  (abridged) The interaction of a fast wind with a spherical Asymptotic Giant
Branch (AGB) wind is thought to be the basic mechanism for shaping
Pre-Planetary Nebulae (PPN) and later Planetary Nebulae (PN). Due to the large
speed of the fast wind, one expects extended X-ray emission from these objects,
but X-ray emission has only been detected in a small fraction of PNs and only
in one PPN. Using numerical simulations we investigate the constraints that can
be set on the physical properties of the fast wind (speed, mass-flux, opening
angle) in order to produce the observed X-ray emission properties of PPNs and
PNs. We combine numerical hydrodynamical simulations including radiative
cooling using the code FLASH with calculations of the X-ray properties of the
resulting expanding hot bubble using the atomic database ATOMDB. In this first
study, we compute X-ray fluxes and spectra using one-dimensional models.
Comparing our results with analytical solutions, we find some agreements and
many disagreements. In particular, we test the effect of different time
histories of the fast wind on the X-ray emission and find that it is determined
by the final stage of the time history during which the fast wind velocity has
its largest value. The disagreements which are both qualitative and
quantitative in nature argue for the necessity of using numerical simulations
for understanding the X-ray properties of PNs.

Astrophysics