Injection of water into an oil-filled reservoir
This is the standard porous media problem called
the quarter five spot problem.
Initially, the well is filled with
oil (zero saturation in blue)
throughout the reservoir.
is injected through a well
at the lower right corner of the computational domain at a constant
rate, and fluid is produced at the same rate through a well in the
upper left corner.
The grid is composed of rectangles
divided into right triangle pairs.
For the computation, we used a mixed finite element method
using lowest order Raviart-Thomas
elements for the approximation of the pressure system followed by a
higher-order Godunov method.
The finite element velocity space is made up of piecewise linear
functions with continuous normal components on the
triangle edges, while the pressure space consists of piecewise