  The sequential fully implicit (SFI) method was introduced along with the
development of the multiscale finite volume (MSFV) framework, and has received
considerable attention in recent years. Each time step for SFI consists of an
outer loop to solve the coupled system, in which there is one inner Newton loop
to implicitly solve the pressure equation and another loop to implicitly solve
the transport equations. Limited research has been conducted that deals with
the outer coupling level to investigate the convergence performance. In this
paper we extend the basic SFI method with several nonlinear acceleration
techniques for improving the outer-loop convergence. Specifically, we consider
numerical relaxation, quasi-Newton (QN) and Anderson acceleration (AA) methods.
The acceleration techniques are adapted and studied for the first time within
the context of SFI for coupled flow and transport in porous media. We reveal
that the iterative form of SFI is equivalent to a nonlinear block Gauss-Seidel
(BGS) process. The effectiveness of the acceleration techniques is demonstrated
using several challenging examples. The results show that the basic SFI method
is quite inefficient, suffering from slow convergence or even convergence
failure. In order to better understand the behaviors of SFI, we carry out
detailed analysis on the coupling mechanisms between the sub-problems. Compared
with the basic SFI method, superior convergence performance is achieved by the
acceleration techniques, which can resolve the convergence difficulties
associated with various types of coupling effects. We show across a wide range
of flow conditions that the acceleration techniques can stabilize the iterative
process, and largely reduce the outer iteration count.
