  Numerical experiments are the primary method of studying the evolution of
circumbinary disks due to the strong nonlinearities involved. Many circumbinary
simulations also require the use of numerical mass sinks: source terms which
prevent gas from unphysically accumulating around the simulated point masses by
removing gas at a given rate. However, special care must be taken when drawing
physical conclusions from such simulations to ensure that results are not
biased by numerical artifacts. We demonstrate how the use of improved sink
methods reduces some of these potential biases in vertically-integrated
simulations of aspect ratio 0.1 accretion disks around binaries with mass
ratios between 0.1 and 1. Specifically, we show that sink terms that do not
reduce the angular momentum of gas relative to the accreting object: 1) reduce
the dependence on the sink rate of physical quantities such as the torque on
the binary, distribution of accretion between binary components, and evolution
of the binary semi-major axis; 2) reduce the degree to which the sink rate
affects the structure of the accretion disks around each binary component; 3)
alter the inferred variability of accretion onto the binary, making it more
regular in time. We also investigate other potential sources of systematic
error, such as the precise from of gravitational softening and previously
employed simplifications to the viscous stress tensor. Because of the strong
dependence of the orbital evolution of the binary on both the torque and
distribution of mass between binary components, the sink methods employed can
have a significant effect on the inferred orbital evolution of the binary.
