A new method to admit large Courant numbers in the numerical simulation of multiphase flow is presented.
The governing equations are discretised in time using an adaptive

-method. However, the use of implicit
discretisations does not guarantee convergence of the non-linear solver for large Courant numbers. In this
work, a double-fixed point iteration method with backtracking is presented that improves both convergence
and convergence rate. Moreover, acceleration techniques are presented to yield a more robust non-linear
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.