Measuring the numerical viscosity in simulations of protoplanetary disks in Cartesian grids
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Volume
678
Pagination
a134 - a134
Publisher
DOI
10.1051/0004-6361/202245601
Journal
Astronomy & Astrophysics
ISSN
0004-6361
Metadata
Show full item recordAbstract
Context. Hydrodynamical simulations solve the governing equations on a discrete grid of space and time. This discretization causes
numerical diffusion similar to a physical viscous diffusion, whose magnitude is often unknown or poorly constrained. With the current
trend of simulating accretion disks with no or very low prescribed physical viscosity, it becomes essential to understand and quantify
this inherent numerical diffusion, in the form of a numerical viscosity.
Aims. We study the behavior of the viscous spreading ring and the spiral instability that develops in it. We then use this setup to
quantify the numerical viscosity in Cartesian grids and study its properties.
Methods. We simulate the viscous spreading ring and the related instability on a two-dimensional polar grid using PLUTO as well as
FARGO, and ensure the convergence of our results with a resolution study. We then repeat our models on a Cartesian grid and measure
the numerical viscosity by comparing results to the known analytical solution, using PLUTO and Athena++.
Results. We find that the numerical viscosity in a Cartesian grid scales with resolution as approximately νnum ∝ ∆x
2
and is equivalent
to an effective α ∼ 10−4
for a common numerical setup. We also show that the spiral instability manifests as a single leading spiral
throughout the whole domain on polar grids. This is contrary to previous results and indicates that sufficient resolution is necessary
in order to correctly resolve the instability.
Conclusions. Our results are relevant in the context of models where the origin should be included in the computational domain,
or when polar grids cannot be used. Examples of such cases include models of disk accretion onto a central binary and inherently
Cartesian codes.