Improving the convergence behaviour of a fixed‐point‐iteration solver for multiphase flow in porous media

Summary A new method to admit large Courant numbers in the numerical simulation of multiphase flow is presented. The governing equations are discretized in time using an adaptive θ‐method. However, the use of implicit discretizations does not guarantee convergence of the nonlinear solver for large Courant numbers. In this work, a double‐fixed point iteration method with backtracking is presented, which improves both convergence and convergence rate. Moreover, acceleration techniques are presented to yield a more robust nonlinear solver with increased effective convergence rate. The new method reduces the computational effort by strengthening the coupling between saturation and velocity, obtaining an efficient backtracking parameter, using a modified version of Anderson's acceleration and adding vanishing artificial diffusion.