Two-Phase Flows with Phase Transition - Modelling, Analysis and Numerics

Starting from existing work in this research group on this topic, our aim is to discuss several open questions in this context. Concerning the modelling it seems in the literature that there is a need to further investigate the derivation and formulation of balance laws in the presence of singularities, e.g.
shocks and phase boundaries. Due to the general character of the underlying theory this will be also helpful for other models and problems. In the preceding work general analytical results for isothermal two-phase flows were obtained. A further objective is to discuss general flows where heat conduction is taken into account. In particular we want to use the hyperbolic formulation introduced by Romenski. For this work we will also collaborate with the group of Prof. Munz in Stuttgart. As in the isothermal case we first want to investigate the corresponding Riemann problem. The numerics of two-phase flows are still a major problem. In particular when multidimensional problems are considered. Effects like surface tension and phase creation have to be considered. In the context of sharp interface models we suggest to investigate algorithms used for combustion problems since we expect some analogies in the numerical treatment of these topics. Parallel to these questions we further seek to compare the obtained results to other diffuse interface models used in the group (Warnecke/Matern) and the literature. Thus this project is also strongly linked to the previous one.