Asynchronous cellular automata subsurface flow simulations in two- and three-dimensional heterogeneous soils
Cellular Automata (CA) are particularly suitable for physically-based modelling of complex hydrological processes due to their inherent aptitude for parallel computing. Nevertheless, other CA specific features like asynchronism could be exploited to enhance further the computational efficiency. This note introduces an innovative activation/deactivation rule enabling for the first time the practical application of asynchronous CA to subsurface flow problems. The asynchronism rule, consisting of a threshold depending on the spatial total hydraulic head difference between each automaton and its neighbourhood, was implemented in the new OpenCAL parallel software library using the Extended CA (XCA) paradigm. It was tested performing hundreds of wet front propagation simulations in a comprehensive probabilistic framework, considering several thresholds and addressing both two- and three-dimensional domains with heterogeneous hydraulic properties. Furthermore, realistic simulations of a drip-irrigated field entailing combined infiltration/exfiltration cycles were carried out. The application of the asynchronism rule generated considerable computational benefits for all the test cases, even adopting low threshold values, reducing the elapsed time by up to 80-85% while preserving numerical accuracy. In particular, the three-dimensional simulation of the drip-irrigated field demonstrated the practical relevance of the approach. The computational improvement produced by the combined effect of parallel computing and the proposed asynchronism strategy enables increased space-time resolution on wider study areas and further developments focusing on the simulation of computationally demanding relevant processes.