Sampling Artifact in Volume Weighted Velocity Measurement.--- II.
  Detection in simulations and comparison with theoretical modelling
  Measuring the volume weighted velocity power spectrum suffers from a severe
systematic error, due to imperfect sampling of the velocity field from
inhomogeneous distribution of dark matter particles/halos in simulations or
galaxies with velocity measurement. This "sampling artifact" depends on both
the mean particle number density $\bar{n}_P$ and the intrinsic large scale
structure (LSS) fluctuation in the particle distribution. (1) We report robust
detection of this sampling artifact in N-body simulations. It causes $\sim 12$%
underestimation of the velocity power spectrum at $k=0.1$h/Mpc for samples with
$\bar{n}_P=6\times10^{-3}$ (Mpc/h)$^{-3}$. This systematic underestimation
increases with decreasing $\bar{n}_P$ and increasing $k$. Its dependence on the
intrinsic LSS fluctuations is also robustly detected. (2) All these findings
are expected by our theoretical modelling in paper I \cite{Zhang14}. In
particular, the leading order theoretical approximation agrees quantitatively
well with simulation result for $\bar{n}_P\gtrsim6\times
10^{-4}$(Mpc/h)$^{-3}$. Furthermore, we provide an ansatz to take high order
terms into account. It improves the model accuracy to $\lesssim1$% at
$k\lesssim0.1$h/Mpc over 3 orders of magnitude in $\bar{n}_P$ and over typical
LSS clustering from $z=0$ to $z=2$. (3) The sampling artifact is determined by
the deflection ${\bf D}$ field, which is straightforwardly available in both
simulations and data of galaxy velocity. Hence the sampling artifact in the
velocity power spectrum measurement can be self-calibrated within our
framework. By applying such self-calibration in simulations, it becomes
promising to determine the {\it real} large scale velocity bias of
$10^{13}M_\odot$ halos with $\sim 1$% accuracy, and that of lower mass halos by
better accuracy. ...[abridged]
