The multiscale finite-volume (MSFV) method is designed to reduce the
computational cost of elliptic and parabolic problems with highly
heterogeneous anisotropic coefficients. The reduction is achieved
by splitting the original global problem into a set of local problems
(with approximate local boundary conditions) coupled by a coarse
global problem. It has been shown recently that the numerical errors
in MSFV results can be reduced systematically with an iterative procedure
that provides a conservative velocity field after any iteration step.
The iterative MSFV (i-MSFV) method can be obtained with an improved
(smoothed) multiscale solution to enhance the localization conditions,
with a Krylov subspace method [e.g., the generalized-minimal-residual
(GMRES) algorithm] preconditioned by the MSFV system, or with a combination
of both. In a multiphase-flow system, a balance between accuracy
and computational efficiency should be achieved by finding a minimum
number of i-MSFV iterations (on pressure), which is necessary to
achieve the desired accuracy in the saturation solution. In this
work, we extend the i-MSFV method to sequential implicit simulation
of time-dependent problems. To control the error of the coupled saturation/pressure
system, we analyze the transport error caused by an approximate velocity
field. We then propose an error-control strategy on the basis of
the residual of the pressure equation. At the beginning of simulation,
the pressure solution is iterated until a specified accuracy is achieved.
To minimize the number of iterations in a multiphase-flow problem,
the solution at the previous timestep is used to improve the localization
assumption at the current timestep. Additional iterations are used
only when the residual becomes larger than a specified threshold
value. Numerical results show that only a few iterations on average
are necessary to improve the MSFV results significantly, even for
very challenging problems. Therefore, the proposed adaptive strategy
yields efficient and accurate simulation of multiphase flow in heterogeneous
porous media.