One of the effective strategies in meso and micro combustors for flame stabilization is to consider a wall cavity in a step. This extends the blow-off limit that can cause flame stagnation and anchoring. In the present work, the premixed hydrogen turbulent flame in a thermo-photovoltaic combustor with a step is simulated, validated and researched in terms of flame stabilization at different operating points including jet temperature, velocity, hydrogen, nitrogen, water content, and equivalence ratios. The effect of preferential transport of species is also evaluated and discussed. The results of simulations were employed to investigate the flame anchoring by showing the interplay between the flow field, heat recirculation, elementary reactions, transport of species. The results confirm that in this combustor the fresh reactant is gradually heated by the channel walls. This shifts the threshold of the combustion to the vicinity of the microchannel interior walls and more intense combustion downstream. The combustion in partially reacted materials is intensified by passing the duct interior walls when it faces the recirculating materials in the channel cavity leading to flame anchoring and stabilization from the cavity wall. The flame anchoring mechanism in this channel is the heat recirculation via channel walls, recirculating materials, and radical pool in the channel cavity for premixed hydrogen/oxygen flame. The effect of heat recirculation is found dominant in flame anchoring as in most case studies the flame stabilizes and evolves from the duct interior walls