Graduate Seminar


Tuesday, 22.01.2013 11:00 am

On convergent schemes for diffuse interface models for two- phase flow of incompressible fluids with general mass densities

Prof. Dr. Günther Grün, Universität Erlangen-Nürnberg

In this talk, we will be concerned with modeling and numerics of two-phase flow
of  immiscible,  incompressible  viscous  fluids  with  different  mass  densities.  In
contrast  to  the  case  of  identical  mass  densities,  for  general  mass  densities  it  has
only  recently  been  possible  to  formulate  diffuse  interface  models  which  are
consistent  with  thermodynamics  and  for  which  numerical  schemes  satisfying
energy estimates can be developed. These models may be derived e.g. by Onsager's
variational  principle  and  they  consist  of  a  momentum  equation  for  the  velocity
field coupled to a Cahn-Hilliard equation for the evolution of the order parameter.
In  the  first  part  of  the  talk,  we  will  discuss  modeling  aspects,  and  by  a  subtle
discretization  of  the convective  coupling between  the  flux  of  the phase-field  and
the  momentum  equation,  we  formulate  a  numerical  scheme  which  is  discretely
consistent with thermodynamics. In the second part of the talk, we will prove its
convergence  in  two  and  in  three  space  dimensions  and  we  present  numerical
simulations showing the full practicality of the approach.

Time: 11:00 am

Location: SG 11, Seminargebäude, Wüllnerstraße 5 b, 52062 Aachen