  We perform numerical simulations of large scale structure evolution in an
inhomogeneous Lemaitre-Tolman-Bondi (LTB) model of the Universe. We follow the
gravitational collapse of a large underdense region (a void) in an otherwise
flat matter-dominated Einstein-deSitter model. We observe how the (background)
density contrast at the centre of the void grows to be of order one, and show
that the density and velocity profiles follow the exact non-linear LTB solution
to the full Einstein equations for all but the most extreme voids. This result
seems to contradict previous claims that fully relativistic codes are needed to
properly handle the non-linear evolution of large scale structures, and that
local Newtonian dynamics with an explicit expansion term is not adequate. We
also find that the (local) matter density contrast grows with the scale factor
in a way analogous to that of an open universe with a value of the matter
density OmegaM(r) corresponding to the appropriate location within the void.
