  We present high resolution numerical simulations of the colliding wind system
$\eta$ Carinae, showing accretion onto the secondary star close to periastron
passage. Our hydrodynamical simulations include self gravity and radiative
cooling. The smooth stellar winds collide and develop instabilities, mainly the
non-linear thin shell instability, and form filaments and clumps. We find that
a few days before periastron passage the dense filaments and clumps flow
towards the secondary as a result of its gravitational attraction, and reach
the zone where we inject the secondary wind. We run our simulations for the
conventional stellar masses, $M_1=120 ~\rm{M_\odot}$ and $M_2=30
~\rm{M_\odot}$, and for a high mass model, $M_1=170 ~\rm{M_\odot}$ and $M_2=80
~\rm{M_\odot}$, that was proposed to better fit the history of giant eruptions.
As expected, the simulations results show that the accretion processes is more
pronounced for a more massive secondary star.
