| Abstract: |
| In the lecture we consider mathematical models for the evolution of two-phase fluids in free flow and porous media settings addressing diffuse-interface approaches. A special focus will be on Navier-Stokes-Korteweg (NSK) systems that describe on a detailed scale compressible liquid-vapour fluids which account for phase transition. We present rigorous results for homogenization in periodic porous media that lead to a Cahn-Hilliard-type evolution equation on the Darcy scale. Furthermore we discuss the upscaling of NSK motion for highy oscillating initial data on the corresponding Baer-Nunziato sacle. The latter limit results in a mixed type continuum-mechanical/kinetic evolution system. |
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