This paper summarizes a comprehensive numerical model that represents the spray dynamics, fluid flow, species transport, mixing, chemical reactions, and accompanying heat release that occur inside the cylinder of an internal combustion engine. The model is embodied in the KIVA computer code. The code calculates both two-dimensional (2D) and three-dimensional (3D) situations. It is an out-growth of the earlier 2D CONCHAS-SPRAY computer program. Sample numerical calculations are presented to indicate the level of detail that is available from these simulations. These calculations are for a direct injection stratified charge engine with swirl. Both a 2D and a 3D example are shown.