  We present a numerical model for the dynamics of thin viscous threads based
on a discrete, Lagrangian formulation of the smooth equations. The model makes
use of a condensed set of coordinates, called the centerline/spin
representation: the kinematical constraints linking the centerline's tangent to
the orientation of the material frame is used to eliminate two out of three
degrees of freedom associated with rotations. Based on a description of twist
inspired from discrete differential geometry and from variational principles,
we build a full-fledged discrete viscous thread model, which includes in
particular a discrete representation of the internal viscous stress.
Consistency of the discrete model with the classical, smooth equations is
established formally in the limit of a vanishing discretization length. The
discrete models lends itself naturally to numerical implementation. Our
numerical method is validated against reference solutions for steady coiling.
The method makes it possible to simulate the unsteady behavior of thin viscous
jets in a robust and efficient way, including the combined effects of inertia,
stretching, bending, twisting, large rotations and surface tension.
