The transport of ions is governed by a species conservation equation and the Nernst-Planck flux expression. The latter requires information on the electrical potential, for which an additional transport equation is required. Traditional numerical approaches, such as solving the Poisson equation or applying the electroneutrality condition, face limitations in their applicability. In this work, a new numerical model is introduced for the electrical potential that effectively functions as a numerical switch between the Poisson equation and the electroneutrality condition. This model is tested for three different scenarios: a small-scale system where charge separation is expected in a large part of the domain, a large-scale system where charge separation is significantly less important, and a multi-ion liquid junction system. This new numerical model is capable of producing accurate results for all the tested systems.