The simulation of realistic multiphase flow problems in porous media requires efficient solution methods and means for handling the complicated structure of the media and heterogeneities. We present an approach for upscaling fine grid information such as absolute permeability to coarse scales in an approximation of flow and transport in heterogeneous porous media. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. A mixed finite element method s combined to a finite volume scheme on unstructured grids for the approximation of the solution of incompressible flow in heterogeneous porous media. We describe the methodology for a coupled system which includes an elliptic pressure-velocity equation and a nonlinear degenerate diffusion-convection saturation equation arising in modeling of flow and transport of two immiscible, incompressible fluids in a porous medium.
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