A multiscale framework for multiphase flow based on the compressible Navier-Stokes-Korteweg system

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.