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

Grid Noise in Moving Mesh Codes: Fixing The Volume Inconsistency Problem