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

Abstract

The spatial-three-dimensional problem of two-phase filtration of incompressible fluid was being considered within the Buckley-Leveret model in view of the gravity and without capillary forces in variables "pressure-water saturation". The advanced modified alternating triangular iterative method (MATM) that takes into account the availability of sources (sinks) in a relatively small number of nodes with delta-shaped (generalized) functions was considered for the discrete model that approximates the boundary-initial filtration problem. The numerical solution of computationally laborious task in the layer with significant heterogeneity of permeabilitywas performed, which are changed to four magnitude orders within the layer with a significant advantage in required iterations to achieve a given accuracy - in 10 and more times on grids with up to 3.2 million nodes. The parallel algorithm of numerical implementation of the developed sequential variant of advanced MATM was proposed in this paper which are based on the decomposition method in two spatial directions. It is performed on a multiprocessor system with shared memory - the computer system of the Southern Federal University in Taganrog that are contained 2048 cores with the peak performance 18.8 teraflops. The significant advantage of the proposed parallel algorithm was shown, compared to traditionally-used methods for numerical solution of these problems - the time simulation of the flooding process of layer system was reduced in tens of times