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 ~ { } { M _ { \odot } } and M _ { 2 } = 30 ~ { } { M _ { \odot } } , and for a high mass model , M _ { 1 } = 170 ~ { } { M _ { \odot } } and M _ { 2 } = 80 ~ { } { 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 .