SFB 1313 Milestone Presentation

The next SFB 1313 public milestone presentation will be held by Lars von Wolff about "A Cahn-Hilliard Navier-Stokes Model for Two Phase Flow with Precipitation and Dissolution".

Date:  Tuesday, November 5, 2019
Time: 4 pm
Place: Pfaffenwaldring 61, MML, U1.003
Title: "A Cahn-Hilliard Navier-Stokes Model for Two Phase Flow with Precipitation and Dissolution"
Advisor: Christian Rohde, Rainer Helmig, Iuliu Sorin Pop

Abstract
Multi-phase flow and reactive transport processes are commonly encountered in the context of porous media. While the modeling of multi-phase flow is challenging in itself, in many applications the solid domain can change in time.  We consider a model for two fluid phases and one solid phase. The solid phase consists of a mineral that can be dissolved into ions by one of the fluids. Vice versa the ions in the fluid phase can precipitate and form new mineral.

We propose a phase-field model, with a smooth diffuse transition zone of non-zero width between the phases. The evolution of the phase field parameters is given by a ternary Cahn--Hilliard equation. It is coupled to a Navier--Stokes equation for the fluid flow. By means of matched asymptotic expansions we investigate the limit of the diffuse transition width going to zero. We recover a sharp interface formulation with a Navier slip condition between the solid phase and the fluid phases.

Using a Galerkin FEM for discretization some numerical examples will be presented.