Data-integrated two-scale modelling of compressible multiphase flow

Compressible liquid-vapour flow with phase change appears in many natural and technical processes providing a paradigm for multi-scale modelling approaches. By now there are reliable but very expensive Navier-Stokes-type models on a microscopic, detailed-scale level with full resolution of phase boundaries. On the other hand, first-order and thus computationally cheap Baer-Nunziato-type models have been developped to describe the mixture evolution on an averaged scale. However, they loose accuracy for phase-change problems. As a remedy we develop a two-scale model that acts on the averaged scale but incorporates a diffuse-interface model as cell problem. This approach exploits a novel homogenization technique based on Wentzel-Kramers-Brillouin expansions for the detailed-scale flow field. A particular feature of this ansatz is its flexibility to substitute the cell-problem solver by a machine-learned surrogate solver. To ensure essential flow properties like mass/momentum/energy conservation or thermodynamical consistency we will adapt constraint-aware neural networks, in particular the previously developped constraint-resolving layer method that allows an analytical treatment of side conditions. Finally, the implementation will be validated using the FLEXI open-source frameworks.