A thorough understanding of the solid oxide fuel cell (SOFC) performance and reactants' distribution through modeling and numerical simulation has become essential. In this paper, a comprehensive numerical model based on a lattice-based Boltzmann method was developed to numerically handle gas flow in the partially blocked channel and concentration polarization in porous electrodes while assessing the performance of such a SOFC. After model validation with available experimental data, effects of the blocks height, their number, and the cathode/anode-side flow channel blockage are investigated. Block insertion has been shown to speed up gas progression while enhancing mass transport from the channel to the anode/electrolyte interface and that the performance of the involved SOFC is better compared to a straight channel. The findings demonstrate that the SOFC performance improves by increasing both the blocks number and their height. Specifically, a 90% block with five blocks would improve power density by 14.4%.