In this paper, we are interested in modeling single-phase flow in a porous medium with known faults seen as interfaces. We mainly focus on how to handle non-matching grids problems arising from rock displacement along the fault. We describe a model that can be extended to multi-phase flow where faults are treated as interfaces. The model is validated in an academic framework and is then extended to 3D non K-orthogonal grids, and a realistic case is presented.

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