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We present nested-grid, high-resolution hydrodynamic simulations of gas andparticle dynamics in the vicinity of Mars- to Earth-mass planetary embryos. Thesimulations extend from the surface of the embryos to a few vertical disk scaleheights, with \rev{a spatial} dynamic range \rev{of} $\sim\! 1.4\times 10^5$.Our results confirm that "pebble"-sized particles are readily accreted, withaccretion rates continuing to increase up to metre-size "boulders" for a 10\%MMSN surface density model. The gas mass flux in and out of the Hill sphere isconsistent with the Hill rate, $\Sigma\Omega R_\mathrm{H}^2 = 4\, 10^{-3}$M$_\oplus$ yr$^{-1}$. While smaller size particles mainly track the gas, a netaccretion rate of $\approx 2\,10^{-5}$ M$_\oplus$ yr$^{-1}$ is reached for0.3--1 cm particles, even though a significant fraction leaves the Hill sphereagain. Effectively all pebble-sized particles that cross the Bondi sphere areaccreted. The resolution of these simulations is sufficient to resolveaccretion-driven convection. Convection driven by a nominal accretion rate of$10^{-6}$ M$_\oplus$ yr$^{-1}$ does not significantly alter the pebbleaccretion rate. We find that, due to cancellation effects, accretion rates ofpebble-sized particles are nearly independent of disk surface density. As aresult, we can estimate accurate growth times for specified particle sizes. For0.3--1 cm size particles, the growth time from a small seed is $\sim$0.15million years for an Earth mass planet at 1 AU and $\sim$0.1 million years fora Mars mass planet at 1.5 AU.

Pebble dynamics and accretion onto rocky planets. I. Adiabatic and convective models