Assessing cellular automata based models using partial differential equations

This paper presents a novel method of assessing cellular automata based models. The cellular model considered in this paper was designed to simulate sediment transport and topographic changes in rivers. It is demonstrated how prior knowledge about partial differential equations and their solution schemes can be used to provide deeper insight into the performance of two numerical implementations for this cellular model. Assessment of the implementations as solution schemes of the derived partial differential equations showed that the cellular model is robust for two numerical implementations, one of which is superior in terms of accuracy, stability and convergence. In comparison with more sophisticated solution methods, both implementations return accurate results. This study encourages the further application of cellular automata based models to complex problems.