  We present an efficient technique to study the 1D evolution of
instability-generated structure in winds of hot stars out to very large
distances (more than 1000 stellar radii). This technique makes use of our
previous finding that external forces play little role in the outer evolution
of structure. Rather than evolving the entire wind, as is traditionally done,
the technique focuses on a representative portion of the structure and follows
it as it moves out with the flow. This requires the problem to be formulated in
a moving reference frame. The lack of Galilean invariance of the spherical
equations of hydrodynamics is circumvented by recasting them in a pseudo-planar
form. By applying the technique to a number of problems we show that it is fast
and accurate, and has considerable conceptual advantages. It is particularly
useful to test the dependence of solutions on the Galilean frame in which they
were obtained. As an illustration, we show that, in a one-dimensional
approximation, the wind can remain structured out to distances of more than
1300 stellar radii from the central star.
