The paper investigates numerically the effect of local extinguishing of a hydrogen flame due to curvature of the flame front and compares it to the stable burning of a methane flame. It is found that, depending on the Lewis number of the fuel, the flame front curvature "polarizes" the processes on the hydrogen flame front: there is a considerable increase of the heat release rate and the chemical reactions in regions of positive curvature (convex towards the fresh gases) and a strong decrease when the curvature is negative. Along the flame front, changes of the curvature correlate well with changes of the displacement flame speed.
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