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Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus(AGN) discs are possible progenitors of black-hole mergers detected ingravitational waves by LIGO/VIRGO. To better understand the hydrodynamicalevolution of BBHs interacting with the disc gas, we perform a suite ofhigh-resolution 2D simulations of binaries in local disc (shearing-box) models,considering various binary mass ratios, eccentricities and background discproperties. We use the $\gamma$-law equation of state and adopt a robustpost-processing treatment to evaluate the mass accretion rate, torque andenergy transfer rate on the binary to determine its long-term orbitalevolution. We find that circular comparable-mass binaries contract, with anorbital decay rate of a few times the mass doubling rate. Eccentric binariesalways experience eccentricity damping. Prograde binaries with highereccentricities or smaller mass ratios generally have slower orbital decayrates, with some extreme cases exhibiting orbital expansion. The averagedbinary mass accretion rate depends on the physical size of the accretor. Theaccretion flows are highly variable, and the dominant variability frequency isthe apparent binary orbital frequency (in the rotating frame around the centralmassive BH) for circular binaries but gradually shifts to the radial epicyclicfrequency as the binary eccentricity increases. Our findings demonstrate thatthe dynamics of BBHs embedded in AGN discs is quite different from that ofisolated binaries in their own circumbinary discs. Furthermore, our resultssuggest that the hardening timescales of the binaries are much shorter thantheir migration timescales in the disc, for all reasonable binary and discparameters.

Hydrodynamical Evolution of Black-Hole Binaries Embedded in AGN Discs