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.
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