Grid noise in moving mesh codes: Fixing the volume inconsistency problem

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.