Numerical Approximation of a Simplified Kinetic Model for a Sedimenting Suspension of Rod-Like Particles Using Hyperbolic Systems of Moment Equations

We provide a review of our recent results obtained on hyperbolic systems of moment equations describing sedimentation in suspensions of rigid rod-like particles [3]. More precisely, we start from a time-dependent coupled system of partial differential equations in space and orientation, introduced by Helzel and Tzavaras [6], which describes the motion of a suspension of rod-like particles under the influence of gravity and derive hierarchies of moment equations which depend only on space and time. Here, we restrict our considerations to a simple shear flow problem and furthermore restrict the orientation of the rod-like particles to \(S^1\) embedded in the plane that is spanned by the direction of shear and the direction of gravity. We proof the hyperbolicity of the moment system and show that the moment system can be interpreted as a lower dimensional approximation of the original problem.