An efficient semi-implicit solver for solid electrolyte interphase growth in Li-ion batteries

Growth of the Solid Electrolyte Interphase is one of the major degradation processes in Li-ion batteries and yields an increase in cell resistance, as well as a reduction in capacity. In order to facilitate computer-aided design of novel cell concepts and omit costly prototyping, it is crucial to incorporate this mechanism into electrochemical simulations on the microscale and to develop efficient numerical solvers. Electrochemical battery models without degradation are commonly discretized with a fully implicit discretization resulting in a monolithic scheme. Solving the resulting systems with a Newton method allows for quadratic convergence, where the major part of the computational effort is spent on solving the underlying linear systems. Hence, finding a suitable preconditioner for the linear solver is essential for overall solver performance. While an efficient algebraic multigrid preconditioner results in a good performance for the model without degradation, we encounter a noticeable loss in performance of the solver when including the coupled degradation model. We attribute the observed performance issues to the implicitly defined interface currents introduced by the degradation model. By taking into account the slow dynamics of the degradation, we propose an alternative semi-implicit solution approach separating the degradation dynamics and eliminating the implicit interface currents, in order to promote the efficient utilization of the algebraic multigrid preconditioner. The monolithic and semi-implicit solvers are evaluated by performing a series of full cell simulations featuring calendar and cyclic aging scenarios and a complex geometry including the binder domain in each electrode. Based on the results, the semi-implicit solver significantly improves the performance, while maintaining the convergence behaviour.