  In this work we consider a new efficient IMplicit Pressure Explicit
Saturation (IMPES) scheme for the simulation of incompressible and immiscible
two-phase flow in heterogeneous porous media with capillary pressure. Compared
with the conventional IMPES schemes, the new IMPES scheme is inherently
physics-preserving, namely, the new algorithm is locally mass conservative for
both phases and it also enjoys another appealing feature that the total
velocity is continuous in the normal direction. Moreover, the new scheme is
unbiased with regard to the two phases and the saturations of both phases are
bounds-preserving if the time step size is smaller than a certain value. The
key ideas in the new scheme include that the Darcy flows for both phases are
rewritten in the formulation based on the total velocity and an auxiliary
velocity referring to as the capillary potential gradient, and the total
discretized conservation equation is obtained by the summation of the
discretized conservation equation for each phase. The upwind strategy is
applied to update the saturations explicitly, and the upwind mixed finite
element methods are used to solve the pressure-velocity systems which can be
decoupled. We also present some interesting examples to demonstrate the
efficiency and robustness of the new algorithm.
