We present the results of 2D hydrodynamical simulations of circumbinary disk accretion using the finite-volume code DISCO . This code solves the 2D viscous Navier-Stokes equations on a high-resolution moving mesh which shears with the fluid flow , greatly reducing advection errors in comparison with a fixed grid . We perform a series of simulations for binary mass ratios in the range 0.026 \leq q \leq 1.0 , each lasting longer than a viscous time so that we reach a quasi-steady accretion state . In each case , we find that gas is efficiently stripped from the inner edge of the circumbinary disk and enters the cavity along accretion streams , which feed persistent “ mini-disks ” surrounding each black hole . We find that for q \gtrsim 0.1 , the binary excites eccentricity in the inner region of the circumbinary disk , creating an overdense lump which gives rise to enhanced periodicity in the accretion rate . The dependence of the periodicity on mass ratio may provide a method for observationally inferring mass ratios from measurements of the accretion rate . We also find that for all mass ratios studied , the magnitude of the accretion onto the secondary is sufficient to drive the binary toward larger mass ratio . This suggests a mechanism for biasing mass ratio distributions toward equal mass .