A finite volume method with staggered grid on time-dependent domains for viscous fiber spinning

The spinning of slender viscous fibers can be described by the special Cosserat theory with one-dimensional models consisting of partial differential and algebraic equations on time-dependent spatial domains. We propose a first-order finite volume method on a staggered grid with flux approximation suitable for the underlying differential-algebraic characteristics and a proper geometric handling of the space-time domain. The numerical results confirm the theoretical convergence orders. As exemplary application a rotational spinning scenario is studied.