A hybrid level-set-phase-field method for two-phase flow with contact lines

We present a hybrid method combining a level set model with a phase field model. Contact line dynamics are represented by the full phase field model, whereas the convective interface transport and the evaluation of surface tension in the bulk of the domain are realized by a conservative level set model. This combination avoids the singularity at the contact line that is present in classical level set models with no-slip boundary conditions. The hybrid method relies on the similar shape of the concentration variable in the phase field model and the level set function. The terms specific to the phase field model are disabled away from the contact region by using a switch function. The benefits of using the level set model instead of the phase field model in the bulk of the domain are quantified by two extensive numerical benchmark computations. The conservative level set method gives considerably higher accuracy at the same mesh size than the phase field method. For the phase field method, a range of interface thicknesses and the mobilities are considered. The best values of these parameters for the two test cases are used in the comparison. Further, the well-posedness and stability of the hybrid method are shown using an a priori energy estimate. Numerical simulation of channel flow with the hybrid method demonstrates the increase in computational efficiency compared to a plain phase field model.