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. © 2016 The Authors. International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd.