In this study, a two-dimensional axisymmetric computational model of spark discharge in air is presented to provide a better understanding of the dynamics of the process. Better understanding of the modeling issues in spark discharge processes is an important issue for the automotive spark plug community. In this work we investigate the evolution of the shock front, temperature, pressure, density, geometry, and flow history of a plasma kernel using various assumptions that are typically used in spark discharge simulations. A continuum, inviscid, heat conducting, single fluid description of the flow is considered with radiative losses. Assuming local thermal equilibrium, the energy input due to resistive heating is determined using a specified current profile and temperature-dependent gas electrical conductivity in the gap. The spark discharge model focuses on the early time flow physics, the relative importance of conduction and radiation losses, the influence of thermodynamic model choice and ambient pressure effects.