Research Topic

Coupled fluid dynamic and electromagnetic simulations using a boundary conforming Discontinuous Galerkin (DG) approximation

Coupled fluid dynamic and electromagnetic simulations are required for a wide variety of applications to obtain reasonable results. An example is the problem of water droplets caused by rain or dew on the surface of high voltage insulators. Droplets oscillate under the influence of  time dependent high voltage fields on the insulator surface. This behavior influences the electric field distribution, especially, at the contact line where water is in contact with both air and the underlying insulator. The field increase at these locations can trigger electric discharges, thus, potentially damaging the insulation layer material.

The project focuses on the development of a higher order boundary conformal Discontinuous Galerkin (DG) approach for the electromagnetic part of the coupled water droplet problem. Furthermore, the DG approach will be coupled to a provided fluid dynamic solver. The idea is to use a DG method on a simple Cartesian mesh in combination with a boundary conformal approximation technique which is exclusively applied in grid cells which are located at the material boundary. We will refer to them as cut-cells. The idea is to subdivide the cut-cells into sub-cells at the material boundary.  A geometry kernel is used for the geometrical description of the cut-cells. For the time integration, the implicit Crank-Nicolson scheme is applied and the linear system of equations is solved with the preconditioned conjugate gradient method.  Furthermore, a merging method is introduced which merges small sub-cells with the neighboring Cartesian grid cell. Finally, a hybridization method reduces the DG degrees of freedoms (DoFs) in normal Cartesian grid cells. Figure 1 and 2 show numerical simulation results demonstrating the accuracy and efficiency of the method.

Figure 1 and 2:  Electric potential and field strength of a droplet placed between two parallel plates which are generating a uniform external field at a frequency of 50 Hz (time = 5ms)

Key Research Area

Multi-Physics – Special Coupled Systems: Fluid- and Electrodynamics


Prof. Dr.-Ing. T. Weiland (TEMF, Theory of Electromagnetic Fields)
Prof. Dr.-Ing. A. Binder (Electrical Energy Conversion)


Annette Fröhlcke


Dolivostraße 15

D-64293 Darmstadt



+49 6151 16 - 24401 or 24402


+49 6151 16 - 24404




froehlcke (at) gsc.tu...

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