This paper reports on two-dimensional (2D) and three-dimensional (3D) direct numerical simulations (DNSs) of the auto-ignition process of a lean H-2/air mixture with temperature stratification in a constant volume enclosure. Detailed chemistry and transport properties are taken into account in the simulations. The combined propagation of spontaneous ignition front and deflagration front is identified and the relation between the reaction front displacement speed and the temperature gradient is verified. The difference between 2D- and 3D-DNS is investigated by comparing the evolutions of global combustion parameters such as the averaged heat release rate, total reaction front area and the averaged displacement speed of the reaction front. The extra spatial dimension in 3D-DNS has been shown to cause a higher velocity strain rate to enhance the heat transfer process, which leads to a delayed but more rapid ignition of the mixture than the 2D-DNS cases. The 3D reaction front surfaces are examined based on the local mean and Gaussian curvatures. By introducing a cutoff Gaussian curvature two types of 3D surface elements, the small sphere fronts and the strong saddle fronts, are defined. The effect of these fronts on the combustion process is studied in terms of their contribution to the total reaction front area, fuel consumption rate and curvature-induced stretch. (c) 2013 The Combustion Institute. Published by Elsevier Inc. All rights reserved.