  We use lattice Boltzmann simulations to solve the Beris-Edwards equations of
motion for a cholesteric liquid crystal subjected to Poiseuille flow along the
direction of the helical axis (permeative flow). The results allow us to
clarify and extend the approximate analytic treatments currently available. We
find that if the cholesteric helix is pinned at the boundaries there is an
enormous viscosity increase. If, instead, the helix is free the velocity
profile is flattened but the viscosity is essentially unchanged. We highlight
the importance of secondary flows and, for higher flow velocities, we identify
a flow-induced double twist structure in the director field -- reminiscent of
the texture characteristic of blue phases.
