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There has been an increased interest in understanding the initial stages of flame kernel formation in internal combustion engines as it offers a potential way of improving their thermal efficiency. For spark-ignited engines, the dynamics that govern the initial spark and its transition into a flame kernel play an important role in determining the overall engine efficiency. In this regard, this paper presents a computational model developed to simulate a spark discharge formed in a premixed fuel air mixture. Additionally, by simultaneously modeling the reactive fluid dynamics that governs combustion with the electromagnetics that governs the spark, the overall objective of this paper is to consistently simulate spark-initiated combustion in a premixed fuel-air mixture. Two different fuel-oxidizer mixtures are considered in this study, hydrogen-oxygen and methane-oxygen. Key mechanisms via which the spark channel ignites the mixture are identified and studied in detail.