  Accurate prediction of the macroscopic flow parameters needed to describe
flow in porous media relies on a good knowledge of flow field distribution at a
much smaller scale---in the pore spaces. The extent of the inertial effect in
the pore spaces can not be underestimated yet is often ignored in large-scale
simulations of fluid flow. We present a multiscale method for solving Oseen's
approximation of incompressible flow in the pore spaces amid non-periodic grain
patterns. The method is based on the multiscale finite element method (MsFEM
[Hou and Wu, 1997]) and is built in the vein of Crouzeix-Raviart elements
[Crouzeix and Raviart, 1973]. Simulations of inertial flow in highly
non-periodic settings are conducted and presented. Convergence studies in terms
of numerical errors relative to the reference solution are given to demonstrate
the accuracy of our method. The weakly enforced continuity across coarse
element edges is shown to maintain accurate solutions in the vicinity of the
grains without the need for any oversampling methods. The penalization method
is employed to allow a complicated grain pattern to be modeled using a simple
Cartesian mesh. This work is a stepping stone towards solving the more
complicated Navier-Stokes equations with a non-linear inertial term.
