The goal of this project was to develop an efficient simulation approach for the numerical modeling of multiphase fluid flow under the influence of strong electric fields. This research was originally motivated by a practical problem arising in high-voltage engineering. Therein, rain droplets gathering on the surface of high-voltage insulators give rise to partial electrical discharges. This leads to damage of the device associated with the loss of its surface hydrophobicity and insulation quality. The frequency and strength of electrical discharges depends on droplet’s shape while the latter is dynamically changing under the influence of the time harmonic electric field. Thus, in order to understand the effect of water droplets on high-voltage insulators, it is necessary to investigate first the fluid dynamical motion of water droplets driven by strong, time dependent electric fields. From the numerical point of view, this task represents a coupled multiphysical problem involving the solution of Navier-Stokes equation for the droplet dynamics as well as the numerical simulation of transient low frequency electric fields in the vicinity of the droplet. The coupled simulation procedure poses several issues which make the modeling task extremely difficult. These issues may be summarized as follows: (i) The spatial resolution of phase boundaries in multiphase flow simulations is very critical for the numerical accuracy of the fluid dynamical solver. Hereby, an extremely fine mesh is needed when conventional discretization methods are used. A much more accurate, alternative discretization approach based on a high-order Discontinuous Galerkin method for Navier-Stokes equation is developed in the framework of a DFG proposal of the Fachgebiet für Strömungsdynamik. (ii) A physics based model for the dynamics of the contact line between droplet and insulating layer is needed. It must take into account the effect of electric fields as well as the hydrophobicity of the insulator surface. The fluid dynamical part of the joint research (issues (i) and (ii), respectively) was performed at the Fachgebiet für Strömungsdynamik. (iii) Similarly to the fluid dynamical solver, also for the electric field solution an extremely high spatial resolution of the phase boundary (droplet surface) is required. This is because electric forces are basically surface forces acting primarily at the air-water interface. Thus, the overall numerical field accuracy is closely related to the quality of the local approximation of the droplet surface by the computational mesh in the electric field simulation. (iv) To improve numerical accuracy it is, furthermore, desirable to apply specialized numerical models for the field singularity arising at the contact line between water droplet, air and insulating layer. The presence of this singularity affects the contact line dynamics and thus the overall fluid dynamical motion of the water droplet.