A novel computational approach for the numerical simulation of electrochemical systems influenced by natural convection phenomena is presented. A stabilized finite element framework for multi-ion transport mechanisms including convection, diffusion and migration coupled to an incompressible flow solver is developed. The role of a galvanostatic Butler-Volmer condition including the interaction of ionic concentration at the surface of the electrode and the surface overpotential is emphasized, to obtain a non-uniform surface overpotential distribution. Additionally, a threedimensional rotationally-symmetric boundary condition is used for modeling rotating cylinder electrodes. The computational framework is tested for various numerical examples exhibiting two- and three-dimensional electrochemical cell configurations including dilute CuSO 4 electrolytes with and without excess of supporting H 2 SO 4 electrolyte.