  We develop a numerical scheme for a two-phase immiscible flow in
heterogeneous porous media using a structured grid finite element method, which
have been successfully used for the computation of various physical
applications involving elliptic equations \cite{li2003new, li2004immersed,
chang2011discontinuous, chou2010optimal, kwak2010analysis}. The proposed method
is based on the implicit pressure-explicit saturation procedure. To solve the
pressure equation, we use an IFEM based on the Rannacher-Turek
\cite{rannacher1992simple} nonconforming space, which is a modification of the
work in \cite{kwak2010analysis} where `broken' $P_1$ nonconforming element of
Crouzeix-Raviart \cite{crouzeix1973conforming} was developed.
  For the Darcy velocity, we apply the mixed finite volume method studied in
\cite{chou2003mixed, kwak2010analysis} on the basis of immersed finite element
method (IFEM). In this way, the Darcy velocity of the flow can be computed
cheaply (locally) after we solve the pressure equation. The computed Darcy
velocity is used to solve the saturation equation explicitly. Thus the whole
procedure can be implemented in an efficient way using a structured grid which
is independent of the underlying heterogeneous porous media. Numerical results
show that our method exhibits optimal order convergence rates for the pressure
and velocity variables, and suboptimal rate for saturation.
