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The sequential fully implicit (SFI) method was introduced along with thedevelopment of the multiscale finite volume (MSFV) framework, and has receivedconsiderable attention in recent years. Each time step for SFI consists of anouter loop to solve the coupled system, in which there is one inner Newton loopto implicitly solve the pressure equation and another loop to implicitly solvethe transport equations. Limited research has been conducted that deals withthe outer coupling level to investigate the convergence performance. In thispaper we extend the basic SFI method with several nonlinear accelerationtechniques for improving the outer-loop convergence. Specifically, we considernumerical relaxation, quasi-Newton (QN) and Anderson acceleration (AA) methods.The acceleration techniques are adapted and studied for the first time withinthe context of SFI for coupled flow and transport in porous media. We revealthat the iterative form of SFI is equivalent to a nonlinear block Gauss-Seidel(BGS) process. The effectiveness of the acceleration techniques is demonstratedusing several challenging examples. The results show that the basic SFI methodis quite inefficient, suffering from slow convergence or even convergencefailure. In order to better understand the behaviors of SFI, we carry outdetailed analysis on the coupling mechanisms between the sub-problems. Comparedwith the basic SFI method, superior convergence performance is achieved by theacceleration techniques, which can resolve the convergence difficultiesassociated with various types of coupling effects. We show across a wide rangeof flow conditions that the acceleration techniques can stabilize the iterativeprocess, and largely reduce the outer iteration count.

Nonlinear Acceleration of Sequential Fully Implicit (SFI) Method for Coupled Flow and Transport in Porous Media