  Motion of vortices in two-dimensional superfluids in the classical limit is
studied by solving the Gross-Pitaevskii equation numerically on a uniform
lattice. We find that, in the presence of a superflow directed along one of the
main lattice periods, vortices move with the superflow on fine lattices but
perpendicular to it on coarse ones. We interpret this result as a transition
from the full Magnus force in the Galilean-invariant limit to vanishing
effective Magnus force in a discrete system, in agreement with the existing
experiments on vortex motion in Josephson junction arrays.
