  We have performed numerical calculations of a binary interacting with a gas
disk, using eleven different numerical methods and a standard binary-disk
setup. The goal of this study is to determine whether all codes agree on a
numerically converged solution, and to determine the necessary resolution for
convergence and the number of binary orbits that must be computed to reach an
agreed-upon relaxed state of the binary-disk system. We find that all codes can
agree on a converged solution (depending on the diagnostic being measured). The
zone spacing required for most codes to reach a converged measurement of the
torques applied to the binary by the disk is roughly 1% of the binary
separation in the vicinity of the binary components. For our disk model to
reach a relaxed state, codes must be run for at least 200 binary orbits,
corresponding to about a viscous time for our parameters, $0.2 (a^2 \Omega_B
/\nu)$ binary orbits, where $\nu$ is the kinematic viscosity. We did not
investigate dependence on binary mass ratio, eccentricity, disk temperature, or
disk viscosity; therefore, these benchmarks may act as guides towards expanding
converged solutions to the wider parameter space but might need to be updated
in a future study that investigates dependence on system parameters. We find
the most major discrepancies between codes resulted from the dimensionality of
the setup (3D vs 2D disks). Beyond this, we find good agreement in the total
torque on the binary between codes, although the partition of this torque
between the gravitational torque, orbital accretion torque, and spin accretion
torque depends sensitively on the sink prescriptions employed. In agreement
with previous studies, we find a modest difference in torques and accretion
variability between 2D and 3D disk models. We find cavity precession rates to
be appreciably faster in 3D than in 2D.
