DAE-index monitoring for semi-discretized viscous Cosserat rod models

The dynamics of viscous jets due to external forces like gravity and aerodynamics can be described by Cosserat rod models consisting of a system of partial and ordinary differential equations. Depending on the formulation of the equations, in particular the compatibility conditions, the semi-discretization in space yields systems of differential-algebraic equations (DAE) in time of different indices. We present a DAE-index monitoring and discuss the numerical results for the application in a rotational 2d fiber spinning scenario.