Abstract The self-accelerating expanding cylindrical stoichiometric hydrogen–air flames at eight atmospheres were studied via two-dimensional direct numerical simulation (DNS) of the full compressible Navier–Stokes equations with detailed chemistry. The flame morphology and propagation were finely resolved by the application of a time step of 2.5 ns and a grid size of 4 μm. Temporally, the intermittent propagation of the flame front is captured through examining its propagation velocity. Spatially, the flame front is found to be comprised of segments exhibiting similar propagation properties, i.e. the intermittent instantaneous propagation of the flame front is attributed to the development of cellular structures induced by hydrodynamic instability. The long-term average propagation velocity of the flame front is described by a power law, with a self-acceleration exponent of 1.22 for the flame radius with respect to time. The increase in the global flame velocity is shown to be primarily a consequence of increased flame surface area, with the local front propagation velocity remaining largely at the constant laminar flame speed for the near-unity Lewis number mixture studied herein.