Talk by Christian Rohde "Applied fluids: Modelling Compressible Two-Phase Flow across Scales using Sharp and Diffuse Interface Ideas"

SFB 1313 principal investigator Christian Rohde will give a talk within the seminar series "Mathematical problems in fluid dynamics" of the Mathematical Science Research Institute of the University of California, Berkeley (USA).

Date: 21 May 2021
Time: 5:30 pm CET / 8:30 am PDT
Speaker: Prof. Christian Rohde, Institute of Applied Analysis and Numerical Simulation (IANS), University of Stuttgart
Talk: "Applied fluids: Modelling Compressible Two-Phase Flow across Scales using Sharp and Diffuse Interface Ideas"
Registration: https://www.msri.org/seminars/25657

Abstract

In the lecture, we will consider the multi-scale modeling and numerics for compressible two-phase flow. A sharp-interface approach appears to be adequate on a continuum scale where phase boundaries are fully resolved. This results in a concept using the compressible Euler equations in the bulk domains and understanding the phase boundary as a discontinuous (shock) wave. We propose a numerical algorithm that relies on new exact solutions of special Riemann problems accounting for molecular-scale information to determine the phase dynamics.  

Two-phase flow with topological changes can hardly be accessed by the sharp-interface ansatz. In the second part of the lecture, we will therefore present a class of diffuse-interface models that build on the classical compressible Navier-Stokes-Korteweg model. We will show that these models can provide the basis for reliable computations of convection-dominated processes (e.g. droplet collision). Moreover, this diffuse-interface ansatz is compatible with homogenization techniques. Therefore, we will conclude the lecture with a discussion of up-scaling compressible two-phase flow in porous media.

About Christian Rohde

Christian Rohde is the head of the Department for Applied Mathematics at the Institute of Applied Analysis and Numerical Simulation (IANS) at the University of Stuttgart. His research area is mathematical modelling, analysis and numerics for partial differential equations. In particular, his research focuses on applications in the field of fluid mechanics such as multi-phase flows, wave dynamics, phase transitions or interaction with electric or magnetic fields. Within SFB 1313 he focuses on the observation of fracture dynamics in porous media and the development of multi-scale methods for chemically reacting fluids.