High-Frequency Voronoi Noise Reduced by Smoothed Mesh Motion
  We describe a technique for improving the performance of hydrodynamics codes which employ a moving Voronoi mesh. Currently, such codes are susceptible to high-frequency noise produced by rapid adjustments in the grid topology on the smallest scales. The treatment for this grid noise is simple; instead of moving the mesh-generating marker points with the local fluid velocity, this velocity field is smoothed on small scales, so that neighboring marker points generally have similar velocities. We demonstrate significant improvement gained by this adjustment in several code tests relevant to the physics which moving-mesh codes are designed to capture. 
Paul C. Duffell, Andrew I. MacFadyen
astro-ph.IM astro-ph.CO physics.flu-dyn