Asynchronous Extended Cellular Automata for subsurface flow modelling: applications in synthetic two and three-dimensional heterogeneous test cases

Abstract:

In the last fifty years, great efforts were made to develop physically-based models of the hydrological processes, aimed at better analysing and understanding many interconnected phenomena. Significant advances were possible thanks to the adoption of several numerical techniques. Nevertheless, the challenge of computational meshes with ever-higher resolution applied to increasingly larger domains, moving from single catchment to large watersheds/regional scales, has dramatically increased the computational burden. To tackle this issue, three main strategies have been proposed in the literature: (i) the adoption of massive parallel approaches; (ii) the application of efficient numerical solution methods; (iii) the limitation of computations only where/when necessary, avoiding redundant calculus. The modelling framework herein proposed, based on the Extended Cellular Automata (XCA) paradigm, integrates all together these three different strategies, since it merges the cellular automata direct compatibility with parallel programming to numerical techniques based on an asynchronous concept, which allows each cell of the domain to evolve only when needed, therefore reducing drastically the problem of redundant calculations while keeping low the calculation error.

This study evaluates the application of the asynchronous technique to an XCA-based subsurface flow model. The model is used both in two- and three-dimensional synthetic heterogeneous test cases (160 × 130 and 100 × 100 × 50 grid points, respectively), generated with a Simple Kriging technique, and characterized by different degrees of variability, fixing the variance to 0.5, 1.0 and 2.0. A statistical approach is used, applying the model to 100 test cases for each value of σ², for both two- and three-dimensional cases, simulating 10-days infiltration produced by constant rainfall.

All simulations are performed in an HPC infrastructure, using an Intel Xeon Gold 6128 and adopting a shared-memory parallel execution with 24 OpenMP threads. Results show that introducing low asynchronicity, a relevant improvement of the computational performance is achieved, reducing the elapsed time by 60-70%, at the cost of small and highly localized errors.