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

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.

A moving-mesh hydrodynamic solver for ChaNGa

“…However, this is usually not the case. According to Steinberg et al (2016), this cellcentered gradient estimate improves this convergence properties to be comparable to the least square gradient estimate used in later versions of AREPO (Pakmor et al 2016a). The gradient is then set to:…”

“…Here, we follow the procedure of Steinberg et al (2016) who improved upon the prescription of S10 in using the Green-Gauss theorem to estimate these gradients. The crucial difference between Steinberg et al (2016) and S10 is that the former estimates the gradient from the cell centers whereas S10 estimates the gradients from mesh generating points and assigns them to the cell centers. If the mesh generating points are at the cell centers, they these methods are the same.…”

“…First, rather than generating the Delaunay tessellation and computing its dual to produce the Voronoi tessellation, we compute the Voronoi tessellation directly using the publicly available library, VORO++ (Rycroft 2009). Second, we use an improved gradient estimate from Steinberg et al (2016) and (optionally) use a total variation diminishing (TVD) limiter proposed by Duffell & MacFadyen (2011). Finally, we perform the reconstruction of face centered values from the half-time step state vector and gradient estimates.…”

The Effect of Impact Parameter on Tidal Disruption Events

“…We use the moving-mesh hydrodynamic solver for ChaNGa, which we call MANGA (Chang et al 2017;Prust & Chang 2019), to conduct numerical simulations of TDEs. The solver is based on the scheme described by S10, but incorporates advances in gradient estimation (Steinberg et al 2016) and limiters (Duffell & Mac-Fadyen 2011). We also use an alternative method for constructing the Voronoi tessellation (Rycroft 2009;C17).…”

Multidimensional upwind hydrodynamics on unstructured meshes using graphics processing units – I. Two-dimensional uniform meshes

“…One problem encountered with moving meshes is grid noise (Bauer & Springel 2012;Hopkins 2015), caused by changes in topology as the mesh evolves which lead to volume inconsistency errors (Yalinewich et al 2015). Several fixes have been proposed, from smoothing the velocities of mesh points (Duffell & Mac-Fadyen 2015), to regularising the mesh (Mocz et al 2015), to directly attacking the volume inconsistency (Steinberg et al 2016).…”