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A Multilevel Multiscale Mimetic Method for Two-Phase Flows in Porous Media

Konstantin Lipnikov
David Moulton
Daniil Svyatskiy

Flow simulations in porous media involve a wide range of strongly coupled scales. The length scale of short and narrow channels is on the order of millimeters, while the size of a simulation domain may be several kilometers (the richest oil reservoir in Saudi Arabia, Ghawar, is 280x30 km). The permeability of rock formations is highly heterogeneous and may span several orders of magnitude, from nearly impermeable barriers to high-permeable flow channels. For such complex systems fully resolved simulations become computationally intractable. To address this problem we developed the new Multilevel Multiscale Mimetic method. The method can handle full permeability tensors and general coarsening strategies which may generate polygonal meshes on the coarse grid. The numerical results demonstrate that even with a large coarsening factor the multiscale solution is in a good agreement with the solution obtained by the straightforward fine-scale discretization.