Most commercially available simulators use the trivial two-point flux approximation (TPFA) method for flux computation. However, the TPFA only gives consistent solutions when used for K-orthogonal grids. In general, multi-point flux approximation (MPFA) methods perform better under both heterogeneous and anisotropic conditions. The mimetic finite difference (MFD) method is designed to preserve properties on unstructured polyhedral grids, and its development for simulating full tensor permeabilities is also crucial step. This paper compares the performance, accuracy, and efficiency of these schemes for simulating complex synthetic and realistic hydrocarbon reservoirs.