Multiphase flow simulations become difficult due to the occurrence of strongly interacting physical phenomena on different space and time scales. In this project, we develop numerical methods, in which multi-X continua models can be included covering a wide range of length/time scales. As the basic mathematical model we consider the Navier-Stokes-Korteweg (NSK) system that describes the compressible motion of a homogeneous fluid in a liquid and a vapour phase with phase transition. For the direct numerical solution of the NSK system we rely on our open-source software framework FLEXI: A high-order discontinuous Galerkin method on curved hexahedral grid cells, allowing non-conform grid refinement and a local sub-cell treatment of interfaces enhancing locality and robustness. The novel simulation code FLEXI-NSK is first applied to the direct numerical simulation of droplets. In the second part of the project, we will extend FLEXI-NSK to control uncertainties concerning the choice of free energy potentials and geometries in case of confined domains. In the third part of the project, we intend to develop a simple multi-domain and multi-scale approach to pave the way towards a holistic NSK approach for coupled free and porous media flow. In this way, we cover different flow regimes contributing to the EXC-2075 Vision on Engineered Geosystems. Data-driven surrogates handle the computationally expensive sub-scale or sub-domain problems.