Homogenized systems for liquid-vapour transition in unsteady compressible two-phase flow

In this project, we consider the liquid vapour flow as a homogenized mixture of the two phases. The resulting models pose a major challenge to mathematics, since there are a number of important open questions to be studied. The primary goal is to improve goal is to improve and validate numerical schemes for such models. Numerical solutions are needed in many diverse engineering applications involving phenomena such as liquid sprays of bubbly flows. In order to improve the quality of numerical results we need to address some mathematical issues concerning the modelling and resulting well-posedness of the equations. Also we will have to develop a deeper understanding of the theory and numerical methods for hyperbolic systems of equations containing non-conservative derivatives. Another challenge is phase extinction, which is related to vacuum states in gas dynamics. Further, it will be necessary to encorporate phase transitions into the models and numerical computations. Gefördert von der DFG im Rahmen der DFG-CNRS-Forschergruppe 563 "Micro-Macro Modelling and Simulation of Liquid-Vapour Flows".