We present a two-scale numerical subgrid technique for simulating waterflooding. Local subgrid computations are combined with a coarse-grid computation to provide a fine-scale resolution of the solution. We use porosity, relative and absolute permeabilities, the location of wells, and capillary pressure curves defined on the fine scale. No explicit macroscopic coefficients nor pseudofunctions result. The method is several times faster than solving the fine-scale problem directly, generally more robust, and yet achieves good results as it requires no ad hoc assumptions at the coarse scale and retains all the physics of the original multiphase flow equations.

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