  We present a numerical discretisation of the coupled moment systems,
previously introduced in Dahm and Helzel, which approximate the kinetic
multi-scale model by Helzel and Tzavaras for sedimentation in suspensions of
rod-like particles for a two-dimensional flow problem and a shear flow problem.
We use a splitting ansatz which, during each time step, separately computes the
update of the macroscopic flow equation and of the moment system. The proof of
the hyperbolicity of the moment systems in \cite{Dahm} suggests solving the
moment systems with standard numerical methods for hyperbolic problems, like
LeVeque's Wave Propagation Algorithm \cite{LeV}. The number of moment equations
used in the hyperbolic moment system can be adapted to locally varying flow
features. An error analysis is proposed, which compares the approximation with
$2N+1$ moment equations to an approximation with $2N+3$ moment equations. This
analysis suggests an error indicator which can be computed from the numerical
approximation of the moment system with $2N+1$ moment equations.
  In order to use moment approximations with a different number of
  moment equations in different parts of the computational domain, we consider
an interface coupling of moment systems with different resolution. Finally, we
derive a conservative high-resolution Wave Propagation Algorithm for solving
moment systems with different numbers of moment equations.
