High-speed schlieren visualization and numerical simulations are used to study the fluid mechanics following a spark discharge and the effect on the ignition process in a hydrogen-air mixture. A two-dimensional axisymmetric model of spark discharge in air and spark ignition was developed using the non-reactive and reactive Navier-Stokes equations including mass and heat diffusion. The numerical method employs structured adaptive mesh refinement software to produce highly-resolved simulations, which is critical for accurate resolution of all the physical scales of the complex fluid mechanics and chemistry. The simulations were performed with three different electrode geometries to investigate the effect of the geometry on the fluid mechanics of the evolving spark kernel and on flame formation. The computational results were compared with high-speed schlieren visualization of spark and ignition kernels. It was shown that the spark channel emits a blast wave that is spherical near the electrode surfaces and cylindrical near the center of the spark gap, and thus is highly influenced by the electrode geometry. The ensuing competition between spherical and cylindrical expansion in the spark $ Full-length article submitted to Combustion and Flame.