## Two-Phase Flows

The incompressible and immiscible flow of two fluids with different properties such as viscosity and density is of importance in many technical applications. At the dynamically moving interfaces, jumps and kinks (i.e., discontinuities) are present in the physical fields such as velocity and pressure. These instationary discontinuities have to be properly treated in the numerical methods for the simulation. Typical applications include tank sloshing, collapsing water columns, dam breaks, and bubble flows.

### Interface Tracking and Interface Capturing

One approach to consider the dynamic interface is to frequently update the mesh such that the element edges

*track* the interface. However, for large movements of the interface including topological changes of the two fluid regions, mesh adaptions are virtually impossible. Another approach is to use fixed background meshes and

*capture the interface* by mesh refinements or by means of the extended finite element method (XFEM). In this case, the location of the interface is not part of the mesh but has to be provided separately, for example with the level-set method. All three approaches, interface tracking and interface capturing with mesh refinement or XFEM are investigated and developed at the Institute of Structural Analysis for two and three-dimensional applications.

## Free-Surface Flows

Free-surface flows can also be seen as a special case of two-phase flows where one phase ("air") has neglible influence on the other ("water"). The location of the interface is not known beforehand and is part of the solution. At the Institute of Structural Analysis, the overflow of objects, flow in spill-ways of dams and the impact on wave breakers have been succesfully simulated in two and three dimensions.

## Fluid-Structure Interaction

The interaction of a fluid with a deforming structure is an important problem in structural dynamics. The famous example of the Tacoma-Narrows bridge, which collapsed under the resonant reaction of the bridge with a moderate wind flow, demonstrates the possible consequences of this interaction and its importance in the safety of structures. The simulation of this coupled problem in two and three dimensions is an important application at the Institute of Structral Analysis.