Numerical solving unsteady problems for the system of the Nernst–Planck equations

The mathematical model of electricity and mass transfer processes is based on the governing equations for the concentration of charged particles (ions and cations) in an electrolyte — the Nernst–Planck equations. These equations are supplemented with the equation for the electric field and the equations for a motion of electrolyte as a continuum medium. In this work we have focused on constructing approximations in time for approximate solving unsteady problems. The system of the Nernst-Planck equations is characterized by a quadratic non-linearity. To take info accont this nonlinearity, we propose special schemes of linearization. Computational algorithms are studied using a model problem for a binary electrolyte (two types of charged particles).