A High-Order Method for Multiphase Problems with Three-Phase Contact Lines

We present a highly accurate extended discontinuous Galerkin method (XDG) for the simulation of multiphase problems with three-phase contact lines, where two fluid phases interact with a third, solid phase. An example for such a configuration is a water droplet sitting on a soft solid surface, where the surface of the droplet pulls on the solid, deforming it at the three-phase contact line. We will briefly outline the basic concepts of the XDG method and then concentrate on its central component: implicit interfaces. We will detail the numerical coupling approach at fluid-fluid and fluid-solid interfaces and at the three-phase contact line. Finally, we will show results of the simulation of a fluid droplet sitting on a flexible substrate.