary coarse mesh in the first step as reference, the problem domain may be discretized by iterative schemes, where RBFs indicate the lack and redundancy of computational points of the domain, from which some computational points may be added or eliminated for the next analysis. This process may be repeated to get the most appropriate mesh with the most accurate results. The principle of causality is taken into account in the proposed method, meaning that the unexcited parts of the domain are not in the solution domain. Similarly, those parts of the domain where the wave has already passed from would be deducted from the solution domain. The results of the proposed approach are compared with numerical and analytical results available in the literature. The comparison illustrates very good agreements between the results of the proposed approach and the results of those already reported in the literature.