Rich: Open Source Hydrodynamic Simulation on a Moving Voronoi Mesh

TL;DR

RICH is an open-source 2D hydrodynamic simulation code utilizing a moving Voronoi mesh, demonstrating improved accuracy over static meshes in many scenarios, with specific advantages and limitations analyzed.

Contribution

This work introduces RICH, a novel hydrodynamic code with a unique parallelization scheme and improved accuracy over AREPO, especially in moving mesh configurations.

Findings

Moving meshes generally outperform static meshes in accuracy.

In some cases, static meshes are more accurate when matter and wave directions oppose.

Voronoi-based moving meshes have a resolution-independent error due to flux-area inconsistencies.

Abstract

We present here RICH, a state of the art 2D hydrodynamic code based on Godunov's method, on an unstructured moving mesh (the acronym stands for Racah Institute Computational Hydrodynamics). This code is largely based on the code AREPO. It differs from AREPO in the interpolation and time advancement scheme as well as a novel parallelization scheme based on Voronoi tessellation. Using our code we study the pros and cons of a moving mesh (in comparison to a static mesh). We also compare its accuracy to other codes. Specifically, we show that our implementation of external sources and time advancement scheme is more accurate and robust than AREPO's, when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Llyod iterations) and it effects. We find that in most cases a moving mesh gives better results than a static mesh, but it is not universally true. In the case where matter moves in one way, and a sound wave is traveling in the other way (such that relative to the grid the wave is not moving) a static mesh gives better results than a moving mesh. Moreover, we show that Voronoi based moving mesh schemes suffer from an error, that is resolution independent, due to inconsistencies between the flux calculation and change in the area of a cell. Our code is publicly available as open source and designed in an object oriented, user friendly way that facilitates incorporation of new algorithms and physical processes.