This work focuses on the validation and analysis of a simplified model of an alkaline water electrolyzer using Code_Saturne software, based on the previous research by the authors Rodriguez and Amores. The reference work provides numerical results through polarization curves obtained using COMSOL software, as well as experimental data for various operating conditions and distances between electrodes and dividing membranes. The developed model addresses several key aspects of the alkaline water electrolysis process. This includes solving the Navier-Stokes equations to describe fluid dynamics, the transport of gas generated, the conservation of electrical current, and the inclusion of energy conservation to account for electrolyte heating due to the Joule effect. Moreover, the model addresses the buoyancy phenomenon, which arises due to density differences between the electrolyte and the generated gas. The main objective of this work is to verify and validate the electrochemical response of the cell, represented by the polarization curve, under various operating conditions