  This paper proposes a fully implicit numerical scheme for immiscible
incompressible two-phase flow in porous media taking into account gravity,
capillary effects, and heterogeneity. The objective is to develop a fully
implicit stable discontinuous Galerkin (DG) solver for this system that is
accurate, bound-preserving, and locally mass conservative. To achieve this, we
augment our DG formulation with post-processing flux and slope limiters. The
proposed framework is applied to several benchmark problems and the discrete
solutions are shown to be accurate, to satisfy the maximum principle and local
mass conservation.
