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A parallel algorithm for two-phase flow in heterogeneous porous media using an adaptive upscaling technique

Abstract We present a parallel algorithm for simulating two-phase flow through heterogeneous porous media in which the global information is resolved on a coarsened grid using a previous developed adaptive scale-up technique, [Aarnes and Espedal, Contemporary Math.]. The coarse scale solution is used to generate boundary conditions at the coarse grid block interfaces to recover the pressure on a nested subgrid of the coarse mesh. We then update the saturation for advective forces and use the advective solution as boundary conditions for a domain splitting of the residual diffusion problem used to modify the saturation profile for capillary forces. We demonstrate the robustness of our numerical method by comparing the simulated flow with a reference solution obtained with a full fine mesh simulation.