n this dissertation we have studied two classes of combustion phenomena, the dynamics of premixed flame propagation, and the ignition of hydrogen and oxygen. The studies of premixed flame propagation examined the dynamics of flame-vortex interaction to gain insight into turbulent combustion. Our initial study assessed the importance of the dependence of the local flame speed on flame stretch in this interaction using a numerical simulation of flame propagation in the limit of zero heat release. The simulations showed that this dependence decreases the mean consumption rate of the flame relative to the case in which the local flame speed is assumed to be independent of stretch. To further study flame-vortex interaction, we developed a numerical algorithm which can simulate flame dynamics with heat release in the limit that the flame is thin relative to the flow scale. This algorithm was used to reinvestigate flame-vortex interaction in this limit. The investigation showed that the Landau-Darrieus flame instability caused by heat release does not generate wrinkles on the flame surface which are smaller than the flow scale. This supports the assumption that in turbulence the smallest scale of flame wrinkling is determined by the eddy scales.;The analytic ignition studies were performed for conditions at which the ignition behavior is mainly determined by the branching of the H radical through
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