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A swept-volume method of calculating the volume swept by the flame during each time step is developed and used to improve the calculation of fuel reaction rates. The improved reaction rates have been applied to the ignition model and coupled with the level set G-equation combustion model. In the ignition model, a single initial kernel is formed after which the kernel is convected by the gas flow and its growth rate is determined by the flame speed and thermal expansion due to the energy transfer from the electrical circuit. The predicted ignition kernel size was compared with the available experimental data and good agreements were achieved. Once the ignition kernel reaches a size when the fully turbulent flame is developed, the G-equation model is switched on to track the mean turbulent flame front propagation.