An implicit-explicit Runge-Kutta-Chebyshev finite element method for the nonlinear Lithium-ion battery equations

We introduce a numerical method to integrate the nonlinear system of equations that model the physical-chemical laws of the Lithium-ion batteries. The mathematical model, formulated in Doyle et al. J. Electrochem. Soc. 140 (1993) 1526-1533, is a system of strongly coupled nonlinear parabolic and elliptic equations. Our numerical method combines a second order implicit-explicit Runge-Kutta-Chebyshev scheme for time discretization of the parabolic equations governing the dynamics of the variables c(e) and c(s), with linear finite element space discretization of the system. The implicit-explicit numerical formulation of the parabolic equations allows us to decouple the strong nonlinear reaction terms, which are treated implicitly, from the linear diffusion terms, treated explicitly. This approach is computationally efficient because (a) it has an extended stability region, and (b) the coupled system of algebraic equations becomes a single variable nonlinear equation per mesh point, which is easily solved by Newton method. (C) 2019 Elsevier Inc. All rights reserved.