  We simulate the hydrodynamics of the wind flow in the B[e] supergiant binary
system GG~Carinae and obtain the mass accretion rate onto the secondary and the
observed lightcurve. We find an inhomogeneous Bondi-Hoyle-Lyttleton accretion
into a curved accretion tail, and confirm that the accretion rate is modulated
along the orbit, with a maximum close to periastron. We show that the accretion
itself cannot account for the periodical variation in brightness. Instead, we
explain the observed variation in the light curve with absorption by the
accretion tail. Our results are in general agreement with previously derived
stellar masses, orbital parameters, and the system orientation, but imply that
the B[e] supergiant is more luminous. We find an effect related to the orbital
motion of the two stars, in which the accretion tail is cut by the primary and
we term it the Lizard Autotomy Effect. As part of the effect, the primary is
self accreting wind that it ejected earlier. The Lizard Autotomy Effect creates
an outwardly expanding spiral shell made up of broken segments. We suggest that
such a tail exists in other B[e] supergiant systems and can be the source of
the circumstellar material observed in such systems. The accretion also forms a
disc around the secondary near periastron that later vanishes. We suggest that
the formation of such a disc can launch jets that account for the bipolar
structure observed around some B[e] supergiants.
