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We propose a variant of the $\theta$-scheme for diffuse interface models fortwo-phase flow, together with three new linearization techniques for thesurface tension. These involve either additional stabilizing force terms, or afully implicit coupling of the Navier-Stokes and Cahn-Hilliard equation. In thecommon case that the equations for interface and flow are coupled explicitly,we find a time step restriction which is very different to other two-phase flowmodels and in particular is independent of the grid size. We also show that theproposed stabilization techniques can lift this time step restriction. Evenmore pronounced is the performance of the proposed fully implicit scheme whichis stable for arbitrarily large time steps. We demonstrate in a Taylor flowapplication that this superior coupling between flow and interface equation canrender diffuse interface models even computationally cheaper and faster thansharp interface models.

Time integration for diffuse interface models for two-phase flow