A computational study was conducted of axisymmetric droplet impingement on a flat surface at low droplet Reynolds numbers. The study was motivated by the problem of deposition of melted volcanic ash particles within aircraft gas turbine engines. The computations were performed using the combined level-set volume-of-fluid method for droplet Reynolds numbers between 0.05 and 10. The computational predictions were validated using existing experimental data. The computations indicate that contact radius increases over short time in proportion to the square root of time, in agreement with short-time analytical predictions. Typical assumptions made in development of approximate droplet impingement models were evaluated for low Reynolds number droplet impingement. The droplet shape was well approximated by a truncated spherical cap through most of the impingement process. The surface area over which the droplet spreads increases with increase in Reynolds number. The axial velocity component was found to be approximately independent of radial location over most of the droplet, and the radial velocity component was observed to vary log-normally in the axial coordinate and linearly in radius. The energy dissipation rate was distributed throughout the droplet for low Reynolds numbers cases, but became increasingly localized near the contact line as the Reynolds number increased past unity.