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Parallel embedded discrete fracture method for flows in fractured porous media

In this work, parallel method for solving single-phase flow problems in a fractured porous media is considered. Method is based on the representation of fractures by surfaces embedded into the computational mesh, and known as the embedded discrete fracture model. Porous medium and fractures are represented as two independent continua within the model framework. A distinctive feature of the considered approach is that fractures do not modify the computational grid, while an additional degree of freedom is introduced for each cell intersected by the fracture. Discretization of fluxes between fractures and porous medium continua uses the pre-calculated intersection characteristics of fracture surfaces with a three-dimensional computational grid. The discretization of fluxes inside a porous medium does not depend on flows between continua. This allows the model to be integrated into existing multiphase flow simulators in porous reservoirs, while accurately describing flow behaviour near fractures. Previously, the author proposed monotonic modifications of the model using nonlinear finite-volume schemes for the discretization of the fluxes inside the porous medium: a monotonic two-point scheme or a compact multi-point scheme with a discrete maximum principle. It was proved that the discrete solution of the obtained nonlinear problem preserves non-negativity or satisfies the discrete maximum principle, depending on the choice of the discretization scheme. This work is a continuation of previous studies. The previously proposed monotonic modification of the model was parallelized using the INMOST open-source software platform for parallel numerical modelling. We used such features of the INMOST as a balanced grid distribution among processors, scalable methods for solving sparse distributed systems of linear equations, and others. Parallel efficiency was demonstrated experimentally.