  The estimation and analysis of large-scale bulk flow moments of peculiar
velocity surveys is complicated by non-spherical survey geometry, the
non-uniform sampling of the matter velocity field by the survey objects and the
typically large measurement errors of the measured line-of-sight velocities.
Previously, we have developed an optimal `minimum variance' (MV) weighting
scheme for using peculiar velocity data to estimate bulk flow moments for
idealized, dense and isotropic surveys with Gaussian radial distributions, that
avoids many of these complications. These moments are designed to be easy to
interpret and are comparable between surveys. In this paper, we test the
robustness of our MV estimators using numerical simulations. Using MV weights,
we estimate the bulk flow moments for various mock catalogues extracted from
the LasDamas and the Horizon Run numerical simulations and compare these
estimates to the moments calculated directly from the simulation boxes. We show
that the MV estimators are unbiased and negligibly affected by non-linear
flows.
