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In water desalination by electrodialysis, the current density i cannot exceed specific constraints, notably the diffusion limit. Working at higher i (overlimiting current regime) would make higher desalination rates possible. The main phenomenon allowing overlimiting current densities is the electrokinetic instability that arises when a sufficiently intense electric potential gradient is imposed, and leads to electroconvective mixing in the near-wall layer. In this study, these phenomena were investigated by CFD. The governing equations were the Nernst-Planck transport equations for anions and cations, the Poisson equation for the electrical potential and the Navier-Stokes and continuity equations for fluid motion (NPP-NS approach). Time-dependent simulations were conducted both in 2-D and 3-D domains for different imposed potential gradients. Computational stability was obtained only by using very small time steps, typically 10-8~10-7 s. Starting from rest, statistically stationary conditions, characterized by intense vortices a few mm in size, were attained after times of the order of milliseconds. In 3-D simulations, coherent structures reminiscent of Rayleigh-Bénard convection were predicted. Current densities well above the diffusion limit were achieved.