Prof. Christian Rohde – Compressible Two-Phase Flow across Scale using Sharp and Diffuse Interface Ideas

Abstract

In the lecture, we will consider some aspects of the modeling and numerics for compressible liquid-vapour flow with phase transition. We first review a hierarchy of thermodynamically consistent sharp- and diffuse-interface models. On the chosen spatial scale, phase boundaries are fully resolved such that the sharp-interface ansatz leads to a free boundary value problem for the compressible Euler equations in the bulk domains. For  the diffuse-interface ansatz we employ variants of the classical Navier-Stokes-Korteweg model that allow  for computing two-phase regimes without special tracking methods.

In the second part of the presentation we will then derive up-scaled models for compressible flow on the  Darcy scale. Whereas the derivation remains formal for the sharp-interface ansatz we can present rigorous homogenization results for some of the diffuse-interface models leading to generalized versions of the Cahn-Hilliard equation.