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

TL;DR

This paper identifies and fixes the volume inconsistency error causing grid noise in Voronoi-based moving mesh codes, enabling second order convergence and improving computational accuracy.

Contribution

The authors introduce a simple fix for volume inconsistency in moving mesh codes, achieving second order convergence and reducing grid noise.

Findings

Significant improvement in computational accuracy with the fix.

Achievement of second order convergence in Voronoi-based codes.

Enhanced gradient estimation method for initial mesh setup.

Abstract

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.