In this paper we analyze a model problem for the convection-diffusion equat
ion where the reduced problem has closed characteristics. A full upwinding
finite difference scheme is used to discretize the problem. Additionally to
the strength of the convection, an arbitrary amount of crosswind-diffusion
can be added on the discrete level. We present a smoother which is robust
w.r.t. the strength of convection and the amount of crosswind-diffusion. It
is of Gauss-Seidel type using a downwind ordering. To handle the cyclic de
pendencies a frequency-filtering algorithm is used. The algorithm is of nea
rly optimal complexity O(n log n). It is proved that it fulfills a robust s
moothing property.