  We numerically investigate the expansion of clouds of hard-core bosons in the
two-dimensional square lattice using a matrix-product-state based method. This
nonequilibrium set-up is induced by quenching the trapping potential to zero
and our work is specifically motivated by a recent experiment with interacting
bosons in an optical lattice [Ronzheimer et al., Phys. Rev. Lett. 110, 205301
(2013)]. As the anisotropy of the amplitudes $J_x$ and $J_y$ for hopping in
different spatial directions is varied from the one- to the two-dimensional
case, we observe a crossover from a fast ballistic expansion in the
one-dimensional limit $J_x \gg J_y$ to much slower dynamics in the isotropic
two-dimensional limit $J_x=J_y$. We further study the dynamics on multi-leg
ladders and long cylinders. For these geometries we compare the expansion of a
cloud to the melting of a domain wall, which helps us to identify several
different regimes of the expansion as a function of time. By studying the
dependence of expansion velocities on both the anisotropy $J_y/J_x$ and the
number of legs, we observe that the expansion on two-leg ladders, while similar
to the two-dimensional case, is slower than on wider ladders. We provide a
qualitative explanation for this observation based on an analysis of the rung
spectrum.
