The framework is based on solving nonlinear coupled ordinary and partial
differential equations that model the kinetics of the following phenomena: (1) mass transport in the electrolyte and electrode using the Nernst - Planck equation; (2)
electrical potential distribution using the Poisson equation; (3) interfacial reactions that determine the boundary conditions or source terms (using the Butler - Volmer equation or constant - flux conditions); and (4) evolution of the electrode / electrolyte interface using the Allen - Cahn equation within the phase - field modeling (PFM) approach.