In many cases, the analysis of the hyperbolicity of multispecies kinematic flow models can be greatly simplified after realizing that the fluxes in these models often have a particular algebraic structure that allows for the (numerical) computation of the (full) eigen-structure of the Jacobian matrix. The relation between the eigen-structure of a matrix and the zeros of a rational function, the 'secular equation' approach, makes it possible to use high resolution, state of the art shock capturing schemes in many situations. It may also serve to identify parameter regions of guaranteed hyperbolicity in polydisperse sedimentation models, and the basic techniques can also be applied in other scenarios, like dispersive models in chromatography.