  Current Voronoi based moving mesh hydro codes suffer from "grid noise". We
identify the cause of this noise as the volume inconsistency error, where the
volume that is transferred between cells is inconsistent with the
hydrodynamical calculations. As a result, the codes do not achieve second order
convergence. In this paper we describe how a simple fix allows Voronoi based
moving mesh codes to attain second order convergence. The fix is based on the
understanding that the volume exchanged between cells should be consistent with
the hydrodynamical calculations. We benchmark our fix with three test problems
and show that it can significantly improve the computational accuracy. We also
examine the effect of initial mesh initialization and present an improved model
for the Green-Gauss based gradient estimator.
