### Project B3

**Principal Investigator:**

*Christiane Helzel, Applied Mathematics, Heinrich-Heine University
DÃ¼sseldorf*

**Main Collaborators in the Research Unit:**

*Gregor Gassner, Division of Mathematics, University of Cologne*

*Manuel Torrilhon, Applied and Computational Mathematics, RWTH Aachen
University*

## Structure-Preserving Methods for Complex Fluids

We construct numerical methods for a system of partial differential
equations consisting of a kinetic equation coupled to a macroscopic
flow equation, which models sedimentation in suspensions of rod-like
particles. A hierarchy of moment equations will be derived which approximates the
high-dimensional scalar kinetic equation with a lower dimensional system. The
number of moment equations will be adjusted locally based on the
dynamics of the problem. This requires an interface coupling of moment
systems with different resolution.
For the underlying mathematical model thermodynamic consistency can be
shown. We will investigate whether this structure can be preserved
by the numerical method.

Kinetic Simulations
Moment Models