This reseach field is particularly supported by the Emmy Noether Research Group.
As multiphase flows are widely encountered in engineering and environmental applications, the development of simulation approaches for such problems has gained particular attention in recent years. Important fields of application range from metallurgical processes via cooling circuits and flows around ships to groundwater flows and wave dynamics.
From a numerical point of view, two-phase flows pose additional challenges compared to single-phase flows. Due to different physical properties of both phases as well as surface-tension effects, velocity and pressure exhibit discontinuities across the interface which have to be taken into account in the numerical approach. Moreover, an accurate representation of the interface including topological changes such as merging or breaking is necessary. An approach which has often been used for describing such topological changes is the level-set method.
The focus of our research is on the development of robust and accurate fixed-grid schemes in the context of finite element methods. As a level-set method is used to capture the interface, the interface is generally not aligned with the edges of the elements. Hence, finite element discretizations which enable reproducing the aforementioned discontinuities are of great importance to obtain accurate results. Extended finite element methods, which have originally been proposed for problems of fracture mechanics, have proven to be an adequate approach for multiphase flows.
We developed a computational approach that unites the extended finite element method with multiscale and stabilized methods and Nitsche-type interface couplings of the different fluid phases. Our current research particularly addresses turbulent two-phase flow problems.
Please find publications on this topic here.