A model based on cellular automata for the parallel simulation of 3D unsaturated flow

Cellular automata (CA) are discrete dynamic systems that have been used for modeling many physical systems. CA are often used as an alternative to model and solve large-scale systems where the use of partial differential equations involve complex and computationally expensive simulations. The purpose of this work is to investigate the use of CA based techniques for modeling and parallel simulation of water flux in unsaturated soils. Unsaturated flow processes are an important topic in several branches of hydrology, soil science and agricultural engineering dealing with soil-atmosphere interaction, subsurface flow and transport processes. In this paper a CA model for 3D unsaturated flow simulation is proposed using an extension of the original computational paradigm of cellular automata. This model, aimed at simulating large-scale systems, uses a macroscopic CA approach where local laws with a clear physical meaning govern interactions among automata and its correctness is proved by CAMELot system, which allows the specification, parallel simulation, visualization, steering and analysis of CA models in the same environment, using a friendly interface providing at the same time considerable flexibility. The model has been validated with reference multidimensional solutions taken from benchmarks in literature, showing a good agreement even in the cases where non-linearity is very marked. Furthermore, using some of these benchmarks we present a scalability analysis of the model and different quantization techniques aimed at reducing the number of messages exchanged, and then the execution time, when simulations are characterized by scarce mass interactions.