  A typical two-phase model for subsurface flow couples the Darcy equation for
pressure and a transport equation for saturation in a nonlinear manner. In this
paper, we study a combined method consisting of continuous Galerkin finite
element methods (CGFEMs) followed by a post-processing technique for Darcy
equation and finite volume method (FVM) with upwind schemes for the saturation
transport equation, in which the coupled nonlinear problem is solved in the
framework of operator decomposition. The postprocessing technique is applied to
CGFEM solutions to obtain locally conservative fluxes which ensures accuracy
and robustness of the FVM solver for the saturation transport equation. We
applied both upwind scheme and upwind scheme with slope limiter for FVM on
triangular meshes in order to eliminate the non-physical oscillations. Various
numerical examples are presented to demonstrate the performance of the overall
methodology.
