The multiscale finite-volume (MSFV) method has been designed to solve
flow problems on large domains efficiently. First, a set of basis
functions, which are local numerical solutions, is employed to
construct a fine-scale pressure approximation; then a conservative
fine-scale velocity approximation is constructed by solving local
problems with boundary conditions obtained from the pressure
approximation; finally, transport is solved at the. ne scale. The
method proved very robust and accurate for multiphase flow simulations
in highly heterogeneous isotropic reservoirs with complex correlation
structures. However, it has recently been pointed out that the
fine-scale details of the MSFV solutions may be lost in the case of
high anisotropy or large grid aspect ratios. This shortcoming is
analyzed in this paper, and it is demonstrated that it is caused by the
appearance of unphysical ``circulation cells.'' We show that
damped-shear boundary conditions for the conservative-velocity problems
or linear boundary conditions for the basis-function problems can
significantly improve the MSFV solution for highly anisotropic
permeability fields without sensitively affecting the solution in the
isotropic case.