Comparison between the Gauss’ law method and the zero current method to calculate multi-species ionic diffusion in saturated uncharged porous materials

A novel numerical method based on the finite element approach is established for the zero current method approach for calculating multi-species ionic diffusion. The proposed numerical method uses the direct calculation of the coupled set of equations in favor of the staggering approach. A one-step truly implicit time stepping scheme is adopted together with an implementation of a modified Newton–Raphson iteration scheme for search of equilibrium at each considered time step calculation. Results from the zero current case are compared with existing results from the solutions of the more general Gauss’ law method.