We present the first hydrodynamic, multidimensional simulations of He shell flash convection. We investigate the properties of shell convection immediately before the He luminosity peak during the 15th thermal pulse of a stellar evolution track with initially 2 solar masses and metallicity Z = 0.01. This choice is a representative example of a low-mass asymptotic giant branch thermal pulse. We construct the initial vertical stratification with a set of polytropes to resemble the stellar evolution structure. Convection is driven by a constant volume heating in a thin layer at the bottom of the unstable layer. We calculate a grid of two-dimensional simulations with different resolutions and heating rates, plus one low-resolution three-dimensional run. The flow field is dominated by large convective cells that are centered in the lower half of the convection zone. It generates a rich spectrum of gravity waves in the stable layers both above and beneath the convective shell. The magnitude of the convective velocities from our one-dimensional mixing-length theory model and the rms-averaged vertical velocities from the hydrodynamic model are consistent within a factor of a few. However, the velocity profile in the hydrodynamic simulation is more asymmetric and decays exponentially inside the convection zone. Both g-modes and convective motions cross the formal convective boundaries, which leads to mixing across the boundaries. Our resolution study shows consistent flow structures among the higher resolution runs, and we see indications for convergence of the vertical velocity profile inside the convection zone for the highest resolution simulations. Many of the convective properties, in particular the exponential decay of the velocities, depend only weakly on the heating rate. However, the amplitudes of the gravity waves increase with both the heating rate and the resolution.
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