Rich: Open-Source Hydrodynamic Simulation on a Moving Voronoi Mesh

Abstract

We present here RICH, a state-of-the-art two-dimensional 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 schemeS 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 is AREPO when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Lloyd iterations) and its 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. We perform an analytic analysis for finite difference schemes that reveals that a Lagrangian simulation is better than aEulerian simulation in the case of a highly supersonic flow. Moreover, we show that Voronoi-based moving mesh schemes suffer from an error, which is resolution independent, due to inconsistencies between the flux calculation and the 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.

Instability of supersonic cold streams feeding galaxies–II. Non-linear evolution of surface and body modes of Kelvin–Helmholtz instability

“…Comparing these terms, we conclude that the deceleration induced by KHI is too small to account for the constant inflow velocity observed in cosmological simulations, which do not resolve stream instabilities. One important caveat to this conclusion is that cylindrical streams are expected to decelerate more efficiently than planar slabs; preliminary analysis and 2D axisymmetric cylindrical simulations using RICH (Yalinewich et al 2015) suggest that cylinder deceleration timescales may be ∼ 10 (∼ 3) times shorter than slab deceleration timescales for δ ∼ 100 (δ ∼ 10). This will be presented and compared with full 3D simulations in the next paper of this series (Mandelker et al in preparation).…”

“…In principle, a different conclusion might be expected for a cylindrical stream. Simulations of 2D axisymmetric cylindrical streams performed using the moving mesh code RICH (Yalinewich et al 2015) show a decrease in overall growth rates as h s → R s , possibly by as much as a factor of ∼ 2 at late times when h s 0.8R s . On the other hand, preliminary RAM-SES simulations of cylindrical streams in full 3D show that h s increases compared to the slab result for h s 0.5R s .…”

Radio emission from the unbound debris of tidal disruption events

“…We ran simulations of tidal disruption events with mass ratio Q = 10 6 and impact parameters β = 1 and β = 7 using the 3D version of the moving mesh RICH code (Yalinewich et al 2015). We chose β = 1 to represent a shallow TDE, and β = 7 to represent a TDE where the star penetrates deep into the tidal radius, following a convention used in previous works (e.g.…”

“…To verify equation A2 and calibrate the coefficient C xz , we ran a simulation using the moving mesh hydrocode RICH (Yalinewich et al 2015). Our computational domain extends from -500 to 500 along the z direction (where length is measured in units of the radius of the cylinder), and in the x direction from -100 to 1000.…”

The Multi-Dimensional Structure of Radiative Shocks: Suppressed Thermal X-rays and Relativistic Ion Acceleration

“…Here we present high-resolution numerical simulations of radiative shocks using the moving-mesh hydrodynamical code RICH (Yalinewich et al 2015). We introduce for the first time a specialized "Lagrangian" numerical technique, which eliminates artificial diffusion of thermal energy across cell boundaries, allowing us to obtain greater convergence on this problem than possible in previous work.…”