  The origin of cosmic rays above the knee in the spectrum is an unsolved
problem. We present a wind model in which interstellar gas flows along a
non-rotating, expanding flux tube with a changing speed and cross-sectional
area. Cosmic rays from Galactic sources, such as supernova remnants, which are
coupled to the plasma via Alfv\'{e}n waves, provide the main pressure source
for driving this outflow. These cosmic rays are then subject to diffusive shock
reacceleration at the Galactic wind termination shock, which is located at a
distance $\sim200\,{\rm kpc}$. Some of the highest-energy reaccelerated
particles propagate upstream against the wind and can contribute to the PeV-EeV
range of the spectrum. We analyze the conditions under which efficient
reacceleration can occur and find that rigidities $\sim$ 10-40 PV can be
obtained and that the termination shock may account for half of the proton
spectrum measured in IceCube/IceTop experiment. The highest-energy particles
that escape downstream from our termination shock, and similar shocks
surrounding most galaxies, can be further accelerated by intergalactic shock
fronts.
