Parallel implementation of three-dimensional model of two-phase fluid filtration based on improved alternating triangular method

In this paper, we consider the Buckley-Leverett model for space-dimensional problems of two-phase filtration of incompressible fluids based on gravity and without capillary forces. An advanced modified alternating triangular iterative method (MATM) that takes into account the availability of sources (sinks) in a relatively small number of nodes characterised by generalised delta-shaped functions is applied for a discrete model that approximates the boundary-initial task of filtration. We investigate the numerical solution of computationally time-consuming tasks in the reservoir with significant heterogeneity of permeability, which changes by four orders of magnitude within the reservoir and has a significant advantage to achieve a given accuracy within the number of iterations. In order to develop a coherent version of the advanced MATM, a parallel algorithm of its numerical implementation, based on decomposition in two spatial directions, is implemented on a multi-processor system with shared memory containing 2048 cores and a peak performance of 18.8 teraflops. Compared with a traditional implementation, a significant efficiency boost is demonstrated leading to a tenfold reduction of the the simulation process.