Numerical treatment of non-stationary viscous cosserat rod in a two-dimensional Eulerian framework

This work deals with the modeling and simulation of the dynamics of a slender viscous jet as it arises in spinning processes. There exist two classes of asymptotic one-dimensional models for such a jet, string and more complex rod models, that are given by systems of partial and ordinary differential equations. In this paper, we present non-stationary simulations of a rod in an Eulerian framework for arbitrary parameter ranges of 2d spinning where the string models failed so far. The numerical treatment is based on a finite volume approach with mixed central, up- and downwinded differences, the time integration is performed by a Radau method