  We here present two-dimensional, time-dependent radiatively cooling
hydrodynamical simulations of the large and little Homunculus nebulae around
$\eta$ Carinae. We employ an alternative scenario to previous interacting
stellar wind models which is supported by both theoretical and observational
evidence, where a non-spherical outburst wind (with a latitudinal velocity
dependence that matches the observations of the large Homunculus), which is
expelled for 20 years, interacts with a pre-eruptive slow wind also with a
toroidal density distribution, but with a much smaller equator-to-polar density
contrast than that assumed in previous models. A second eruptive wind with
spherical shape is ejected about 50 years after the first outburst, and causes
the development of the little internal nebula. We find that, as a result of an
appropriate combination of the parameters that control the degree of asymmetry
of the interacting winds, we are able to produce not only the structure and
kinematics of both Homunculus, but also the high-velocity equatorial ejecta.
These arise from the impact between the non-spherical outburst and the
pre-outburst winds in the equatorial plane.
