  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.
