This thesis proposes a hybrid numerical scheme for immiscible, two-phase flow in porous media, for two separate partial differential equation (PDE) formulations. Discontinuous Galerkin (DG) methods are a commonly used numerical scheme in such applications due to their local mass conservation and ability to handle discontinuous coefficients. Another popular choice are fi nite volume (FV) methods, which are computationally cheaper than their DG counterparts but are only first order accurate and struggle when discontinuous coefficients are introduced. The proposed hybrid numerical scheme uses the DG method in areas of the domain where accuracy is important or around regions where coefficients are discontinuous, and the FV method in all other areas. Preliminary numerical results show that such a hybrid method produces similar results to the standard DG and FV methods in cases of homogeneous and heterogeneous fluid flow, at a fraction of the computational cost. Applications of this work include simulating the quarter- five spot validation test and the channel-flow problem.