I³MS - Helzel Seminar
Prof. Dr. Christiane Helzel
Starting point of our considerations is a coupled system consisting of a kinetic equation coupled to a macroscopic Navier-Stokes equation describing the motion of a suspension of rigid rods under the influence of gravity. A reciprocal coupling leads to the formation of clusters: The buoyancy force creates a macroscopic velocity gradient that causes the microscopic particles to align so that their sedimentation reinforces the formation of clusters of higher particle density. Since the coupled system is high-dimensional, we are interested in the derivation of simpler systems which describe the dynamics without resolving the kinetic equation. We discuss two different approaches to obtain such systems. Furthermore, we discuss the numerical methods which were used to approximate the different mathematical models and show numerical results. This is joint work with Athanasios E. Tzavaras from KAUST.