The main goal of this work is the computational study of the Poisson–Boltzmann (PB) equation for a circular and elliptical charges immerse in a strong electrolyte using the lattice-Boltzmann method. We remark that this kind of charge distributions has no analytical results due to the non-linearity of PB equation and the complexity of the charge distributions. The model describes the electrical potential and his interactions produced by ions adsorption on the surface of circular or elliptical charged particles. Finally, we analyze the stability of the method.