Planet-disc interaction on a freely moving mesh

TL;DR

This paper investigates the use of moving-mesh hydrodynamics for simulating planet-disc interactions, demonstrating that it can accurately model the system with adaptive resolution and minimal numerical diffusion, comparable to polar grid methods.

Contribution

The study applies a moving-mesh code to planet-disc interactions, showing it effectively captures dynamics and offers adaptive resolution without excessive numerical diffusion, unlike traditional polar grids.

Findings

Moving-mesh code results align with existing grid-based studies.

Grid noise and mesh distortions do not cause significant numerical diffusion.

The approach naturally increases resolution around planets and wakes.

Abstract

General-purpose, moving-mesh schemes for hydrodynamics have opened the possibility of combining the accuracy of grid-based numerical methods with the flexibility and automatic resolution adaptivity of particle-based methods. Due to their supersonic nature, Keplerian accretion discs are in principle a very attractive system for applying such freely moving mesh techniques. However, the high degree of symmetry of simple accretion disc models can be difficult to capture accurately by these methods, due to the generation of geometric grid noise and associated numerical diffusion, which is absent in polar grids. To explore these and other issues, in this work we study the idealized problem of two-dimensional planet-disc interaction with the moving-mesh code AREPO. We explore the hydrodynamic evolution of discs with planets through a series of numerical experiments that vary the planet mass, the disc viscosity and the mesh resolution, and compare the resulting surface density, vortensity field and tidal torque with results from the literature. We find that the performance of the moving-mesh code in this problem is in accordance with published results, showing good consistency with grid codes written in polar coordinates. We also conclude that grid noise and mesh distortions do not introduce excessive numerical diffusion. Finally, we show how the moving-mesh approach can naturally increase resolution in regions of high densityaround planets and planetary wakes, while retaining the background flow at low resolution. This provides an alternative to the difficult task of implementing adaptive mesh refinement in conventional polar-coordinate codes.