Three-dimensional numerical simulations of flame kernel growth produced by a spark in a combustible propane-air mixture are presented. Different configurations using a conventional spark plug geometry in a combustion chamber with constant volume have been tested. The first simulation, corresponding to a homogeneous turbulent medium without a mean velocity field, presents the different phases of the flame kernel growth and its interaction with the electrodes. This simulation shows that the flame kernel growth and its structure are governed by the flow induced by the spark discharge and the geometry of the ground electrode. These results appear to be coherent with recent experimental visualizations. Secondly, a plane jet is applied in the combustion chamber to provoke a mean velocity field resembling tumble in real spark ignition engines; this is done in order to study the influence of three different orientations of the ground electrode. Concerning the initial flame growth in a mean velocity field, the presence of the ground electrode has an important role in the development of the initial flame. The simulations prove that, in accordance with previous experimental observations, the optimal positions of the ground electrode are perpendicular or downstream of the mean velocity field, in order to move the kernel away from the electrodes. However, these two orientations lead to higher heat losses to the electrode, due to a larger contact surface between the flame kernel and the spark plug. The velocity field seems to be a determining factor governing the early flame growth.