Reducing noise in moving-grid codes with strongly-centroidal Lloyd mesh regularization

TL;DR

This paper introduces a new regularization scheme for moving Voronoi mesh hydrodynamical codes that significantly reduces mesh noise and improves accuracy in simulations involving shear instabilities and mixing.

Contribution

The paper presents a strongly-centroidal Lloyd mesh regularization method that maintains mesh regularity while allowing cells to move with the fluid, reducing mesh noise in hydrodynamical simulations.

Findings

Reduces mesh noise in shear and Kelvin-Helmholtz instability simulations.

Improves accuracy in mixing and angular momentum conservation.

Nearly no impact on galaxy formation simulations, indicating robustness.

Abstract

A method for improving the accuracy of hydrodynamical codes that use a moving Voronoi mesh is described. Our scheme is based on a new regularization scheme that constrains the mesh to be centroidal to high precision while still allowing the cells to move approximately with the local fluid velocity, thereby retaining the quasi-Lagrangian nature of the approach. Our regularization technique significantly reduces mesh noise that is attributed to changes in mesh topology and deviations from mesh regularity. We demonstrate the advantages of our method on various test problems, and note in particular improvements obtained in handling shear instabilities, mixing, and in angular momentum conservation. Calculations of adiabatic jets in which shear excites Kelvin Helmholtz instability show reduction of mesh noise and entropy generation. In contrast, simulations of the collapse and formation of an isolated disc galaxy are nearly unaffected, showing that numerical errors due to the choice of regularization do not impact the outcome in this case.