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Diesel engine in-cylinder combustion processes have been studied using computational models with particular attention to spray development, vaporization, fuel/air mixture formation and combustion. A thermodynamic zero-dimensional cycle analysis program was used to determine initial conditions for the multidimensional calculations. A modified version of the time-dependent, three-dimensional computational fluid dynamics code KIVA-II was used for the computations, with a detailed treatment for the spray calculations and a simplified model for combustion. The calculations were used to obtain an understanding of the potential predictive capabilities of the models. It was found that there is a strong sensitivity of the results to numerical grid resolution. With proper grid resolution, the calculations were found to reproduce experimental data for non- vaporizing and vaporizing sprays. However, for vaporizing sprays with combustion, extremely fine grids are needed.