A Discrete Stochastic Model of Water Permeation through a Porous Substance: Parallel Implementation Peculiarities

In this paper, some peculiarities of parallel implementation of a discrete stochastic model simulating water permeation through a porous substance (soil) with complexmorphology are studied. The model simulates fluid flow along pore curves and filling wets and cavities. The discrete stochastic model of the process, which was proposed earlier, is a stochastic cellular automaton (SCA) whose functioning is represented by a set of elementary local operators acting in the cellular space and imitating displacements (by diffusion, convection, adsorption) and transformations (by reactions, phase transitions) of abstract or real particles. The microlevel representation of the process requires a cellular space of huge size. Hence, the computations have to be implemented on supercomputers. The main problem is that obtaining an acceptable parallelization efficiency is possible only by introducing some determinism into the computation algorithm, that is, by decreasing the model stochasticity. Although stochastic models have been intensively investigated, parallel implementation methods for them have been poorly studied. This gap is partially filled by the results of computational experiments presented in this paper. These allow assessing the advantages and shortcomings of various methods of implementation on a multicore cluster of the discrete stochastic model of water permeation through a porous medium.